Topics in Stochastic Processes and Machine Learning

Summer semester 2026, Free University Berlin

General information

Topics

• Basic of stochastic processes:
  Langevin dynamics, generators, Ito's formula, Fokker-Planck equation,
  Markov chains, convergence to equilibrium,
  Markov state modeling, variational approach
• Machine learning techniques for stochastic dynamics:
  regression, classification,
  stochastic gradient descent,
  clustering, dimensionality reduction techniques,
  solving eigenvalue problems by deep learning,
  generative modeling,
  convolution neural networks, residual networks, transformers

Plan of lectures

Lecture notes and slides are provided on the university's whiteboard system.

Jupytor notebooks for practice sessions

References

Theory of stochastic processes:

1. Bernt Øksendal. Stochastic Differential Equations: An Introduction with Applications. 5th. Springer, 2000. book
2. G.A. Pavliotis. Stochastic Processes and Applications: Diffusion Processes, the Fokker--Planck and Langevin Equations, Springer, 2014. book
3. G.A. Pavliotis and A.M. Stuart. Multiscale Methods: Averaging and Homogenization, Springer, 2008. book
4. J.-H. Prinz et al. Markov models of molecular kinetics: Generation and validation. J. Chem. Phys. 134.17, 174105 (2011), p. 174105 doi

Machine learning:

1. Kevin P. Murphy. Probabilistic Machine Learning: An introduction. MIT Press, 2022. url: probml.ai. book
2. Yang Song et al. Score-Based Generative Modeling through Stochastic Differential Equations, ICLR 2021. arxiv Song's blog
3. Xingchao Liu, Chengyue Gong and Qiang Liu. Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow, ICLR 2023. arxiv
4. Michael S. Albergo and Eric Vanden-Eijnden. Building Normalizing Flows with Stochastic Interpolants, ICLR 2023. arxiv
5. Jonathan Ho, Ajay Jain and Pieter Abbeel. Denoising Diffusion Probabilistic Models, NeurIPS 2020. link
6. George Papamakarios et al. Normalizing Flows for Probabilistic Modeling and Inference, Journal of Machine Learning Research 22 (2021) 1-64. pdf
7. Kaiming He et al. Deep Residual Learning for Image Recognition, arxiv
8. Ashish Vaswani et al. Attention Is All You Need, arxiv