Physics-Informed Machine Learning

The module covers selected topics in machine learning ranging from introductory principles to new-fashioned techniques. Different areas and approaches in the field (supervised, unsupervised, and reinforcement learning, parametric vs. non-parametric, etc.) are introduced through recent success examples. The focus is on (i) models for classification and regression (linear regression, Bayesian Uncertainty Quantification and model selection, regularization and sparsity-aware learning, deep neural networks, stochastic gradient descent), (ii) models for clustering and dimensionality reduction (k-means, PCA, autoencoders, self-organizing maps), and (iii) generative models (variational autoencoders, generative adversarial networks).

Upon successful completion of the module, students will
- understand key concepts underlying various machine learning algorithms
- be capable of applying discussed methods to test problems
- be able to implement the algorithms and use them on real data
- be able to integrate physical constraints and invariances into machine learning methods
- be able to compare and evaluate different methods in terms of their area of application, advantages/disadvantages, limitations, etc.

Basic knowledge in linear algebra and probability theory.

The module consists of a lecture and an exercise. In the lecture, the course material is presented with a mixture of slides (motivational examples, key concepts), blackboard (important mathematical background), and animations (algorithm demonstrations). During the exercise the students will gain a hands-on experience with machine learning techniques by applying them to practical problems. The solutions of the exercises will be provided in Python, however the exam will not require knowledge of the Python programming language.

So the students learn for example to understand key concepts underlying various machine learning algorithms, to implement the algorithms and use them on real data as well as to compare and evaluate different methods in terms of their area of application, advantages/disadvantages, limitations, etc..

Lecture notes, slides, exercise handouts and solutions with Python source code.

Entire course material is available for download. Additional readings from various sources will be provided throughout the semester.

The final grade is based on a written exam (90 min, pen and paper, allowed aid: non-programmable calculator). The theoretical aspects and understanding of key concepts are examined with short questions. Problem-solving abilities and the ability to apply machine learning algorithms are tested with simple numerical problems and pseudo-code type problems. So the students’ ability to compare and evaluate different methods in terms of their area of application, advantages/disadvantages, limitations, etc. are examined.