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doc/src/Projects/2023/Project3/Project3.do.txt

@@ -14,11 +14,14 @@ o Or other sources.
 
 
 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_. You could for example explore  all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into _convolutional neural networks_ or _recurrent neural networks_, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attention to supervised learning. 
+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_.
+Feel also free to use support vector machines, $k$-means and principal components analysis, although the latter have not been covered during the lectures. This material can be found in the lecture notes.
+
+You could for example explore  all of the approaches from decision trees, via bagging and voting classifiers, to random forests, boosting and finally XGboost. If you wish to venture into _convolutional neural networks_ or _recurrent neural networks_, or extensions of neural networkds, feel free to do so. You can also study unsupervised methods, although we in this course have mainly paid attention to supervised learning. 
 
 For Boosting, feel also free to write your own codes.
 
-o For project 3, you should feel free to use your own codes from projects 1 and 2, eventually write your own for Decision trees/random forests/bagging/boosting' or use the available functionality of _Scikit-Learn_, _Tensorflow_, etc. 
+o For project 3, you should feel free to use your own codes from projects 1 and 2, eventually write your own for Decision trees/random forests/bagging/boosting' or use the available functionality of _Scikit-Learn_, _Tensorflow_, PyTorch etc. 
 
 o The estimates you used and tested in projects 1 and 2 should also be included, that is the $R2$-score, _MSE_, confusion matrix, accuracy score, information gain,  ROC and Cumulative gains curves and other, cross-validation and/or bootstrap if these are relevant.
 
@@ -32,7 +35,7 @@ All in all, the report should follow the same pattern as the two previous ones,
 
 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 a large interest recently, 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 =====
@@ -68,9 +71,14 @@ 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":"https://github.com/CompPhysics/ComputationalPhysics/blob/master/doc/Lectures/lectures2015.pdf" or alternative sources. For the solution of ordinary and partial differential equations using neural networks, the lectures by "Kristine Baluka Hein and 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 "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 machine learning part you can use your own code from project 2 or the functionality of for example _Tensorflow/Keras_.. 
+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/". 
+
+=== Alternative differential equations ===
+
+Note that you can replace the one-dimensional diffusion equation discussed below with other sets of either ordinary differential equations or partial differential equations.
+Please discuss such a change with us at the lab.
 
 === Part a), setting up the problem ===
 
@@ -157,13 +165,18 @@ explicit scheme. Include also the analytical solution and compare with
 that.
 
 
+=== Part d) Neural network complexity ===
 
+Here we study the stability of the results of the results as functions of the number of hidden nodes, layers and activation functions for the hidden layers.
+Increase the number of hidden nodes and layers in order to see if this improves your results. Try also different activation functions for the hidden layers, such as the _tanh_, _ReLU_, and other activation functions. 
+Discuss your results.
 
-=== Part d) ===
+=== Part e) ===
 
 Finally, present a critical assessment of the methods you have studied
-and discuss the potential for the solving differential equations and
-eigenvalue problems with machine learning methods.
+and discuss the potential for the solving differential equations with machine learning methods.
+
+
 
 
 
@@ -246,3 +259,8 @@ of code developers and contributors keeps increasing.
 
 
 
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