Summer semester 2025

Course at FUB: Mathematical strategies for complex stochastic dynamics

Information:

• Lectures

  Location:	T9/053 Seminarraum (Takustr. 9)
  Schedule:	Wednesday from 14:00-16:00
  Class starts on:	2025-04-23
  FU link:	19234501

• Practice courses

  Location:	T9/046 Seminarraum (Takustr. 9)
  Schedule:	Friday from 10:00-12:00
  Class starts on:	2025-04-25
  FU link:	19234502

Contents:

• Basic of stochastic processes
  • Langevin dynamics, Markov chains, generators, Fokker-Planck equation,
    convergence to equilibrium, Ito's formula
• Model reduction for stochastic dynamics
  • averaging technique, effective dynamics, Markov state modeling
• Machine learning techniques for stochastic dynamics
  • stochastic gradient descent, autoencoders, PDE eigenvalue problems by deep learning,
    diffusion models, continuous normalizing flow, flow-matching

Course Material:

• Exercises
• April 23, 2025
  introduction slides, lecture_01 on ODEs and Gaussian variables
• April 25, 2025
  notebook 01 on solving ODEs and random variable generation
• April 30, 2025
  slides_02 and lecture_02 on Ito integral, Ito's lemma, and Fokker-Planck equation
• May 02, 2025
  notebook 02-1, notebook 02-2, and notebook 02-3 on Python, numpy, matplotlib tutorials
• May 07, 2025
  slides_03 and lecture_03 on Feynman-Kac, invariant distribution, Brownian and Langevin dynamics
  slides_03-DL on a short introduction to machine/deep learning
• May 09, 2025
  notebook 03-1, notebook 03-2, and notebook 03-3 on simulating SDEs, PyTorch tensor and PyTorch autodiff
• May 14, 2025
  lecture_04 on eigenvalues, convergence to equilibrium, and Markov chains
• May 16, 2025
  notebook 04-1, notebook 04-2 on feedforward neural networks and MNINST dataset
• May 21, 2025
  lecture_05 on Markov state models and variational principle
  slides_05 on PyTorch tutorial