updated typos on project 2017
This commit is contained in:
mhjensen
@@ -157,8 +157,7 @@ MathJax.Hub.Config({
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<p>
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The aim of this project is to use an already developed Monte Carlo program for the one-dimensional and two-dimensional <a href="https://github.com/CompPhysics/MachineLearning/tree/master/doc/Programs/IsingModel" target="_self">Ising model</a>, in order to produce the spin configurations for a series of energies \( E_i \) (10000 in total) for a system of \( L=40 \) spins in one dimension and \( L=40\times 40 \) in two dimensions at three different temperatures.
|
||||
In its simplest form
|
||||
the energy of the Ising model is expressed as, without an externally applied magnetic field,
|
||||
In its simplest form the energy of the Ising model is expressed as, without an externally applied magnetic field,
|
||||
$$
|
||||
E=-J\sum_{< kl >}^{N}s_ks_l
|
||||
$$
|
||||
@@ -169,10 +168,10 @@ constant expressing the strength of the interaction between
|
||||
neighboring spins. The symbol \( < kl> \) indicates that we sum over
|
||||
nearest neighbors only. We will assume that we have a ferromagnetic
|
||||
ordering, viz \( J> 0 \). We will use periodic boundary conditions and
|
||||
the Metropolis algorithm only.
|
||||
the Metropolis algorithm only. The spins take values \( -1 \) and \( +1 \) only.
|
||||
|
||||
<p>
|
||||
We will use the Ising model to generate our training data and will focus mainly on supervised training. We will follow closely the recent article of <a href="https://arxiv.org/abs/1803.08823" target="_self">Mehta et al, arXiv 1803.08823</a>. This article stands out as an excellent review of machine learning (ML) algorithms applied to typical physics problems. The added benefit is that each figure and model presented in <a href="https://physics.bu.edu/~pankajm/MLnotebooks.html" target="_self">this article is accompanied by its jupyter notebook</a>. This means that we can start using these and compare with our own results. In case you wish to use their data for the Ising model, thir data can be downloaded from the same link which lists to the jupyter notebooks. See also at the end of the project description for more information on how to install various Python packages.
|
||||
We will use the Ising model to generate our training data and will focus mainly on supervised training. We will follow closely the recent article of <a href="https://arxiv.org/abs/1803.08823" target="_self">Mehta et al, arXiv 1803.08823</a>. This article stands out as an excellent review on machine learning (ML) algorithms applied to typical physics problems. The added benefit is that each figure and model presented in <a href="https://physics.bu.edu/~pankajm/MLnotebooks.html" target="_self">this article is accompanied by its jupyter notebook</a>. This means that we can start using these and compare with our own results. In case you wish to use their data for the Ising model, their data can be downloaded from the same link which lists to the jupyter notebooks. See also at the end of the project description for more information on how to install various Python packages.
|
||||
|
||||
<p>
|
||||
With the abovementioned configurations we will determine, using first various
|
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@@ -180,16 +179,16 @@ regression methods, the value of the coupling constant for the energy
|
||||
of the one-dimensional Ising model. Thereafter, we will use the
|
||||
two-dimensional data, but now computed at different temperatures, in
|
||||
order to classify the phase of the Ising model. Below the critical
|
||||
temperature, the system will be in so-called ferromagnetic
|
||||
phase. Close to the critical temperature, the final magnetizations
|
||||
starts becoming close to zero while above the critical temperature,
|
||||
the net magnetization is zero. The latter case, that is the
|
||||
two-dimensional Ising model, will be studied using a <b>random forest</b>
|
||||
temperature, the system will be in a so-called ferromagnetic
|
||||
phase. Close to the critical temperature, the final magnetization becomes smaller and smaller in absolute value
|
||||
while above the critical temperature,
|
||||
the net magnetization is zero. This classification case, that is the
|
||||
two-dimensional Ising model, will be studied using logistic regression, a <b>random forest</b>
|
||||
algorithm and deep neural networks.
|
||||
|
||||
<p>
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You should try to program at least one of these methods yourself (choose the one you prefer).
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||||
Feel free to use the notebooks to benchmark your code. If you wish to write your C++ or Fortran program for say a simple neural network model, please feel free to do so.
|
||||
Feel free to use the notebooks to benchmark your code. If you wish to write your own C++ or Fortran program for say a simple neural network model, please feel free to do so.
|
||||
You can then benchmark your results against the above jupyter notebooks. More information can also be found at the link for the lecture notes of <a href="https://compphysics.github.io/MachineLearning/doc/web/course.html" target="_self">FYS-STK4155</a>.
|
||||
|
||||
<p>
|
||||
@@ -235,7 +234,8 @@ You can use scikit-learn to perform these analyses. See below for instruction on
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<h3 id="___sec5" class="anchor">Part d): Classifying the Ising model phase using neural networks </h3>
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|
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We end the classification problem of the phases of the Ising model by emplpying feed-forward deep neural networks (see section 9 of Mehta <em>et al.</em>). The method is described in <a href="https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html" target="_self">notebook 12</a>.
|
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<p>
|
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We end the classification problem of the phases of the Ising model by employing the algorithm for so-called feed-forward deep neural networks (see section 9 of Mehta <em>et al.</em>). The method is described in <a href="https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html" target="_self">notebook 12</a>.
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|
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<p>
|
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You can use tensorflow to perform these analyses. See below for instruction on how to install tensorflow.
|
||||
|
||||
@@ -157,8 +157,7 @@ MathJax.Hub.Config({
|
||||
|
||||
<p>
|
||||
The aim of this project is to use an already developed Monte Carlo program for the one-dimensional and two-dimensional <a href="https://github.com/CompPhysics/MachineLearning/tree/master/doc/Programs/IsingModel" target="_self">Ising model</a>, in order to produce the spin configurations for a series of energies \( E_i \) (10000 in total) for a system of \( L=40 \) spins in one dimension and \( L=40\times 40 \) in two dimensions at three different temperatures.
|
||||
In its simplest form
|
||||
the energy of the Ising model is expressed as, without an externally applied magnetic field,
|
||||
In its simplest form the energy of the Ising model is expressed as, without an externally applied magnetic field,
|
||||
$$
|
||||
E=-J\sum_{< kl >}^{N}s_ks_l
|
||||
$$
|
||||
@@ -169,10 +168,10 @@ constant expressing the strength of the interaction between
|
||||
neighboring spins. The symbol \( < kl> \) indicates that we sum over
|
||||
nearest neighbors only. We will assume that we have a ferromagnetic
|
||||
ordering, viz \( J> 0 \). We will use periodic boundary conditions and
|
||||
the Metropolis algorithm only.
|
||||
the Metropolis algorithm only. The spins take values \( -1 \) and \( +1 \) only.
|
||||
|
||||
<p>
|
||||
We will use the Ising model to generate our training data and will focus mainly on supervised training. We will follow closely the recent article of <a href="https://arxiv.org/abs/1803.08823" target="_self">Mehta et al, arXiv 1803.08823</a>. This article stands out as an excellent review of machine learning (ML) algorithms applied to typical physics problems. The added benefit is that each figure and model presented in <a href="https://physics.bu.edu/~pankajm/MLnotebooks.html" target="_self">this article is accompanied by its jupyter notebook</a>. This means that we can start using these and compare with our own results. In case you wish to use their data for the Ising model, thir data can be downloaded from the same link which lists to the jupyter notebooks. See also at the end of the project description for more information on how to install various Python packages.
|
||||
We will use the Ising model to generate our training data and will focus mainly on supervised training. We will follow closely the recent article of <a href="https://arxiv.org/abs/1803.08823" target="_self">Mehta et al, arXiv 1803.08823</a>. This article stands out as an excellent review on machine learning (ML) algorithms applied to typical physics problems. The added benefit is that each figure and model presented in <a href="https://physics.bu.edu/~pankajm/MLnotebooks.html" target="_self">this article is accompanied by its jupyter notebook</a>. This means that we can start using these and compare with our own results. In case you wish to use their data for the Ising model, their data can be downloaded from the same link which lists to the jupyter notebooks. See also at the end of the project description for more information on how to install various Python packages.
|
||||
|
||||
<p>
|
||||
With the abovementioned configurations we will determine, using first various
|
||||
@@ -180,16 +179,16 @@ regression methods, the value of the coupling constant for the energy
|
||||
of the one-dimensional Ising model. Thereafter, we will use the
|
||||
two-dimensional data, but now computed at different temperatures, in
|
||||
order to classify the phase of the Ising model. Below the critical
|
||||
temperature, the system will be in so-called ferromagnetic
|
||||
phase. Close to the critical temperature, the final magnetizations
|
||||
starts becoming close to zero while above the critical temperature,
|
||||
the net magnetization is zero. The latter case, that is the
|
||||
two-dimensional Ising model, will be studied using a <b>random forest</b>
|
||||
temperature, the system will be in a so-called ferromagnetic
|
||||
phase. Close to the critical temperature, the final magnetization becomes smaller and smaller in absolute value
|
||||
while above the critical temperature,
|
||||
the net magnetization is zero. This classification case, that is the
|
||||
two-dimensional Ising model, will be studied using logistic regression, a <b>random forest</b>
|
||||
algorithm and deep neural networks.
|
||||
|
||||
<p>
|
||||
You should try to program at least one of these methods yourself (choose the one you prefer).
|
||||
Feel free to use the notebooks to benchmark your code. If you wish to write your C++ or Fortran program for say a simple neural network model, please feel free to do so.
|
||||
Feel free to use the notebooks to benchmark your code. If you wish to write your own C++ or Fortran program for say a simple neural network model, please feel free to do so.
|
||||
You can then benchmark your results against the above jupyter notebooks. More information can also be found at the link for the lecture notes of <a href="https://compphysics.github.io/MachineLearning/doc/web/course.html" target="_self">FYS-STK4155</a>.
|
||||
|
||||
<p>
|
||||
@@ -235,7 +234,8 @@ You can use scikit-learn to perform these analyses. See below for instruction on
|
||||
|
||||
<h3 id="___sec5" class="anchor">Part d): Classifying the Ising model phase using neural networks </h3>
|
||||
|
||||
We end the classification problem of the phases of the Ising model by emplpying feed-forward deep neural networks (see section 9 of Mehta <em>et al.</em>). The method is described in <a href="https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html" target="_self">notebook 12</a>.
|
||||
<p>
|
||||
We end the classification problem of the phases of the Ising model by employing the algorithm for so-called feed-forward deep neural networks (see section 9 of Mehta <em>et al.</em>). The method is described in <a href="https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html" target="_self">notebook 12</a>.
|
||||
|
||||
<p>
|
||||
You can use tensorflow to perform these analyses. See below for instruction on how to install tensorflow.
|
||||
|
||||
@@ -114,8 +114,7 @@ MathJax.Hub.Config({
|
||||
|
||||
<p>
|
||||
The aim of this project is to use an already developed Monte Carlo program for the one-dimensional and two-dimensional <a href="https://github.com/CompPhysics/MachineLearning/tree/master/doc/Programs/IsingModel" target="_blank">Ising model</a>, in order to produce the spin configurations for a series of energies \( E_i \) (10000 in total) for a system of \( L=40 \) spins in one dimension and \( L=40\times 40 \) in two dimensions at three different temperatures.
|
||||
In its simplest form
|
||||
the energy of the Ising model is expressed as, without an externally applied magnetic field,
|
||||
In its simplest form the energy of the Ising model is expressed as, without an externally applied magnetic field,
|
||||
$$
|
||||
E=-J\sum_{< kl >}^{N}s_ks_l
|
||||
$$
|
||||
@@ -126,10 +125,10 @@ constant expressing the strength of the interaction between
|
||||
neighboring spins. The symbol \( < kl> \) indicates that we sum over
|
||||
nearest neighbors only. We will assume that we have a ferromagnetic
|
||||
ordering, viz \( J> 0 \). We will use periodic boundary conditions and
|
||||
the Metropolis algorithm only.
|
||||
the Metropolis algorithm only. The spins take values \( -1 \) and \( +1 \) only.
|
||||
|
||||
<p>
|
||||
We will use the Ising model to generate our training data and will focus mainly on supervised training. We will follow closely the recent article of <a href="https://arxiv.org/abs/1803.08823" target="_blank">Mehta et al, arXiv 1803.08823</a>. This article stands out as an excellent review of machine learning (ML) algorithms applied to typical physics problems. The added benefit is that each figure and model presented in <a href="https://physics.bu.edu/~pankajm/MLnotebooks.html" target="_blank">this article is accompanied by its jupyter notebook</a>. This means that we can start using these and compare with our own results. In case you wish to use their data for the Ising model, thir data can be downloaded from the same link which lists to the jupyter notebooks. See also at the end of the project description for more information on how to install various Python packages.
|
||||
We will use the Ising model to generate our training data and will focus mainly on supervised training. We will follow closely the recent article of <a href="https://arxiv.org/abs/1803.08823" target="_blank">Mehta et al, arXiv 1803.08823</a>. This article stands out as an excellent review on machine learning (ML) algorithms applied to typical physics problems. The added benefit is that each figure and model presented in <a href="https://physics.bu.edu/~pankajm/MLnotebooks.html" target="_blank">this article is accompanied by its jupyter notebook</a>. This means that we can start using these and compare with our own results. In case you wish to use their data for the Ising model, their data can be downloaded from the same link which lists to the jupyter notebooks. See also at the end of the project description for more information on how to install various Python packages.
|
||||
|
||||
<p>
|
||||
With the abovementioned configurations we will determine, using first various
|
||||
@@ -137,16 +136,16 @@ regression methods, the value of the coupling constant for the energy
|
||||
of the one-dimensional Ising model. Thereafter, we will use the
|
||||
two-dimensional data, but now computed at different temperatures, in
|
||||
order to classify the phase of the Ising model. Below the critical
|
||||
temperature, the system will be in so-called ferromagnetic
|
||||
phase. Close to the critical temperature, the final magnetizations
|
||||
starts becoming close to zero while above the critical temperature,
|
||||
the net magnetization is zero. The latter case, that is the
|
||||
two-dimensional Ising model, will be studied using a <b>random forest</b>
|
||||
temperature, the system will be in a so-called ferromagnetic
|
||||
phase. Close to the critical temperature, the final magnetization becomes smaller and smaller in absolute value
|
||||
while above the critical temperature,
|
||||
the net magnetization is zero. This classification case, that is the
|
||||
two-dimensional Ising model, will be studied using logistic regression, a <b>random forest</b>
|
||||
algorithm and deep neural networks.
|
||||
|
||||
<p>
|
||||
You should try to program at least one of these methods yourself (choose the one you prefer).
|
||||
Feel free to use the notebooks to benchmark your code. If you wish to write your C++ or Fortran program for say a simple neural network model, please feel free to do so.
|
||||
Feel free to use the notebooks to benchmark your code. If you wish to write your own C++ or Fortran program for say a simple neural network model, please feel free to do so.
|
||||
You can then benchmark your results against the above jupyter notebooks. More information can also be found at the link for the lecture notes of <a href="https://compphysics.github.io/MachineLearning/doc/web/course.html" target="_blank">FYS-STK4155</a>.
|
||||
|
||||
<p>
|
||||
@@ -192,7 +191,8 @@ You can use scikit-learn to perform these analyses. See below for instruction on
|
||||
|
||||
<h3 id="___sec5">Part d): Classifying the Ising model phase using neural networks </h3>
|
||||
|
||||
We end the classification problem of the phases of the Ising model by emplpying feed-forward deep neural networks (see section 9 of Mehta <em>et al.</em>). The method is described in <a href="https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html" target="_blank">notebook 12</a>.
|
||||
<p>
|
||||
We end the classification problem of the phases of the Ising model by employing the algorithm for so-called feed-forward deep neural networks (see section 9 of Mehta <em>et al.</em>). The method is described in <a href="https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html" target="_blank">notebook 12</a>.
|
||||
|
||||
<p>
|
||||
You can use tensorflow to perform these analyses. See below for instruction on how to install tensorflow.
|
||||
|
||||
Binary file not shown.
@@ -160,8 +160,7 @@ May 2018
|
||||
|
||||
\paragraph{Introduction.}
|
||||
The aim of this project is to use an already developed Monte Carlo program for the one-dimensional and two-dimensional \href{{https://github.com/CompPhysics/MachineLearning/tree/master/doc/Programs/IsingModel}}{Ising model}, in order to produce the spin configurations for a series of energies $E_i$ (10000 in total) for a system of $L=40$ spins in one dimension and $L=40\times 40$ in two dimensions at three different temperatures.
|
||||
In its simplest form
|
||||
the energy of the Ising model is expressed as, without an externally applied magnetic field,
|
||||
In its simplest form the energy of the Ising model is expressed as, without an externally applied magnetic field,
|
||||
\[
|
||||
E=-J\sum_{< kl >}^{N}s_ks_l
|
||||
\]
|
||||
@@ -171,10 +170,10 @@ constant expressing the strength of the interaction between
|
||||
neighboring spins. The symbol $<kl>$ indicates that we sum over
|
||||
nearest neighbors only. We will assume that we have a ferromagnetic
|
||||
ordering, viz $J> 0$. We will use periodic boundary conditions and
|
||||
the Metropolis algorithm only.
|
||||
the Metropolis algorithm only. The spins take values $-1$ and $+1$ only.
|
||||
|
||||
|
||||
We will use the Ising model to generate our training data and will focus mainly on supervised training. We will follow closely the recent article of \href{{https://arxiv.org/abs/1803.08823}}{Mehta et al, arXiv 1803.08823}. This article stands out as an excellent review of machine learning (ML) algorithms applied to typical physics problems. The added benefit is that each figure and model presented in \href{{https://physics.bu.edu/~pankajm/MLnotebooks.html}}{this article is accompanied by its jupyter notebook}. This means that we can start using these and compare with our own results. In case you wish to use their data for the Ising model, thir data can be downloaded from the same link which lists to the jupyter notebooks. See also at the end of the project description for more information on how to install various Python packages.
|
||||
We will use the Ising model to generate our training data and will focus mainly on supervised training. We will follow closely the recent article of \href{{https://arxiv.org/abs/1803.08823}}{Mehta et al, arXiv 1803.08823}. This article stands out as an excellent review on machine learning (ML) algorithms applied to typical physics problems. The added benefit is that each figure and model presented in \href{{https://physics.bu.edu/~pankajm/MLnotebooks.html}}{this article is accompanied by its jupyter notebook}. This means that we can start using these and compare with our own results. In case you wish to use their data for the Ising model, their data can be downloaded from the same link which lists to the jupyter notebooks. See also at the end of the project description for more information on how to install various Python packages.
|
||||
|
||||
|
||||
|
||||
@@ -183,15 +182,15 @@ regression methods, the value of the coupling constant for the energy
|
||||
of the one-dimensional Ising model. Thereafter, we will use the
|
||||
two-dimensional data, but now computed at different temperatures, in
|
||||
order to classify the phase of the Ising model. Below the critical
|
||||
temperature, the system will be in so-called ferromagnetic
|
||||
phase. Close to the critical temperature, the final magnetizations
|
||||
starts becoming close to zero while above the critical temperature,
|
||||
the net magnetization is zero. The latter case, that is the
|
||||
two-dimensional Ising model, will be studied using a \textbf{random forest}
|
||||
temperature, the system will be in a so-called ferromagnetic
|
||||
phase. Close to the critical temperature, the final magnetization becomes smaller and smaller in absolute value
|
||||
while above the critical temperature,
|
||||
the net magnetization is zero. This classification case, that is the
|
||||
two-dimensional Ising model, will be studied using logistic regression, a \textbf{random forest}
|
||||
algorithm and deep neural networks.
|
||||
|
||||
You should try to program at least one of these methods yourself (choose the one you prefer).
|
||||
Feel free to use the notebooks to benchmark your code. If you wish to write your C++ or Fortran program for say a simple neural network model, please feel free to do so.
|
||||
Feel free to use the notebooks to benchmark your code. If you wish to write your own C++ or Fortran program for say a simple neural network model, please feel free to do so.
|
||||
You can then benchmark your results against the above jupyter notebooks. More information can also be found at the link for the lecture notes of \href{{https://compphysics.github.io/MachineLearning/doc/web/course.html}}{FYS-STK4155}.
|
||||
|
||||
|
||||
@@ -231,7 +230,7 @@ Use described section 7 and in Notebook 6 of \href{{https://physics.bu.edu/~pank
|
||||
You can use scikit-learn to perform these analyses. See below for instruction on how to install scikit-learn.
|
||||
|
||||
\paragraph{Part d): Classifying the Ising model phase using neural networks.}
|
||||
We end the classification problem of the phases of the Ising model by emplpying feed-forward deep neural networks (see section 9 of Mehta \emph{et al.}). The method is described in \href{{https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html}}{notebook 12}.
|
||||
We end the classification problem of the phases of the Ising model by employing the algorithm for so-called feed-forward deep neural networks (see section 9 of Mehta \emph{et al.}). The method is described in \href{{https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html}}{notebook 12}.
|
||||
|
||||
You can use tensorflow to perform these analyses. See below for instruction on how to install tensorflow.
|
||||
|
||||
|
||||
Binary file not shown.
@@ -134,8 +134,7 @@ May 2018
|
||||
|
||||
\paragraph{Introduction.}
|
||||
The aim of this project is to use an already developed Monte Carlo program for the one-dimensional and two-dimensional \href{{https://github.com/CompPhysics/MachineLearning/tree/master/doc/Programs/IsingModel}}{Ising model}, in order to produce the spin configurations for a series of energies $E_i$ (10000 in total) for a system of $L=40$ spins in one dimension and $L=40\times 40$ in two dimensions at three different temperatures.
|
||||
In its simplest form
|
||||
the energy of the Ising model is expressed as, without an externally applied magnetic field,
|
||||
In its simplest form the energy of the Ising model is expressed as, without an externally applied magnetic field,
|
||||
\[
|
||||
E=-J\sum_{< kl >}^{N}s_ks_l
|
||||
\]
|
||||
@@ -145,10 +144,10 @@ constant expressing the strength of the interaction between
|
||||
neighboring spins. The symbol $<kl>$ indicates that we sum over
|
||||
nearest neighbors only. We will assume that we have a ferromagnetic
|
||||
ordering, viz $J> 0$. We will use periodic boundary conditions and
|
||||
the Metropolis algorithm only.
|
||||
the Metropolis algorithm only. The spins take values $-1$ and $+1$ only.
|
||||
|
||||
|
||||
We will use the Ising model to generate our training data and will focus mainly on supervised training. We will follow closely the recent article of \href{{https://arxiv.org/abs/1803.08823}}{Mehta et al, arXiv 1803.08823}. This article stands out as an excellent review of machine learning (ML) algorithms applied to typical physics problems. The added benefit is that each figure and model presented in \href{{https://physics.bu.edu/~pankajm/MLnotebooks.html}}{this article is accompanied by its jupyter notebook}. This means that we can start using these and compare with our own results. In case you wish to use their data for the Ising model, thir data can be downloaded from the same link which lists to the jupyter notebooks. See also at the end of the project description for more information on how to install various Python packages.
|
||||
We will use the Ising model to generate our training data and will focus mainly on supervised training. We will follow closely the recent article of \href{{https://arxiv.org/abs/1803.08823}}{Mehta et al, arXiv 1803.08823}. This article stands out as an excellent review on machine learning (ML) algorithms applied to typical physics problems. The added benefit is that each figure and model presented in \href{{https://physics.bu.edu/~pankajm/MLnotebooks.html}}{this article is accompanied by its jupyter notebook}. This means that we can start using these and compare with our own results. In case you wish to use their data for the Ising model, their data can be downloaded from the same link which lists to the jupyter notebooks. See also at the end of the project description for more information on how to install various Python packages.
|
||||
|
||||
|
||||
|
||||
@@ -157,15 +156,15 @@ regression methods, the value of the coupling constant for the energy
|
||||
of the one-dimensional Ising model. Thereafter, we will use the
|
||||
two-dimensional data, but now computed at different temperatures, in
|
||||
order to classify the phase of the Ising model. Below the critical
|
||||
temperature, the system will be in so-called ferromagnetic
|
||||
phase. Close to the critical temperature, the final magnetizations
|
||||
starts becoming close to zero while above the critical temperature,
|
||||
the net magnetization is zero. The latter case, that is the
|
||||
two-dimensional Ising model, will be studied using a \textbf{random forest}
|
||||
temperature, the system will be in a so-called ferromagnetic
|
||||
phase. Close to the critical temperature, the final magnetization becomes smaller and smaller in absolute value
|
||||
while above the critical temperature,
|
||||
the net magnetization is zero. This classification case, that is the
|
||||
two-dimensional Ising model, will be studied using logistic regression, a \textbf{random forest}
|
||||
algorithm and deep neural networks.
|
||||
|
||||
You should try to program at least one of these methods yourself (choose the one you prefer).
|
||||
Feel free to use the notebooks to benchmark your code. If you wish to write your C++ or Fortran program for say a simple neural network model, please feel free to do so.
|
||||
Feel free to use the notebooks to benchmark your code. If you wish to write your own C++ or Fortran program for say a simple neural network model, please feel free to do so.
|
||||
You can then benchmark your results against the above jupyter notebooks. More information can also be found at the link for the lecture notes of \href{{https://compphysics.github.io/MachineLearning/doc/web/course.html}}{FYS-STK4155}.
|
||||
|
||||
|
||||
@@ -205,7 +204,7 @@ Use described section 7 and in Notebook 6 of \href{{https://physics.bu.edu/~pank
|
||||
You can use scikit-learn to perform these analyses. See below for instruction on how to install scikit-learn.
|
||||
|
||||
\paragraph{Part d): Classifying the Ising model phase using neural networks.}
|
||||
We end the classification problem of the phases of the Ising model by emplpying feed-forward deep neural networks (see section 9 of Mehta \emph{et al.}). The method is described in \href{{https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html}}{notebook 12}.
|
||||
We end the classification problem of the phases of the Ising model by employing the algorithm for so-called feed-forward deep neural networks (see section 9 of Mehta \emph{et al.}). The method is described in \href{{https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html}}{notebook 12}.
|
||||
|
||||
You can use tensorflow to perform these analyses. See below for instruction on how to install tensorflow.
|
||||
|
||||
|
||||
@@ -8,8 +8,7 @@ DATE: May 2018
|
||||
=== Introduction ===
|
||||
|
||||
The aim of this project is to use an already developed Monte Carlo program for the one-dimensional and two-dimensional "Ising model":"https://github.com/CompPhysics/MachineLearning/tree/master/doc/Programs/IsingModel", in order to produce the spin configurations for a series of energies $E_i$ (10000 in total) for a system of $L=40$ spins in one dimension and $L=40\times 40$ in two dimensions at three different temperatures.
|
||||
In its simplest form
|
||||
the energy of the Ising model is expressed as, without an externally applied magnetic field,
|
||||
In its simplest form the energy of the Ising model is expressed as, without an externally applied magnetic field,
|
||||
!bt
|
||||
\[
|
||||
E=-J\sum_{< kl >}^{N}s_ks_l
|
||||
@@ -21,10 +20,10 @@ constant expressing the strength of the interaction between
|
||||
neighboring spins. The symbol $<kl>$ indicates that we sum over
|
||||
nearest neighbors only. We will assume that we have a ferromagnetic
|
||||
ordering, viz $J> 0$. We will use periodic boundary conditions and
|
||||
the Metropolis algorithm only.
|
||||
the Metropolis algorithm only. The spins take values $-1$ and $+1$ only.
|
||||
|
||||
|
||||
We will use the Ising model to generate our training data and will focus mainly on supervised training. We will follow closely the recent article of "Mehta et al, arXiv 1803.08823":"https://arxiv.org/abs/1803.08823". This article stands out as an excellent review of machine learning (ML) algorithms applied to typical physics problems. The added benefit is that each figure and model presented in "this article is accompanied by its jupyter notebook":"https://physics.bu.edu/~pankajm/MLnotebooks.html". This means that we can start using these and compare with our own results. In case you wish to use their data for the Ising model, thir data can be downloaded from the same link which lists to the jupyter notebooks. See also at the end of the project description for more information on how to install various Python packages.
|
||||
We will use the Ising model to generate our training data and will focus mainly on supervised training. We will follow closely the recent article of "Mehta et al, arXiv 1803.08823":"https://arxiv.org/abs/1803.08823". This article stands out as an excellent review on machine learning (ML) algorithms applied to typical physics problems. The added benefit is that each figure and model presented in "this article is accompanied by its jupyter notebook":"https://physics.bu.edu/~pankajm/MLnotebooks.html". This means that we can start using these and compare with our own results. In case you wish to use their data for the Ising model, their data can be downloaded from the same link which lists to the jupyter notebooks. See also at the end of the project description for more information on how to install various Python packages.
|
||||
|
||||
|
||||
|
||||
@@ -33,15 +32,15 @@ regression methods, the value of the coupling constant for the energy
|
||||
of the one-dimensional Ising model. Thereafter, we will use the
|
||||
two-dimensional data, but now computed at different temperatures, in
|
||||
order to classify the phase of the Ising model. Below the critical
|
||||
temperature, the system will be in so-called ferromagnetic
|
||||
phase. Close to the critical temperature, the final magnetizations
|
||||
starts becoming close to zero while above the critical temperature,
|
||||
the net magnetization is zero. The latter case, that is the
|
||||
two-dimensional Ising model, will be studied using a _random forest_
|
||||
temperature, the system will be in a so-called ferromagnetic
|
||||
phase. Close to the critical temperature, the final magnetization becomes smaller and smaller in absolute value
|
||||
while above the critical temperature,
|
||||
the net magnetization is zero. This classification case, that is the
|
||||
two-dimensional Ising model, will be studied using logistic regression, a _random forest_
|
||||
algorithm and deep neural networks.
|
||||
|
||||
You should try to program at least one of these methods yourself (choose the one you prefer).
|
||||
Feel free to use the notebooks to benchmark your code. If you wish to write your C++ or Fortran program for say a simple neural network model, please feel free to do so.
|
||||
Feel free to use the notebooks to benchmark your code. If you wish to write your own C++ or Fortran program for say a simple neural network model, please feel free to do so.
|
||||
You can then benchmark your results against the above jupyter notebooks. More information can also be found at the link for the lecture notes of "FYS-STK4155":"https://compphysics.github.io/MachineLearning/doc/web/course.html".
|
||||
|
||||
|
||||
@@ -84,7 +83,8 @@ Use described section 7 and in Notebook 6 of "Mehta *et al.*":"https://physics.b
|
||||
You can use scikit-learn to perform these analyses. See below for instruction on how to install scikit-learn.
|
||||
|
||||
=== Part d): Classifying the Ising model phase using neural networks ===
|
||||
We end the classification problem of the phases of the Ising model by emplpying feed-forward deep neural networks (see section 9 of Mehta *et al.*). The method is described in "notebook 12":"https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html".
|
||||
|
||||
We end the classification problem of the phases of the Ising model by employing the algorithm for so-called feed-forward deep neural networks (see section 9 of Mehta *et al.*). The method is described in "notebook 12":"https://physics.bu.edu/~pankajm/ML-Notebooks/HTML/NB_CIX-DNN_ising_TFlow.html".
|
||||
|
||||
You can use tensorflow to perform these analyses. See below for instruction on how to install tensorflow.
|
||||
|
||||
|
||||
Reference in New Issue
Block a user