After successful completion of the course, students are able to intimately understand the "tool" of machine learning and its application to problems in physics.

For a given problem in physics, they will be able to:

• analyze whether Machine Learning is applicable,
• translate the problem into a suitable optimization problem,
• decide which learning algorithm to employ for its solution,
• program simple routines themselves as well as use libraries where applicable, and
• understand and verify the results of the learning procedure.

We will cover the following topics in the lectures:

1. Simple optimization problems, gradient descent
2. Supervised learning, over-/underfitting, regularization
3. Linear model, singular value decomposition
4. Non-linear models, classification problems
5. Artificial neural networks
6. Unsupervised learning, clustering
7. Low-rank decompositions, principal component analysis

In the exercises, you will then apply these methods to problems from physics, e.g.:

• temperature deblurring of spectral functions
• classification of proton collisions in the LHC
• recognizing magnetic phases in the Ising model

The course is made up of about 12 weeks, each consisting of:

• Lecture, where we will introduce the theoretical concepts behind machine learning.  At your option, you can either follow the live lecture or watch the lecture videos totalling around 75 minutes per week.
• Programming exercise, where you are required to apply the material to physics problem.  You can solve and are to hand in the exercise notebooks online via JupyterHub.
• Q&A and discussion session, during which we will discuss the current exercise, previous exercise, and lecture materials, followed by work in groups.

The course starts with a crash course into the Python programming language, which we will then use throughout the semester.

Institutsweite Vorbesprechung für Wahlpflichlehre: Dienstag, 01.03.2022, 16.00-18.00 Uhr, FH 8 Nöbauer HS

Due to the current volatility of the epidemiological situation, the teaching methods may have to be slightly altered.  In particular:

• hybrid online/presence sessions may have to be replaced by online sessions
• instead of a written exam, there may be an oral exam via Zoom

With the possible exception of the exam, full distance learning is possible for this course in any case.

Requirements for this class are:

1. weekly coding exercises, where you will appliy ML concepts to simple problems. Each exercise has equal weight (70 per cent of the grade).
2. a short written exam, where you will have to demonstrate that you understood the concepts (30 per cent of the grade).

Attendance at the weekly Q&A sessions is strongly recommended, but not required.

Grading scheme:  "Genügend" requires above 50, "Befriedigend" requires 65, "Gut" requires 80, "Sehr gut" requires 91 per cent of points.  No further point cutoffs.

There is a substitute exam.  If you choose to partake in the substitute exam, it will replace the marks of your exam.

Further reading:

• M. P. Deisenroth, A. A. Faisal, and Cheng Soon Ong: Mathematics for Machine Learning, Cambridge University Press (2020)
• T. Hastie, R. Tibshirani, and J. Friedman: Elements of Statistical Learning, 2nd edition, Springer (2017).
• P. Mehta et. al: A high-bias, low-variance introduction to Machine Learning for physicists, Phys. Rep. 810, 1-124 (2019)
• G. James, D. Witten, T. Hastie and R. Tibshirani: An Introduction to Statistical Learning, Springer (2010)
• P. C. Hansen: Discrete Inverse Problems, SIAM (2010)

• Linear algebra: vector spaces, inner products, matrix products, linear equations, vector and matrix norms, eigendecomposition
• Basic coding skills: basic language constructs, loops, I/O, functions, arrays
• (Recommended: intro quantum theory)