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added project 3

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Morten Hjorth-Jensen
2024-11-04 15:46:48 -05:00
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doc/src/Projects/2024/Project3/Project3.do.txt
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@@ -11,7 +11,7 @@ For project 3, you can propose own data sets that relate to your research intere
o "Kaggle":"https://www.kaggle.com/datasets"
o The "University of California at Irvine (UCI) with its machine learning repository":"https://archive.ics.uci.edu/ml/index.php".
o Or other sources.
o Or you can propose own problems (but please do write to us before you start)
The approach to the analysis of these new data sets should follow to a large extent what you did in projects 1 and 2. That is:
o Whether you end up with a regression or a classification problem, you should employ at least two of the methods we have discussed among _linear regression (including Ridge and Lasso)_, _Logistic Regression_, _Neural Networks_, _Convolution Neural Networks_, _Recurrent Neural Networks_, and _Decision Trees, Random Forests, Bagging and Boosting_.
@@ -33,9 +33,19 @@ o A critical assessment of the methods with ditto perspectives and recommendatio
All in all, the report should follow the same pattern as the two previous ones, with abstract, introduction, methods, code, results, conclusions etc..
We propose also an alternative to the above. This is a project on using machine learning methods (neural networks mainly) to the solution of ordinary differential equations and partial differential equations, with a final twist on how to diagonalize a symmetric matrix with neural networks.
We propose also an alternative to the above. This is a project on
using machine learning methods (neural networks mainly) to the
solution of ordinary differential equations and partial differential
equations, with a final twist on how to diagonalize a symmetric matrix
with neural networks.
This is a field with large scientific interest, spanning from studies of turbulence in fluid mechanics and meteorology to the solution of quantum mechanical systems. As reading background you can use the slides "from week 43":"https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week42.html" and/or the textbook by "Yadav et al":"https://www.springer.com/gp/book/9789401798150".
This is a field with large scientific interest, spanning from studies
of turbulence in fluid mechanics and meteorology to the solution of
quantum mechanical systems. As reading background you can use the
slides "from week
43":"https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week42.html"
and/or the textbook by "Yadav et
al":"https://www.springer.com/gp/book/9789401798150".
===== The basic structure of your project =====
@@ -65,15 +75,21 @@ Finally, here you should present a critical assessment of the methods you have s
===== Solving partial differential equations with neural networks =====
This variant of project 3 is tailored to those of you who are
interested in studying differential equations and may have followed
popular courses on these methods, see below.
For this variant of project 3, we will assume that you have some
background in the solution of partial differential equations using
finite difference schemes. We will study the solution of the diffusion
equation in one dimension using a standard explicit scheme and neural
networks to solve the same equations.
For the explicit scheme, you can study for example chapter 10 of the lecture notes in "Computational Physics, FYS3150/4150":"https://github.com/CompPhysics/ComputationalPhysics/blob/master/doc/Lectures/lectures2015.pdf" or alternative sources from courses like "MAT-MEK4270":"https://www.uio.no/studier/emner/matnat/math/MAT-MEK4270/index.html". For the solution of ordinary and partial differential equations using neural networks, the lectures by "included in the lectures of week 43":"https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week43.html" at this course are highly recommended.
For the explicit scheme, you can study for example chapter 10 of the lecture notes in "Computational Physics, FYS3150/4150":"https://github.com/CompPhysics/ComputationalPhysics/blob/master/doc/Lectures/lectures2015.pdf" or alternative sources from courses like "MAT-MEK4270":"https://www.uio.no/studier/emner/matnat/math/MAT-MEK4270/index.html". For the solution of ordinary and partial differential equations using neural networks, the lectures by of week 43 at for example URL:"https://compphysics.github.io/MachineLearning/doc/pub/week42/html/week43.html" at this course are highly recommended.
For the machine learning part you can use your own code from project 2 or the functionality of for example _Tensorflow/Keras_, _PyTorch_ or other libraries such "Physics informed machine learning":"https://maziarraissi.github.io/PINNs/".
For the machine learning part you can use your own code from project 2
or the functionality of for example _Tensorflow/Keras_, _PyTorch_ or
other libraries such as "Physics informed machine learning":"https://maziarraissi.github.io/PINNs/".
=== Alternative differential equations ===