Machine Learning in Physics

lecture notes:

• machine learning fundamentals
• deep neural networks
• convolutional NNs
• recurrent neural nets
• attention and transformers
• autoencoders and GANs
• graph CNNs
• group-equivariant CNNs
• physics informed NNs
• self- and semi-supervised learning

laboratory classes:

1. Preliminary problems
   • simple perceptron networks
   • Universal Approximation Theorem
   • Colab notebook, see also updated notebook
2. Image classification using MNIST dataset
   • models: perceptron, deep fully-connected network, generic CNN
   • overfitting, regularization, early stopping
   • Colab notebook
     Extra tasks:
   • augmentation: apply some simple geometric transformations (see e.g. here), and check if such dataset extending improves accuracy:
   • use simple transformations (e.g. flip, rotate, translate, scale) using scikit-image, or open-cv,
   • or use TorchVision library online during the training.
   • Verify if applying flips or rotations > 45 deg improve accuracy or not, why? - generalization on wallpaper groups dataset:
   • repeat the classifier training for a 2D crystallographic structures dataset;
   • can we extract similarities between the classes from the confusion matrix?
3. ECG signal classification
   • classifiers comparison: SVM, decision trees, random forests
   • feature vectors and dimensionality reduction (PCA)
   • scikit-learn library
4. Group equivariant CNNs
5. Physics-informed NNs
6. Transformer encoder or GANs?

Literature:

• KP Murphy, Probabilistic Machine Learning: An Introduction
• KP Murphy, Probabilistic Machine Learning: Advanced Topics
• MM Bronstein et al., Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

proposed seminar topics

• list of proposed topics