The course aims at two aspects of machine learning.
The first goal is an introduction to statistical mechanics of learning, which aims at describing the typical learning behavior of neural networks, discussion of the generalization performance of strongly overparametrized neural networks. Information field theoretic description of ultrawide neural networks. The second aim is to give an introduction to machine learning techniques and its applications in natural sciences. It will include fields of image recognition, time series analysis and reinforcement learning with examples and applications of neural networks in fluid mechanics.
- Knowledge of statistical mechanics
- Basic Knowledge of Linear Algebra
- Programming knowledge is of advantage
- Introduction to Machine Learning and Deep Learning Techniques
- Deep Learning Statistical Physics: Mapping of ultrawide neural networks to Gaussian processes, description of neural networks with the help of functional integrals
- Machine Learning Applications: Image Segmentation, Tracking and Feature Extraction with Convolutional Neural Networks
- Time Series Analysis with Recurrent Neural Networks
- Applications of Reinforcement Learning in Physics
- Machine Learning for Fluid Mechanics
- Theoretical methods of modern statistical mechanics
- Image Processing Methods
- Time Series Analysis Programming
- Statistical Mechanics of Learning, A. Engel and C. Van den Broeck, Cambridge University Press (2001).
- Theory Of Neural Information Processing Systems, Anthony C.C. Coolen, Peter Sollich, and Reimer Kühn, Oxford University Press (2009).
- Neural Networks and Deep Learning, Michael A. Nielsen, Determination Press (2015).
- Sutton, R. S. & Barto, A. G. Reinforcement Learning: An Introduction. MIT Press, Cambridge (1998).
- Deep Learning with Python. F. Chollet, Manning (2017).
- Neural Networks and Deep Learning: A Textbook. C. C. Agarwal, Springer (2018).
- Deep Learning. I. Goodfellow, Y. Bengio & A. Courville, MIT Press (2016).
- Brunton, S., Noack, B. & Koumoutsakos, P. Machine learning for fluid mechanics. arXiv preprint arXiv:1905.11075 (2019).
- Brunton, S. L., Proctor, J. L. & Kutz, J. N. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc National Acad Sci 113, 3932-3937 (2016).
- Cichos, F., Gustavsson, K., Mehlig, B. & Volpe, G. Machine learning for active matter. Nat Mach Intell 2, 94-103 (2020).
Date: Septermber 16-17, 2021 (9.30-16.00)
Exam: Written examination
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