updating BMs
This commit is contained in:
mhjensen
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
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('Optimization / Training', 2, None, '___sec58'),
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('More on RBMs', 2, None, '___sec59'),
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('Which sampling to use', 2, None, '___sec60'),
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('RBMs for the quantum many body problem', 2, None, '___sec61'),
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('Choose the right RBM', 2, None, '___sec62'),
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('Representing the wave function', 2, None, '___sec63'),
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('Choose the cost function', 2, None, '___sec64'),
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('Running the codes', 2, None, '___sec65'),
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('Energy as function of iterations, $N=2$ electrons',
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('Recent examples: RBMs for the quantum many body problem',
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2,
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None,
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'___sec66'),
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('Energy as function of iterations, $N=6$ electrons',
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2,
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None,
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'___sec67'),
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('Conclusions and where do we stand', 2, None, '___sec68')]}
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'___sec61'),
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('Choose the right RBM', 2, None, '___sec62')]}
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end of tocinfo -->
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<body>
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@@ -317,14 +308,8 @@ MathJax.Hub.Config({
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<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
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</ul>
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</li>
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@@ -358,7 +343,7 @@ MathJax.Hub.Config({
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<center><b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University and Department of Physics, University of Oslo, Norway</b></center>
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<br>
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<p>
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<center><h4>Nov 22, 2018 </h4></center> <!-- date -->
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<center><h4>Nov 23, 2018 </h4></center> <!-- date -->
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<br>
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<p>
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@@ -382,7 +367,7 @@ MathJax.Hub.Config({
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<li><a href="._BM-bs008.html">9</a></li>
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<li><a href="._BM-bs009.html">10</a></li>
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<li><a href="">...</a></li>
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<li><a href="._BM-bs069.html">70</a></li>
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<li><a href="._BM-bs063.html">64</a></li>
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<li><a href="._BM-bs001.html">»</a></li>
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
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('Optimization / Training', 2, None, '___sec58'),
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('More on RBMs', 2, None, '___sec59'),
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('Which sampling to use', 2, None, '___sec60'),
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('RBMs for the quantum many body problem', 2, None, '___sec61'),
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('Choose the right RBM', 2, None, '___sec62'),
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('Representing the wave function', 2, None, '___sec63'),
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('Choose the cost function', 2, None, '___sec64'),
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('Running the codes', 2, None, '___sec65'),
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('Energy as function of iterations, $N=2$ electrons',
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('Recent examples: RBMs for the quantum many body problem',
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2,
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None,
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'___sec66'),
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('Energy as function of iterations, $N=6$ electrons',
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2,
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None,
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'___sec67'),
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('Conclusions and where do we stand', 2, None, '___sec68')]}
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'___sec61'),
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('Choose the right RBM', 2, None, '___sec62')]}
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end of tocinfo -->
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<body>
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@@ -317,14 +308,8 @@ MathJax.Hub.Config({
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<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
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<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
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</ul>
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</li>
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@@ -385,7 +370,7 @@ Some of the most common tasks are:
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<li><a href="._BM-bs009.html">10</a></li>
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<li><a href="._BM-bs010.html">11</a></li>
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<li><a href="">...</a></li>
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<li><a href="._BM-bs069.html">70</a></li>
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<li><a href="._BM-bs063.html">64</a></li>
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<li><a href="._BM-bs002.html">»</a></li>
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</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
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('More on RBMs', 2, None, '___sec59'),
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('Which sampling to use', 2, None, '___sec60'),
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('RBMs for the quantum many body problem', 2, None, '___sec61'),
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('Choose the right RBM', 2, None, '___sec62'),
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('Representing the wave function', 2, None, '___sec63'),
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||||
('Choose the cost function', 2, None, '___sec64'),
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||||
('Running the codes', 2, None, '___sec65'),
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('Energy as function of iterations, $N=2$ electrons',
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('Recent examples: RBMs for the quantum many body problem',
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2,
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None,
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'___sec66'),
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('Energy as function of iterations, $N=6$ electrons',
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2,
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None,
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'___sec67'),
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('Conclusions and where do we stand', 2, None, '___sec68')]}
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'___sec61'),
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('Choose the right RBM', 2, None, '___sec62')]}
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||||
end of tocinfo -->
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||||
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<body>
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@@ -317,14 +308,8 @@ MathJax.Hub.Config({
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||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
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</ul>
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</li>
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@@ -370,7 +355,7 @@ Furthermore, they have been used to solve complicated quantum mechanical many-pa
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<li><a href="._BM-bs010.html">11</a></li>
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<li><a href="._BM-bs011.html">12</a></li>
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||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
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||||
<li><a href="._BM-bs003.html">»</a></li>
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||||
</ul>
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||||
<!-- ------------------- end of main content --------------- -->
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||||
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||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
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||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
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2,
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||||
None,
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||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
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||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
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||||
('Choose the right RBM', 2, None, '___sec62')]}
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||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
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||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
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||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
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</ul>
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</li>
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@@ -342,6 +327,9 @@ MathJax.Hub.Config({
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<h2 id="___sec2" class="anchor">An intermediate step, the Hopfield network and links to the Ising and Potts models </h2>
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<p>
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More material on Hopfield networks will come here
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<p>
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<p>
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<!-- navigation buttons at the bottom of the page -->
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@@ -361,7 +349,7 @@ MathJax.Hub.Config({
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<li><a href="._BM-bs011.html">12</a></li>
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<li><a href="._BM-bs012.html">13</a></li>
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||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
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||||
<li><a href="._BM-bs004.html">»</a></li>
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||||
</ul>
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<!-- ------------------- end of main content --------------- -->
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@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
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('Choose the cost function', 2, None, '___sec64'),
|
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('Running the codes', 2, None, '___sec65'),
|
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('Energy as function of iterations, $N=2$ electrons',
|
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('Recent examples: RBMs for the quantum many body problem',
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2,
|
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None,
|
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'___sec66'),
|
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('Energy as function of iterations, $N=6$ electrons',
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2,
|
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None,
|
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'___sec67'),
|
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('Conclusions and where do we stand', 2, None, '___sec68')]}
|
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'___sec61'),
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('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
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<body>
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@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
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</ul>
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</li>
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@@ -375,7 +360,7 @@ MathJax.Hub.Config({
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<li><a href="._BM-bs012.html">13</a></li>
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<li><a href="._BM-bs013.html">14</a></li>
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<li><a href="">...</a></li>
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||||
<li><a href="._BM-bs069.html">70</a></li>
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||||
<li><a href="._BM-bs063.html">64</a></li>
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||||
<li><a href="._BM-bs005.html">»</a></li>
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||||
</ul>
|
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<!-- ------------------- end of main content --------------- -->
|
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@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
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('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
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('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
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('Recent examples: RBMs for the quantum many body problem',
|
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2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -381,7 +366,7 @@ its most likely state at a given temperature of the surroundings.
|
||||
<li><a href="._BM-bs013.html">14</a></li>
|
||||
<li><a href="._BM-bs014.html">15</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs006.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
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|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
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|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
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|
||||
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|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -378,7 +363,7 @@ the interpretation of random walks and Markov processes.
|
||||
<li><a href="._BM-bs014.html">15</a></li>
|
||||
<li><a href="._BM-bs015.html">16</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs007.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -383,7 +368,7 @@ This sequence of steps forms a <b>chain</b>.
|
||||
<li><a href="._BM-bs015.html">16</a></li>
|
||||
<li><a href="._BM-bs016.html">17</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs008.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -372,7 +357,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._BM-bs016.html">17</a></li>
|
||||
<li><a href="._BM-bs017.html">18</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs009.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -386,7 +371,7 @@ The list of applications is endless.
|
||||
<li><a href="._BM-bs017.html">18</a></li>
|
||||
<li><a href="._BM-bs018.html">19</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs010.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -387,7 +372,7 @@ We can regard the discretized PDF as a vector.
|
||||
<li><a href="._BM-bs018.html">19</a></li>
|
||||
<li><a href="._BM-bs019.html">20</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs011.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -401,7 +386,7 @@ PDF with equal probability of jumping left or right.
|
||||
<li><a href="._BM-bs019.html">20</a></li>
|
||||
<li><a href="._BM-bs020.html">21</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
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|
||||
</ul>
|
||||
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||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
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|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
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|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -398,7 +383,7 @@ not necessarily equal zero.
|
||||
<li><a href="._BM-bs020.html">21</a></li>
|
||||
<li><a href="._BM-bs021.html">22</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs013.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
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|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -406,7 +391,7 @@ $$
|
||||
<li><a href="._BM-bs021.html">22</a></li>
|
||||
<li><a href="._BM-bs022.html">23</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs014.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
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|
||||
'___sec66'),
|
||||
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|
||||
2,
|
||||
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|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -399,7 +384,7 @@ $$
|
||||
<li><a href="._BM-bs022.html">23</a></li>
|
||||
<li><a href="._BM-bs023.html">24</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs015.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -396,7 +381,7 @@ $$
|
||||
<li><a href="._BM-bs023.html">24</a></li>
|
||||
<li><a href="._BM-bs024.html">25</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs016.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -395,7 +380,7 @@ Note that the vector \( \hat{w} \) is always normalized to \( 1 \).
|
||||
<li><a href="._BM-bs024.html">25</a></li>
|
||||
<li><a href="._BM-bs025.html">26</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs017.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
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|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -410,7 +395,7 @@ $$
|
||||
<li><a href="._BM-bs025.html">26</a></li>
|
||||
<li><a href="._BM-bs026.html">27</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs018.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
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|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
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|
||||
'___sec66'),
|
||||
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|
||||
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|
||||
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|
||||
'___sec67'),
|
||||
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|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -407,7 +392,7 @@ time steps. After twelve iterations we have reached the exact value with six le
|
||||
<li><a href="._BM-bs026.html">27</a></li>
|
||||
<li><a href="._BM-bs027.html">28</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs019.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
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|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
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|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -388,7 +373,7 @@ transition probability matrix.
|
||||
<li><a href="._BM-bs027.html">28</a></li>
|
||||
<li><a href="._BM-bs028.html">29</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs020.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
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|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -403,7 +388,7 @@ If we assume that \( \lambda_0 \) is the largest eigenvector we see that in the
|
||||
<li><a href="._BM-bs028.html">29</a></li>
|
||||
<li><a href="._BM-bs029.html">30</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs021.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -409,7 +394,7 @@ $$
|
||||
<li><a href="._BM-bs029.html">30</a></li>
|
||||
<li><a href="._BM-bs030.html">31</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs022.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -400,7 +385,7 @@ Here we have written the previous matrix \( W_{ij}=W(j\rightarrow i) \).
|
||||
<li><a href="._BM-bs030.html">31</a></li>
|
||||
<li><a href="._BM-bs031.html">32</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs023.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -399,7 +384,7 @@ we have reached the most likely state of the system, the so-called steady state
|
||||
<li><a href="._BM-bs031.html">32</a></li>
|
||||
<li><a href="._BM-bs032.html">33</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs024.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
'___sec66'),
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
'___sec61'),
|
||||
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|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -383,7 +368,7 @@ $$
|
||||
<li><a href="._BM-bs032.html">33</a></li>
|
||||
<li><a href="._BM-bs033.html">34</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs025.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -391,7 +376,7 @@ The algorithm can then be expressed as
|
||||
<li><a href="._BM-bs033.html">34</a></li>
|
||||
<li><a href="._BM-bs034.html">35</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs026.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
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|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
'___sec66'),
|
||||
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|
||||
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|
||||
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|
||||
'___sec67'),
|
||||
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|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -384,7 +369,7 @@ to the probability of being in a state \( j \) and performing a transition to th
|
||||
<li><a href="._BM-bs034.html">35</a></li>
|
||||
<li><a href="._BM-bs035.html">36</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs027.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
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|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
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|
||||
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|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -388,7 +373,7 @@ $$
|
||||
<li><a href="._BM-bs035.html">36</a></li>
|
||||
<li><a href="._BM-bs036.html">37</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs028.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -398,7 +383,7 @@ $$
|
||||
<li><a href="._BM-bs036.html">37</a></li>
|
||||
<li><a href="._BM-bs037.html">38</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs029.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
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|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
None,
|
||||
'___sec66'),
|
||||
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|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -396,7 +381,7 @@ $$
|
||||
<li><a href="._BM-bs037.html">38</a></li>
|
||||
<li><a href="._BM-bs038.html">39</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs030.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
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|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
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|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -406,7 +391,7 @@ which is nothing but the standard equation for a Markov chain when the steady st
|
||||
<li><a href="._BM-bs038.html">39</a></li>
|
||||
<li><a href="._BM-bs039.html">40</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs031.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
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|
||||
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|
||||
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|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -400,7 +385,7 @@ $$
|
||||
<li><a href="._BM-bs039.html">40</a></li>
|
||||
<li><a href="._BM-bs040.html">41</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs032.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -384,7 +369,7 @@ $$
|
||||
<li><a href="._BM-bs040.html">41</a></li>
|
||||
<li><a href="._BM-bs041.html">42</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs033.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -399,7 +384,7 @@ $$
|
||||
<li><a href="._BM-bs041.html">42</a></li>
|
||||
<li><a href="._BM-bs042.html">43</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs034.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -401,7 +386,7 @@ we never need to evaluate the partition function \( Z \).
|
||||
<li><a href="._BM-bs042.html">43</a></li>
|
||||
<li><a href="._BM-bs043.html">44</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs035.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -394,7 +379,7 @@ $$
|
||||
<li><a href="._BM-bs043.html">44</a></li>
|
||||
<li><a href="._BM-bs044.html">45</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs036.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
'___sec67'),
|
||||
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|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -389,7 +374,7 @@ one place to another in space, we 'jump' from one microstate to another.
|
||||
<li><a href="._BM-bs044.html">45</a></li>
|
||||
<li><a href="._BM-bs045.html">46</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs037.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
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|
||||
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|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
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|
||||
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|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
'___sec66'),
|
||||
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|
||||
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|
||||
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|
||||
'___sec67'),
|
||||
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|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -397,7 +382,7 @@ the transition probability \( T(i\rightarrow j) \) is symmetric, implying that \
|
||||
<li><a href="._BM-bs045.html">46</a></li>
|
||||
<li><a href="._BM-bs046.html">47</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs038.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
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|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
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|
||||
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|
||||
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|
||||
'___sec66'),
|
||||
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|
||||
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|
||||
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|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -391,7 +376,7 @@ Our desired energy is \( E_0 \).
|
||||
<li><a href="._BM-bs046.html">47</a></li>
|
||||
<li><a href="._BM-bs047.html">48</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs039.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
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|
||||
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|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -390,7 +375,7 @@ we simulate long enough it should be included in our computation of an expectati
|
||||
<li><a href="._BM-bs047.html">48</a></li>
|
||||
<li><a href="._BM-bs048.html">49</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs040.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
None,
|
||||
'___sec66'),
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -389,7 +374,7 @@ to this constraint.
|
||||
<li><a href="._BM-bs048.html">49</a></li>
|
||||
<li><a href="._BM-bs049.html">50</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs041.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -388,7 +373,7 @@ $$
|
||||
<li><a href="._BM-bs049.html">50</a></li>
|
||||
<li><a href="._BM-bs050.html">51</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs042.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
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|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -392,7 +377,7 @@ If the ratio is smaller than a given random number we accept the move to a highe
|
||||
<li><a href="._BM-bs050.html">51</a></li>
|
||||
<li><a href="._BM-bs051.html">52</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs043.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
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|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
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|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
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|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
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|
||||
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|
||||
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|
||||
'___sec66'),
|
||||
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|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -386,7 +371,7 @@ fewer accepted moves.
|
||||
<li><a href="._BM-bs051.html">52</a></li>
|
||||
<li><a href="._BM-bs052.html">53</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs044.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -395,7 +380,7 @@ $$
|
||||
<li><a href="._BM-bs052.html">53</a></li>
|
||||
<li><a href="._BM-bs053.html">54</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs045.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -371,7 +356,7 @@ More text to come.
|
||||
<li><a href="._BM-bs053.html">54</a></li>
|
||||
<li><a href="._BM-bs054.html">55</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs046.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
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|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
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|
||||
'___sec67'),
|
||||
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|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -382,7 +367,7 @@ Why use a generative model rather than the more well known discriminative deep n
|
||||
<li><a href="._BM-bs054.html">55</a></li>
|
||||
<li><a href="._BM-bs055.html">56</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs047.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -376,7 +361,7 @@ History: The RBM was developed by amongst others Geoffrey Hinton, called by some
|
||||
<li><a href="._BM-bs055.html">56</a></li>
|
||||
<li><a href="._BM-bs056.html">57</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs048.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -371,7 +356,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._BM-bs056.html">57</a></li>
|
||||
<li><a href="._BM-bs057.html">58</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs049.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -375,7 +360,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._BM-bs057.html">58</a></li>
|
||||
<li><a href="._BM-bs058.html">59</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs050.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -387,7 +372,7 @@ Examples of this trick being employed in physics:
|
||||
<li><a href="._BM-bs058.html">59</a></li>
|
||||
<li><a href="._BM-bs059.html">60</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs051.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -385,7 +370,7 @@ It is common to ignore \( T_0 \) by setting it to one.
|
||||
<li><a href="._BM-bs059.html">60</a></li>
|
||||
<li><a href="._BM-bs060.html">61</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs052.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -376,7 +361,7 @@ adjusting the energy function to best fit our problem.
|
||||
<li><a href="._BM-bs060.html">61</a></li>
|
||||
<li><a href="._BM-bs061.html">62</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs053.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
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|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
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|
||||
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|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
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|
||||
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|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -403,7 +388,7 @@ $$
|
||||
<li><a href="._BM-bs061.html">62</a></li>
|
||||
<li><a href="._BM-bs062.html">63</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs054.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -380,8 +365,6 @@ Other types of units include:
|
||||
<li><a href="._BM-bs061.html">62</a></li>
|
||||
<li><a href="._BM-bs062.html">63</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs055.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -386,9 +371,6 @@ $$
|
||||
<li><a href="._BM-bs061.html">62</a></li>
|
||||
<li><a href="._BM-bs062.html">63</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs064.html">65</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs056.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -382,10 +367,6 @@ where we recognize the logistic sigmoid function \( \sigma (x) = 1/(1+exp(-x)) \
|
||||
<li><a href="._BM-bs061.html">62</a></li>
|
||||
<li><a href="._BM-bs062.html">63</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs064.html">65</a></li>
|
||||
<li><a href="._BM-bs065.html">66</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs057.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -375,11 +360,6 @@ while the visible units now follow a normal distribution, we see the hidden unit
|
||||
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||||
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|
||||
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|
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|
||||
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||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
</ul>
|
||||
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|
||||
@@ -378,12 +363,6 @@ Our cost function is the negative log-likelihood, \( \mathcal{C}(\{ \theta_i \})
|
||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
</ul>
|
||||
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|
||||
@@ -400,13 +385,6 @@ $$
|
||||
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|
||||
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||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -380,12 +365,6 @@ To get the expecation values with respect to the <em>data</em>, we set the visib
|
||||
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|
||||
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|
||||
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||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
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|
||||
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|
||||
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|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -363,12 +348,6 @@ To get the expectation values with respect to the <em>model</em>, we use Gibbs s
|
||||
<li class="active"><a href="._BM-bs061.html">62</a></li>
|
||||
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||||
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|
||||
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||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
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|
||||
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|
||||
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|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
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|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
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|
||||
@@ -340,7 +325,7 @@ MathJax.Hub.Config({
|
||||
<a name="part0062"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec61" class="anchor">RBMs for the quantum many body problem </h2>
|
||||
<h2 id="___sec61" class="anchor">Recent examples: RBMs for the quantum many body problem </h2>
|
||||
|
||||
<p>
|
||||
The idea of applying RBMs to quantum many body problems was presented by G. Carleo and M. Troyer, working with ETH Zurich and Microsoft Research.
|
||||
@@ -378,12 +363,6 @@ Some of their motivation included
|
||||
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|
||||
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||||
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||||
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|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
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|
||||
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|
||||
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|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -346,6 +331,7 @@ MathJax.Hub.Config({
|
||||
Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems of the Ising model and Heisenberg model, with encouraging results. Our goal is to test the method on systems of moving particles. For the spin lattice systems it was natural to use a binary-binary RBM, with the nodes taking values of 1 and -1. For moving particles, on the other hand, we want the visible nodes to be continuous, representing position coordinates. Thus, we start by choosing a Gaussian-binary RBM, where the visible nodes are continuous and hidden nodes take on values of 0 or 1. If eventually we would like the hidden nodes to be continuous as well the rectified linear units seem like the most relevant choice.
|
||||
|
||||
<p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
@@ -361,13 +347,6 @@ Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems
|
||||
<li><a href="._BM-bs061.html">62</a></li>
|
||||
<li><a href="._BM-bs062.html">63</a></li>
|
||||
<li class="active"><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs064.html">65</a></li>
|
||||
<li><a href="._BM-bs065.html">66</a></li>
|
||||
<li><a href="._BM-bs066.html">67</a></li>
|
||||
<li><a href="._BM-bs067.html">68</a></li>
|
||||
<li><a href="._BM-bs068.html">69</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs064.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
|
||||
@@ -205,20 +205,11 @@ Automatically generated HTML file from DocOnce source
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -317,14 +308,8 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs059.html#___sec58" style="font-size: 80%;">Optimization / Training</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs060.html#___sec59" style="font-size: 80%;">More on RBMs</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs061.html#___sec60" style="font-size: 80%;">Which sampling to use</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs062.html#___sec61" style="font-size: 80%;">Recent examples: RBMs for the quantum many body problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs063.html#___sec62" style="font-size: 80%;">Choose the right RBM</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs064.html#___sec63" style="font-size: 80%;">Representing the wave function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs065.html#___sec64" style="font-size: 80%;">Choose the cost function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs066.html#___sec65" style="font-size: 80%;">Running the codes</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs067.html#___sec66" style="font-size: 80%;">Energy as function of iterations, \( N=2 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs068.html#___sec67" style="font-size: 80%;">Energy as function of iterations, \( N=6 \) electrons</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._BM-bs069.html#___sec68" style="font-size: 80%;">Conclusions and where do we stand</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -358,7 +343,7 @@ MathJax.Hub.Config({
|
||||
<center><b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University and Department of Physics, University of Oslo, Norway</b></center>
|
||||
<br>
|
||||
<p>
|
||||
<center><h4>Nov 22, 2018 </h4></center> <!-- date -->
|
||||
<center><h4>Nov 23, 2018 </h4></center> <!-- date -->
|
||||
<br>
|
||||
<p>
|
||||
|
||||
@@ -382,7 +367,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._BM-bs008.html">9</a></li>
|
||||
<li><a href="._BM-bs009.html">10</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._BM-bs069.html">70</a></li>
|
||||
<li><a href="._BM-bs063.html">64</a></li>
|
||||
<li><a href="._BM-bs001.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -147,7 +147,7 @@ MathJax.Hub.Config({
|
||||
<center><b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University and Department of Physics, University of Oslo, Norway</b></center>
|
||||
<br>
|
||||
<p> <br>
|
||||
<center><h4>Nov 22, 2018 </h4></center> <!-- date -->
|
||||
<center><h4>Nov 23, 2018 </h4></center> <!-- date -->
|
||||
<br>
|
||||
<p>
|
||||
|
||||
@@ -207,6 +207,9 @@ Furthermore, they have been used to solve complicated quantum mechanical many-pa
|
||||
|
||||
<section>
|
||||
<h2 id="___sec2">An intermediate step, the Hopfield network and links to the Ising and Potts models </h2>
|
||||
|
||||
<p>
|
||||
More material on Hopfield networks will come here
|
||||
</section>
|
||||
|
||||
|
||||
@@ -1820,7 +1823,7 @@ To get the expectation values with respect to the <em>model</em>, we use Gibbs s
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec61">RBMs for the quantum many body problem </h2>
|
||||
<h2 id="___sec61">Recent examples: RBMs for the quantum many body problem </h2>
|
||||
|
||||
<p>
|
||||
The idea of applying RBMs to quantum many body problems was presented by G. Carleo and M. Troyer, working with ETH Zurich and Microsoft Research.
|
||||
@@ -1851,134 +1854,6 @@ Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec63">Representing the wave function </h2>
|
||||
The wavefunction should be a probability amplitude depending on \( \boldsymbol{x} \). The RBM model is given by the joint distribution of \( \boldsymbol{x} \) and \( \boldsymbol{h} \)
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{align}
|
||||
F_{rbm}(\mathbf{x},\mathbf{h}) = \frac{1}{Z} e^{-\frac{1}{T_0}E(\mathbf{x},\mathbf{h})}.
|
||||
\tag{27}
|
||||
\end{align}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
To find the marginal distribution of \( \boldsymbol{x} \) we set:
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{align}
|
||||
F_{rbm}(\mathbf{x}) &= \sum_\mathbf{h} F_{rbm}(\mathbf{x}, \mathbf{h})
|
||||
\tag{28}\\
|
||||
&= \frac{1}{Z}\sum_\mathbf{h} e^{-E(\mathbf{x}, \mathbf{h})}.
|
||||
\tag{29}
|
||||
\end{align}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
Now this is what we use to represent the wave function, calling it a neural-network quantum state (NQS)
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{align}
|
||||
\Psi (\mathbf{X}) &= F_{rbm}(\mathbf{x})
|
||||
\tag{30}\\
|
||||
&= \frac{1}{Z}\sum_{\boldsymbol{h}} e^{-E(\mathbf{x}, \mathbf{h})}
|
||||
\tag{31}\\
|
||||
&= \frac{1}{Z} \sum_{\{h_j\}} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2} + \sum_j^N b_j h_j + \sum_{i,j}^{M,N} \frac{x_i w_{ij} h_j}{\sigma^2}}
|
||||
\tag{32}\\
|
||||
&= \frac{1}{Z} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2}} \prod_j^N (1 + e^{b_j + \sum_i^M \frac{x_i w_{ij}}{\sigma^2}}).
|
||||
\tag{33}\\
|
||||
\tag{34}
|
||||
\end{align}
|
||||
$$
|
||||
<p> <br>
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec64">Choose the cost function </h2>
|
||||
Now we don't necessarily have training data (unless we generate it by using some other method). However, what we do have is the variational principle which allows us to obtain the ground state wave function by minimizing the expectation value of the energy of a trial wavefunction (corresponding to the untrained NQS). Similarly to the traditional variational Monte Carlo method then, it is the local energy we wish to minimize. The gradient to use for the stochastic gradient descent procedure is
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{align}
|
||||
G_i = \frac{\partial \langle E_L \rangle}{\partial \theta_i}
|
||||
= 2(\langle E_L \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle - \langle E_L \rangle \langle \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle ),
|
||||
\tag{35}
|
||||
\end{align}
|
||||
$$
|
||||
<p> <br>
|
||||
|
||||
where the local energy is given by
|
||||
<p> <br>
|
||||
$$
|
||||
\begin{align}
|
||||
E_L = \frac{1}{\Psi} \hat{\mathbf{H}} \Psi.
|
||||
\tag{36}
|
||||
\end{align}
|
||||
$$
|
||||
<p> <br>
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec65">Running the codes </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
You can find the codes for the simple two-electron case at the Github repository <a href="https://github.com/mhjensenseminars/MachineLearningTalk/tree/master/doc/Programs/MLcpp/src" target="_blank"><tt>https://github.com/mhjensenseminars/MachineLearningTalk/tree/master/doc/Programs/MLcpp/src</tt></a>. Python codes to come, only c++ as of now.
|
||||
|
||||
<p>
|
||||
The trial wave function is based on the product of a Slater determinant with Gaussian orbitals, a simple Jastrow factor \( \exp{(r_{ij})} \) and the reduced Boltzmann machines.
|
||||
|
||||
<p>
|
||||
The Broyden-Fletcher-Goldfarb-Shanno algorithm was used to perform the minimization. We used \( 14 \) hidden nodes in the calculations below.
|
||||
|
||||
|
||||
</div>
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec66">Energy as function of iterations, \( N=2 \) electrons </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<br /><br /><center><p><img src="figures/figN2.png" align="bottom" width=700></p></center><br /><br />
|
||||
</div>
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec67">Energy as function of iterations, \( N=6 \) electrons </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<br /><br /><center><p><img src="figures/figN6.png" align="bottom" width=700></p></center><br /><br />
|
||||
</div>
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec68">Conclusions and where do we stand </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<ul>
|
||||
<p><li> A simple extension of the work of <a href="http://science.sciencemag.org/content/355/6325/602" target="_blank">G. Carleo and M. Troyer, Science <b>355</b>, Issue 6325, pp. 602-606 (2017)</a> gives excellent results for two-electron systems as well as good agreement with standard VMC calculations for \( N=6 \) and \( N=12 \) electrons.</li>
|
||||
<p><li> Minimization problem can be tricky.</li>
|
||||
<p><li> Anti-symmetry dealt with multiplying the trail wave function with an optimized Slater determinant.</li>
|
||||
<p><li> To come: Analysis of wave function from ML and compare with diffusion and Variational Monte Carlo calculations as well as the analytical results of Taut for the two-electron case.</li>
|
||||
<p><li> Extend to more fermions. How do we deal with the antisymmetry of the multi-fermion wave function?
|
||||
|
||||
<ol type="a"></li>
|
||||
<p><li> Here we used standard Hartree-Fock theory to define an optimal Slater determinant. Takes care of the antisymmetry. What about constructing an anti-symmetrized network function?</li>
|
||||
<p><li> Use thereafter ML to determine the correlated part of the wafe function (including a standard Jastrow factor).</li>
|
||||
<p><li> Test this for multi-fermion systems and compare with other many-body methods.</li>
|
||||
</ol>
|
||||
<p><li> Can we use ML to find out which correlations are relevant and thereby diminish the dimensionality problem in say CC or SRG theories?</li>
|
||||
</ul>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
|
||||
|
||||
</div> <!-- class="slides" -->
|
||||
</div> <!-- class="reveal" -->
|
||||
|
||||
@@ -225,20 +225,11 @@ div { text-align: justify; text-justify: inter-word; }
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -279,7 +270,7 @@ MathJax.Hub.Config({
|
||||
<center><b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University and Department of Physics, University of Oslo, Norway</b></center>
|
||||
<br>
|
||||
<p>
|
||||
<center><h4>Nov 22, 2018 </h4></center> <!-- date -->
|
||||
<center><h4>Nov 23, 2018 </h4></center> <!-- date -->
|
||||
<br>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
@@ -331,6 +322,9 @@ Furthermore, they have been used to solve complicated quantum mechanical many-pa
|
||||
|
||||
<h2 id="___sec2">An intermediate step, the Hopfield network and links to the Ising and Potts models </h2>
|
||||
|
||||
<p>
|
||||
More material on Hopfield networks will come here
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
@@ -1880,7 +1874,7 @@ To get the expectation values with respect to the <em>model</em>, we use Gibbs s
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec61">RBMs for the quantum many body problem </h2>
|
||||
<h2 id="___sec61">Recent examples: RBMs for the quantum many body problem </h2>
|
||||
|
||||
<p>
|
||||
The idea of applying RBMs to quantum many body problems was presented by G. Carleo and M. Troyer, working with ETH Zurich and Microsoft Research.
|
||||
@@ -1909,131 +1903,6 @@ Some of their motivation included
|
||||
<p>
|
||||
Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems of the Ising model and Heisenberg model, with encouraging results. Our goal is to test the method on systems of moving particles. For the spin lattice systems it was natural to use a binary-binary RBM, with the nodes taking values of 1 and -1. For moving particles, on the other hand, we want the visible nodes to be continuous, representing position coordinates. Thus, we start by choosing a Gaussian-binary RBM, where the visible nodes are continuous and hidden nodes take on values of 0 or 1. If eventually we would like the hidden nodes to be continuous as well the rectified linear units seem like the most relevant choice.
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec63">Representing the wave function </h2>
|
||||
The wavefunction should be a probability amplitude depending on \( \boldsymbol{x} \). The RBM model is given by the joint distribution of \( \boldsymbol{x} \) and \( \boldsymbol{h} \)
|
||||
$$
|
||||
\begin{align}
|
||||
F_{rbm}(\mathbf{x},\mathbf{h}) = \frac{1}{Z} e^{-\frac{1}{T_0}E(\mathbf{x},\mathbf{h})}.
|
||||
\label{_auto25}
|
||||
\end{align}
|
||||
$$
|
||||
|
||||
To find the marginal distribution of \( \boldsymbol{x} \) we set:
|
||||
$$
|
||||
\begin{align}
|
||||
F_{rbm}(\mathbf{x}) &= \sum_\mathbf{h} F_{rbm}(\mathbf{x}, \mathbf{h})
|
||||
\label{_auto26}\\
|
||||
&= \frac{1}{Z}\sum_\mathbf{h} e^{-E(\mathbf{x}, \mathbf{h})}.
|
||||
\label{_auto27}
|
||||
\end{align}
|
||||
$$
|
||||
|
||||
Now this is what we use to represent the wave function, calling it a neural-network quantum state (NQS)
|
||||
$$
|
||||
\begin{align}
|
||||
\Psi (\mathbf{X}) &= F_{rbm}(\mathbf{x})
|
||||
\label{_auto28}\\
|
||||
&= \frac{1}{Z}\sum_{\boldsymbol{h}} e^{-E(\mathbf{x}, \mathbf{h})}
|
||||
\label{_auto29}\\
|
||||
&= \frac{1}{Z} \sum_{\{h_j\}} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2} + \sum_j^N b_j h_j + \sum_{i,j}^{M,N} \frac{x_i w_{ij} h_j}{\sigma^2}}
|
||||
\label{_auto30}\\
|
||||
&= \frac{1}{Z} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2}} \prod_j^N (1 + e^{b_j + \sum_i^M \frac{x_i w_{ij}}{\sigma^2}}).
|
||||
\label{_auto31}\\
|
||||
\label{_auto32}
|
||||
\end{align}
|
||||
$$
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec64">Choose the cost function </h2>
|
||||
Now we don't necessarily have training data (unless we generate it by using some other method). However, what we do have is the variational principle which allows us to obtain the ground state wave function by minimizing the expectation value of the energy of a trial wavefunction (corresponding to the untrained NQS). Similarly to the traditional variational Monte Carlo method then, it is the local energy we wish to minimize. The gradient to use for the stochastic gradient descent procedure is
|
||||
$$
|
||||
\begin{align}
|
||||
G_i = \frac{\partial \langle E_L \rangle}{\partial \theta_i}
|
||||
= 2(\langle E_L \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle - \langle E_L \rangle \langle \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle ),
|
||||
\label{_auto33}
|
||||
\end{align}
|
||||
$$
|
||||
|
||||
where the local energy is given by
|
||||
$$
|
||||
\begin{align}
|
||||
E_L = \frac{1}{\Psi} \hat{\mathbf{H}} \Psi.
|
||||
\label{_auto34}
|
||||
\end{align}
|
||||
$$
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec65">Running the codes </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
You can find the codes for the simple two-electron case at the Github repository <a href="https://github.com/mhjensenseminars/MachineLearningTalk/tree/master/doc/Programs/MLcpp/src" target="_blank"><tt>https://github.com/mhjensenseminars/MachineLearningTalk/tree/master/doc/Programs/MLcpp/src</tt></a>. Python codes to come, only c++ as of now.
|
||||
|
||||
<p>
|
||||
The trial wave function is based on the product of a Slater determinant with Gaussian orbitals, a simple Jastrow factor \( \exp{(r_{ij})} \) and the reduced Boltzmann machines.
|
||||
|
||||
<p>
|
||||
The Broyden-Fletcher-Goldfarb-Shanno algorithm was used to perform the minimization. We used \( 14 \) hidden nodes in the calculations below.
|
||||
|
||||
|
||||
</div>
|
||||
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec66">Energy as function of iterations, \( N=2 \) electrons </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<br /><br /><center><p><img src="figures/figN2.png" align="bottom" width=700></p></center><br /><br />
|
||||
</div>
|
||||
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec67">Energy as function of iterations, \( N=6 \) electrons </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<br /><br /><center><p><img src="figures/figN6.png" align="bottom" width=700></p></center><br /><br />
|
||||
</div>
|
||||
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec68">Conclusions and where do we stand </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
|
||||
<ul>
|
||||
<li> A simple extension of the work of <a href="http://science.sciencemag.org/content/355/6325/602" target="_blank">G. Carleo and M. Troyer, Science <b>355</b>, Issue 6325, pp. 602-606 (2017)</a> gives excellent results for two-electron systems as well as good agreement with standard VMC calculations for \( N=6 \) and \( N=12 \) electrons.</li>
|
||||
<li> Minimization problem can be tricky.</li>
|
||||
<li> Anti-symmetry dealt with multiplying the trail wave function with an optimized Slater determinant.</li>
|
||||
<li> To come: Analysis of wave function from ML and compare with diffusion and Variational Monte Carlo calculations as well as the analytical results of Taut for the two-electron case.</li>
|
||||
<li> Extend to more fermions. How do we deal with the antisymmetry of the multi-fermion wave function?
|
||||
|
||||
<ol type="a"></li>
|
||||
<li> Here we used standard Hartree-Fock theory to define an optimal Slater determinant. Takes care of the antisymmetry. What about constructing an anti-symmetrized network function?</li>
|
||||
<li> Use thereafter ML to determine the correlated part of the wafe function (including a standard Jastrow factor).</li>
|
||||
<li> Test this for multi-fermion systems and compare with other many-body methods.</li>
|
||||
</ol>
|
||||
|
||||
<li> Can we use ML to find out which correlations are relevant and thereby diminish the dimensionality problem in say CC or SRG theories?</li>
|
||||
</ul>
|
||||
</div>
|
||||
|
||||
|
||||
<p>
|
||||
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
+8
-139
@@ -230,20 +230,11 @@ div { text-align: justify; text-justify: inter-word; }
|
||||
('Optimization / Training', 2, None, '___sec58'),
|
||||
('More on RBMs', 2, None, '___sec59'),
|
||||
('Which sampling to use', 2, None, '___sec60'),
|
||||
('RBMs for the quantum many body problem', 2, None, '___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62'),
|
||||
('Representing the wave function', 2, None, '___sec63'),
|
||||
('Choose the cost function', 2, None, '___sec64'),
|
||||
('Running the codes', 2, None, '___sec65'),
|
||||
('Energy as function of iterations, $N=2$ electrons',
|
||||
('Recent examples: RBMs for the quantum many body problem',
|
||||
2,
|
||||
None,
|
||||
'___sec66'),
|
||||
('Energy as function of iterations, $N=6$ electrons',
|
||||
2,
|
||||
None,
|
||||
'___sec67'),
|
||||
('Conclusions and where do we stand', 2, None, '___sec68')]}
|
||||
'___sec61'),
|
||||
('Choose the right RBM', 2, None, '___sec62')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -284,7 +275,7 @@ MathJax.Hub.Config({
|
||||
<center><b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University and Department of Physics, University of Oslo, Norway</b></center>
|
||||
<br>
|
||||
<p>
|
||||
<center><h4>Nov 22, 2018 </h4></center> <!-- date -->
|
||||
<center><h4>Nov 23, 2018 </h4></center> <!-- date -->
|
||||
<br>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
@@ -336,6 +327,9 @@ Furthermore, they have been used to solve complicated quantum mechanical many-pa
|
||||
|
||||
<h2 id="___sec2">An intermediate step, the Hopfield network and links to the Ising and Potts models </h2>
|
||||
|
||||
<p>
|
||||
More material on Hopfield networks will come here
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
@@ -1885,7 +1879,7 @@ To get the expectation values with respect to the <em>model</em>, we use Gibbs s
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec61">RBMs for the quantum many body problem </h2>
|
||||
<h2 id="___sec61">Recent examples: RBMs for the quantum many body problem </h2>
|
||||
|
||||
<p>
|
||||
The idea of applying RBMs to quantum many body problems was presented by G. Carleo and M. Troyer, working with ETH Zurich and Microsoft Research.
|
||||
@@ -1914,131 +1908,6 @@ Some of their motivation included
|
||||
<p>
|
||||
Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems of the Ising model and Heisenberg model, with encouraging results. Our goal is to test the method on systems of moving particles. For the spin lattice systems it was natural to use a binary-binary RBM, with the nodes taking values of 1 and -1. For moving particles, on the other hand, we want the visible nodes to be continuous, representing position coordinates. Thus, we start by choosing a Gaussian-binary RBM, where the visible nodes are continuous and hidden nodes take on values of 0 or 1. If eventually we would like the hidden nodes to be continuous as well the rectified linear units seem like the most relevant choice.
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec63">Representing the wave function </h2>
|
||||
The wavefunction should be a probability amplitude depending on \( \boldsymbol{x} \). The RBM model is given by the joint distribution of \( \boldsymbol{x} \) and \( \boldsymbol{h} \)
|
||||
$$
|
||||
\begin{align}
|
||||
F_{rbm}(\mathbf{x},\mathbf{h}) = \frac{1}{Z} e^{-\frac{1}{T_0}E(\mathbf{x},\mathbf{h})}.
|
||||
\label{_auto25}
|
||||
\end{align}
|
||||
$$
|
||||
|
||||
To find the marginal distribution of \( \boldsymbol{x} \) we set:
|
||||
$$
|
||||
\begin{align}
|
||||
F_{rbm}(\mathbf{x}) &= \sum_\mathbf{h} F_{rbm}(\mathbf{x}, \mathbf{h})
|
||||
\label{_auto26}\\
|
||||
&= \frac{1}{Z}\sum_\mathbf{h} e^{-E(\mathbf{x}, \mathbf{h})}.
|
||||
\label{_auto27}
|
||||
\end{align}
|
||||
$$
|
||||
|
||||
Now this is what we use to represent the wave function, calling it a neural-network quantum state (NQS)
|
||||
$$
|
||||
\begin{align}
|
||||
\Psi (\mathbf{X}) &= F_{rbm}(\mathbf{x})
|
||||
\label{_auto28}\\
|
||||
&= \frac{1}{Z}\sum_{\boldsymbol{h}} e^{-E(\mathbf{x}, \mathbf{h})}
|
||||
\label{_auto29}\\
|
||||
&= \frac{1}{Z} \sum_{\{h_j\}} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2} + \sum_j^N b_j h_j + \sum_{i,j}^{M,N} \frac{x_i w_{ij} h_j}{\sigma^2}}
|
||||
\label{_auto30}\\
|
||||
&= \frac{1}{Z} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2}} \prod_j^N (1 + e^{b_j + \sum_i^M \frac{x_i w_{ij}}{\sigma^2}}).
|
||||
\label{_auto31}\\
|
||||
\label{_auto32}
|
||||
\end{align}
|
||||
$$
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec64">Choose the cost function </h2>
|
||||
Now we don't necessarily have training data (unless we generate it by using some other method). However, what we do have is the variational principle which allows us to obtain the ground state wave function by minimizing the expectation value of the energy of a trial wavefunction (corresponding to the untrained NQS). Similarly to the traditional variational Monte Carlo method then, it is the local energy we wish to minimize. The gradient to use for the stochastic gradient descent procedure is
|
||||
$$
|
||||
\begin{align}
|
||||
G_i = \frac{\partial \langle E_L \rangle}{\partial \theta_i}
|
||||
= 2(\langle E_L \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle - \langle E_L \rangle \langle \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle ),
|
||||
\label{_auto33}
|
||||
\end{align}
|
||||
$$
|
||||
|
||||
where the local energy is given by
|
||||
$$
|
||||
\begin{align}
|
||||
E_L = \frac{1}{\Psi} \hat{\mathbf{H}} \Psi.
|
||||
\label{_auto34}
|
||||
\end{align}
|
||||
$$
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec65">Running the codes </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
You can find the codes for the simple two-electron case at the Github repository <a href="https://github.com/mhjensenseminars/MachineLearningTalk/tree/master/doc/Programs/MLcpp/src" target="_blank"><tt>https://github.com/mhjensenseminars/MachineLearningTalk/tree/master/doc/Programs/MLcpp/src</tt></a>. Python codes to come, only c++ as of now.
|
||||
|
||||
<p>
|
||||
The trial wave function is based on the product of a Slater determinant with Gaussian orbitals, a simple Jastrow factor \( \exp{(r_{ij})} \) and the reduced Boltzmann machines.
|
||||
|
||||
<p>
|
||||
The Broyden-Fletcher-Goldfarb-Shanno algorithm was used to perform the minimization. We used \( 14 \) hidden nodes in the calculations below.
|
||||
|
||||
|
||||
</div>
|
||||
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec66">Energy as function of iterations, \( N=2 \) electrons </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<br /><br /><center><p><img src="figures/figN2.png" align="bottom" width=700></p></center><br /><br />
|
||||
</div>
|
||||
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec67">Energy as function of iterations, \( N=6 \) electrons </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
<br /><br /><center><p><img src="figures/figN6.png" align="bottom" width=700></p></center><br /><br />
|
||||
</div>
|
||||
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec68">Conclusions and where do we stand </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
|
||||
<ul>
|
||||
<li> A simple extension of the work of <a href="http://science.sciencemag.org/content/355/6325/602" target="_blank">G. Carleo and M. Troyer, Science <b>355</b>, Issue 6325, pp. 602-606 (2017)</a> gives excellent results for two-electron systems as well as good agreement with standard VMC calculations for \( N=6 \) and \( N=12 \) electrons.</li>
|
||||
<li> Minimization problem can be tricky.</li>
|
||||
<li> Anti-symmetry dealt with multiplying the trail wave function with an optimized Slater determinant.</li>
|
||||
<li> To come: Analysis of wave function from ML and compare with diffusion and Variational Monte Carlo calculations as well as the analytical results of Taut for the two-electron case.</li>
|
||||
<li> Extend to more fermions. How do we deal with the antisymmetry of the multi-fermion wave function?
|
||||
|
||||
<ol type="a"></li>
|
||||
<li> Here we used standard Hartree-Fock theory to define an optimal Slater determinant. Takes care of the antisymmetry. What about constructing an anti-symmetrized network function?</li>
|
||||
<li> Use thereafter ML to determine the correlated part of the wafe function (including a standard Jastrow factor).</li>
|
||||
<li> Test this for multi-fermion systems and compare with other many-body methods.</li>
|
||||
</ol>
|
||||
|
||||
<li> Can we use ML to find out which correlations are relevant and thereby diminish the dimensionality problem in say CC or SRG theories?</li>
|
||||
</ul>
|
||||
</div>
|
||||
|
||||
|
||||
<p>
|
||||
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
+5
-247
@@ -10,7 +10,7 @@
|
||||
"<!-- Author: --> \n",
|
||||
"**Morten Hjorth-Jensen**, Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University and Department of Physics, University of Oslo, Norway\n",
|
||||
"\n",
|
||||
"Date: **Nov 22, 2018**\n",
|
||||
"Date: **Nov 23, 2018**\n",
|
||||
"\n",
|
||||
"Copyright 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
|
||||
"\n",
|
||||
@@ -54,6 +54,8 @@
|
||||
"\n",
|
||||
"## An intermediate step, the Hopfield network and links to the Ising and Potts models\n",
|
||||
"\n",
|
||||
"More material on Hopfield networks will come here\n",
|
||||
"\n",
|
||||
"## A brief review on Markov Chains, Metropolis and Gibbs sampling\n",
|
||||
"\n",
|
||||
"\n",
|
||||
@@ -2036,7 +2038,7 @@
|
||||
"\n",
|
||||
"To get the expectation values with respect to the *model*, we use Gibbs sampling. We can either initialize the $\\boldsymbol{x}$ randomly or with a training sample. While we ideally want a large number of Gibbs iterations $n\\rightarrow n$, one might decide to truncate it earlier for efficiency. Doing this while having intialized $\\boldsymbol{x}$ with a training data vector is referred to as contrastive divergence (CD), because one is then closer to approximating the gradient of this function than the negative log-likelihood. The contrastive divergence function is the difference between two Kullback-Leibler divergences (also called relative entropy), which measure how one probability distribution diverges from a second, expected probability distribution (in this case the estimated one from the ground truth one).\n",
|
||||
"\n",
|
||||
"## RBMs for the quantum many body problem\n",
|
||||
"## Recent examples: RBMs for the quantum many body problem\n",
|
||||
"\n",
|
||||
"The idea of applying RBMs to quantum many body problems was presented by G. Carleo and M. Troyer, working with ETH Zurich and Microsoft Research.\n",
|
||||
"\n",
|
||||
@@ -2059,251 +2061,7 @@
|
||||
"\n",
|
||||
"## Choose the right RBM\n",
|
||||
"\n",
|
||||
"Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems of the Ising model and Heisenberg model, with encouraging results. Our goal is to test the method on systems of moving particles. For the spin lattice systems it was natural to use a binary-binary RBM, with the nodes taking values of 1 and -1. For moving particles, on the other hand, we want the visible nodes to be continuous, representing position coordinates. Thus, we start by choosing a Gaussian-binary RBM, where the visible nodes are continuous and hidden nodes take on values of 0 or 1. If eventually we would like the hidden nodes to be continuous as well the rectified linear units seem like the most relevant choice.\n",
|
||||
"\n",
|
||||
"## Representing the wave function\n",
|
||||
"The wavefunction should be a probability amplitude depending on $\\boldsymbol{x}$. The RBM model is given by the joint distribution of $\\boldsymbol{x}$ and $\\boldsymbol{h}$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<!-- Equation labels as ordinary links -->\n",
|
||||
"<div id=\"_auto25\"></div>\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\begin{equation}\n",
|
||||
"\tF_{rbm}(\\mathbf{x},\\mathbf{h}) = \\frac{1}{Z} e^{-\\frac{1}{T_0}E(\\mathbf{x},\\mathbf{h})}.\n",
|
||||
"\\label{_auto25} \\tag{27}\n",
|
||||
"\\end{equation}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"To find the marginal distribution of $\\boldsymbol{x}$ we set:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<!-- Equation labels as ordinary links -->\n",
|
||||
"<div id=\"_auto26\"></div>\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\begin{equation}\n",
|
||||
"\tF_{rbm}(\\mathbf{x}) = \\sum_\\mathbf{h} F_{rbm}(\\mathbf{x}, \\mathbf{h}) \n",
|
||||
"\\label{_auto26} \\tag{28}\n",
|
||||
"\\end{equation}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<!-- Equation labels as ordinary links -->\n",
|
||||
"<div id=\"_auto27\"></div>\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\begin{equation} \n",
|
||||
"\t\t\t\t= \\frac{1}{Z}\\sum_\\mathbf{h} e^{-E(\\mathbf{x}, \\mathbf{h})}.\n",
|
||||
"\\label{_auto27} \\tag{29}\n",
|
||||
"\\end{equation}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Now this is what we use to represent the wave function, calling it a neural-network quantum state (NQS)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<!-- Equation labels as ordinary links -->\n",
|
||||
"<div id=\"_auto28\"></div>\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\begin{equation}\n",
|
||||
"\t\\Psi (\\mathbf{X}) = F_{rbm}(\\mathbf{x}) \n",
|
||||
"\\label{_auto28} \\tag{30}\n",
|
||||
"\\end{equation}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<!-- Equation labels as ordinary links -->\n",
|
||||
"<div id=\"_auto29\"></div>\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\begin{equation} \n",
|
||||
"\t= \\frac{1}{Z}\\sum_{\\boldsymbol{h}} e^{-E(\\mathbf{x}, \\mathbf{h})} \n",
|
||||
"\\label{_auto29} \\tag{31}\n",
|
||||
"\\end{equation}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<!-- Equation labels as ordinary links -->\n",
|
||||
"<div id=\"_auto30\"></div>\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\begin{equation} \n",
|
||||
"\t= \\frac{1}{Z} \\sum_{\\{h_j\\}} e^{-\\sum_i^M \\frac{(x_i - a_i)^2}{2\\sigma^2} + \\sum_j^N b_j h_j + \\sum_{i,j}^{M,N} \\frac{x_i w_{ij} h_j}{\\sigma^2}} \n",
|
||||
"\\label{_auto30} \\tag{32}\n",
|
||||
"\\end{equation}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<!-- Equation labels as ordinary links -->\n",
|
||||
"<div id=\"_auto31\"></div>\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\begin{equation} \n",
|
||||
"\t= \\frac{1}{Z} e^{-\\sum_i^M \\frac{(x_i - a_i)^2}{2\\sigma^2}} \\prod_j^N (1 + e^{b_j + \\sum_i^M \\frac{x_i w_{ij}}{\\sigma^2}}). \n",
|
||||
"\\label{_auto31} \\tag{33}\n",
|
||||
"\\end{equation}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<!-- Equation labels as ordinary links -->\n",
|
||||
"<div id=\"_auto32\"></div>\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\begin{equation} \n",
|
||||
"\\label{_auto32} \\tag{34}\n",
|
||||
"\\end{equation}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Choose the cost function\n",
|
||||
"Now we don't necessarily have training data (unless we generate it by using some other method). However, what we do have is the variational principle which allows us to obtain the ground state wave function by minimizing the expectation value of the energy of a trial wavefunction (corresponding to the untrained NQS). Similarly to the traditional variational Monte Carlo method then, it is the local energy we wish to minimize. The gradient to use for the stochastic gradient descent procedure is"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<!-- Equation labels as ordinary links -->\n",
|
||||
"<div id=\"_auto33\"></div>\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\begin{equation}\n",
|
||||
"\tG_i = \\frac{\\partial \\langle E_L \\rangle}{\\partial \\theta_i}\n",
|
||||
"\t= 2(\\langle E_L \\frac{1}{\\Psi}\\frac{\\partial \\Psi}{\\partial \\theta_i} \\rangle - \\langle E_L \\rangle \\langle \\frac{1}{\\Psi}\\frac{\\partial \\Psi}{\\partial \\theta_i} \\rangle ),\n",
|
||||
"\\label{_auto33} \\tag{35}\n",
|
||||
"\\end{equation}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"where the local energy is given by"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<!-- Equation labels as ordinary links -->\n",
|
||||
"<div id=\"_auto34\"></div>\n",
|
||||
"\n",
|
||||
"$$\n",
|
||||
"\\begin{equation}\n",
|
||||
"\tE_L = \\frac{1}{\\Psi} \\hat{\\mathbf{H}} \\Psi.\n",
|
||||
"\\label{_auto34} \\tag{36}\n",
|
||||
"\\end{equation}\n",
|
||||
"$$"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Running the codes\n",
|
||||
"You can find the codes for the simple two-electron case at the Github repository <https://github.com/mhjensenseminars/MachineLearningTalk/tree/master/doc/Programs/MLcpp/src>. Python codes to come, only c++ as of now. \n",
|
||||
"\n",
|
||||
"The trial wave function is based on the product of a Slater determinant with Gaussian orbitals, a simple Jastrow factor $\\exp{(r_{ij})}$ and the reduced Boltzmann machines. \n",
|
||||
"\n",
|
||||
"The Broyden-Fletcher-Goldfarb-Shanno algorithm was used to perform the minimization. We used $14$ hidden nodes in the calculations below.\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"## Energy as function of iterations, $N=2$ electrons\n",
|
||||
"<!-- dom:FIGURE: [figures/figN2.png, width=700 frac=0.9] -->\n",
|
||||
"<!-- begin figure -->\n",
|
||||
"\n",
|
||||
"<p></p>\n",
|
||||
"<img src=\"figures/figN2.png\" width=700>\n",
|
||||
"\n",
|
||||
"<!-- end figure -->\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"## Energy as function of iterations, $N=6$ electrons\n",
|
||||
"<!-- dom:FIGURE: [figures/figN6.png, width=700 frac=0.9] -->\n",
|
||||
"<!-- begin figure -->\n",
|
||||
"\n",
|
||||
"<p></p>\n",
|
||||
"<img src=\"figures/figN6.png\" width=700>\n",
|
||||
"\n",
|
||||
"<!-- end figure -->\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"## Conclusions and where do we stand\n",
|
||||
"* A simple extension of the work of [G. Carleo and M. Troyer, Science **355**, Issue 6325, pp. 602-606 (2017)](http://science.sciencemag.org/content/355/6325/602) gives excellent results for two-electron systems as well as good agreement with standard VMC calculations for $N=6$ and $N=12$ electrons.\n",
|
||||
"\n",
|
||||
"* Minimization problem can be tricky.\n",
|
||||
"\n",
|
||||
"* Anti-symmetry dealt with multiplying the trail wave function with an optimized Slater determinant.\n",
|
||||
"\n",
|
||||
"* To come: Analysis of wave function from ML and compare with diffusion and Variational Monte Carlo calculations as well as the analytical results of Taut for the two-electron case.\n",
|
||||
"\n",
|
||||
"* Extend to more fermions. How do we deal with the antisymmetry of the multi-fermion wave function?\n",
|
||||
"\n",
|
||||
" a. Here we used standard Hartree-Fock theory to define an optimal Slater determinant. Takes care of the antisymmetry. What about constructing an anti-symmetrized network function?\n",
|
||||
"\n",
|
||||
" b. Use thereafter ML to determine the correlated part of the wafe function (including a standard Jastrow factor).\n",
|
||||
"\n",
|
||||
" c. Test this for multi-fermion systems and compare with other many-body methods.\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"* Can we use ML to find out which correlations are relevant and thereby diminish the dimensionality problem in say CC or SRG theories?"
|
||||
"Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems of the Ising model and Heisenberg model, with encouraging results. Our goal is to test the method on systems of moving particles. For the spin lattice systems it was natural to use a binary-binary RBM, with the nodes taking values of 1 and -1. For moving particles, on the other hand, we want the visible nodes to be continuous, representing position coordinates. Thus, we start by choosing a Gaussian-binary RBM, where the visible nodes are continuous and hidden nodes take on values of 0 or 1. If eventually we would like the hidden nodes to be continuous as well the rectified linear units seem like the most relevant choice."
|
||||
]
|
||||
}
|
||||
],
|
||||
|
||||
Binary file not shown.
Binary file not shown.
@@ -43,6 +43,8 @@ Furthermore, they have been used to solve complicated quantum mechanical many-pa
|
||||
!split
|
||||
===== An intermediate step, the Hopfield network and links to the Ising and Potts models =====
|
||||
|
||||
More material on Hopfield networks will come here
|
||||
|
||||
!split
|
||||
===== A brief review on Markov Chains, Metropolis and Gibbs sampling =====
|
||||
|
||||
@@ -1184,7 +1186,7 @@ To get the expecation values with respect to the *data*, we set the visible unit
|
||||
To get the expectation values with respect to the *model*, we use Gibbs sampling. We can either initialize the $\bm{x}$ randomly or with a training sample. While we ideally want a large number of Gibbs iterations $n\rightarrow n$, one might decide to truncate it earlier for efficiency. Doing this while having intialized $\bm{x}$ with a training data vector is referred to as contrastive divergence (CD), because one is then closer to approximating the gradient of this function than the negative log-likelihood. The contrastive divergence function is the difference between two Kullback-Leibler divergences (also called relative entropy), which measure how one probability distribution diverges from a second, expected probability distribution (in this case the estimated one from the ground truth one).
|
||||
|
||||
!split
|
||||
===== RBMs for the quantum many body problem =====
|
||||
===== Recent examples: RBMs for the quantum many body problem =====
|
||||
|
||||
The idea of applying RBMs to quantum many body problems was presented by G. Carleo and M. Troyer, working with ETH Zurich and Microsoft Research.
|
||||
|
||||
@@ -1203,90 +1205,5 @@ Some of their motivation included
|
||||
|
||||
Carleo and Troyer applied the RBM to the quantum mechanical spin lattice systems of the Ising model and Heisenberg model, with encouraging results. Our goal is to test the method on systems of moving particles. For the spin lattice systems it was natural to use a binary-binary RBM, with the nodes taking values of 1 and -1. For moving particles, on the other hand, we want the visible nodes to be continuous, representing position coordinates. Thus, we start by choosing a Gaussian-binary RBM, where the visible nodes are continuous and hidden nodes take on values of 0 or 1. If eventually we would like the hidden nodes to be continuous as well the rectified linear units seem like the most relevant choice.
|
||||
|
||||
!split
|
||||
===== Representing the wave function =====
|
||||
The wavefunction should be a probability amplitude depending on $\bm{x}$. The RBM model is given by the joint distribution of $\bm{x}$ and $\bm{h}$
|
||||
!bt
|
||||
\begin{align}
|
||||
F_{rbm}(\mathbf{x},\mathbf{h}) = \frac{1}{Z} e^{-\frac{1}{T_0}E(\mathbf{x},\mathbf{h})}.
|
||||
\end{align}
|
||||
!et
|
||||
To find the marginal distribution of $\bm{x}$ we set:
|
||||
!bt
|
||||
\begin{align}
|
||||
F_{rbm}(\mathbf{x}) &= \sum_\mathbf{h} F_{rbm}(\mathbf{x}, \mathbf{h}) \\
|
||||
&= \frac{1}{Z}\sum_\mathbf{h} e^{-E(\mathbf{x}, \mathbf{h})}.
|
||||
\end{align}
|
||||
!et
|
||||
Now this is what we use to represent the wave function, calling it a neural-network quantum state (NQS)
|
||||
!bt
|
||||
\begin{align}
|
||||
\Psi (\mathbf{X}) &= F_{rbm}(\mathbf{x}) \\
|
||||
&= \frac{1}{Z}\sum_{\bm{h}} e^{-E(\mathbf{x}, \mathbf{h})} \\
|
||||
&= \frac{1}{Z} \sum_{\{h_j\}} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2} + \sum_j^N b_j h_j + \sum_{i,j}^{M,N} \frac{x_i w_{ij} h_j}{\sigma^2}} \\
|
||||
&= \frac{1}{Z} e^{-\sum_i^M \frac{(x_i - a_i)^2}{2\sigma^2}} \prod_j^N (1 + e^{b_j + \sum_i^M \frac{x_i w_{ij}}{\sigma^2}}). \\
|
||||
\end{align}
|
||||
!et
|
||||
|
||||
!split
|
||||
===== Choose the cost function =====
|
||||
Now we don't necessarily have training data (unless we generate it by using some other method). However, what we do have is the variational principle which allows us to obtain the ground state wave function by minimizing the expectation value of the energy of a trial wavefunction (corresponding to the untrained NQS). Similarly to the traditional variational Monte Carlo method then, it is the local energy we wish to minimize. The gradient to use for the stochastic gradient descent procedure is
|
||||
!bt
|
||||
\begin{align}
|
||||
G_i = \frac{\partial \langle E_L \rangle}{\partial \theta_i}
|
||||
= 2(\langle E_L \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle - \langle E_L \rangle \langle \frac{1}{\Psi}\frac{\partial \Psi}{\partial \theta_i} \rangle ),
|
||||
\end{align}
|
||||
!et
|
||||
where the local energy is given by
|
||||
!bt
|
||||
\begin{align}
|
||||
E_L = \frac{1}{\Psi} \hat{\mathbf{H}} \Psi.
|
||||
\end{align}
|
||||
!et
|
||||
|
||||
|
||||
!split
|
||||
===== Running the codes =====
|
||||
!bblock
|
||||
You can find the codes for the simple two-electron case at the Github repository URL:"https://github.com/mhjensenseminars/MachineLearningTalk/tree/master/doc/Programs/MLcpp/src". Python codes to come, only c++ as of now.
|
||||
|
||||
The trial wave function is based on the product of a Slater determinant with Gaussian orbitals, a simple Jastrow factor $\exp{(r_{ij})}$ and the reduced Boltzmann machines.
|
||||
|
||||
The Broyden-Fletcher-Goldfarb-Shanno algorithm was used to perform the minimization. We used $14$ hidden nodes in the calculations below.
|
||||
|
||||
!eblock
|
||||
|
||||
|
||||
|
||||
|
||||
!split
|
||||
===== Energy as function of iterations, $N=2$ electrons =====
|
||||
!bblock
|
||||
FIGURE: [figures/figN2.pdf, width=700 frac=0.9]
|
||||
!eblock
|
||||
|
||||
|
||||
!split
|
||||
===== Energy as function of iterations, $N=6$ electrons =====
|
||||
!bblock
|
||||
FIGURE: [figures/figN6.pdf, width=700 frac=0.9]
|
||||
!eblock
|
||||
|
||||
|
||||
|
||||
!split
|
||||
===== Conclusions and where do we stand =====
|
||||
!bblock
|
||||
* A simple extension of the work of "G. Carleo and M. Troyer, Science _355_, Issue 6325, pp. 602-606 (2017)":"http://science.sciencemag.org/content/355/6325/602" gives excellent results for two-electron systems as well as good agreement with standard VMC calculations for $N=6$ and $N=12$ electrons.
|
||||
* Minimization problem can be tricky.
|
||||
* Anti-symmetry dealt with multiplying the trail wave function with an optimized Slater determinant.
|
||||
* To come: Analysis of wave function from ML and compare with diffusion and Variational Monte Carlo calculations as well as the analytical results of Taut for the two-electron case.
|
||||
* Extend to more fermions. How do we deal with the antisymmetry of the multi-fermion wave function?
|
||||
o Here we used standard Hartree-Fock theory to define an optimal Slater determinant. Takes care of the antisymmetry. What about constructing an anti-symmetrized network function?
|
||||
o Use thereafter ML to determine the correlated part of the wafe function (including a standard Jastrow factor).
|
||||
o Test this for multi-fermion systems and compare with other many-body methods.
|
||||
* Can we use ML to find out which correlations are relevant and thereby diminish the dimensionality problem in say CC or SRG theories?
|
||||
|
||||
!eblock
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user