Wei Zhang's homepage

Summer semester 2025

Course at FUB: Mathematical strategies for complex stochastic dynamics

General 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 materials

Date	Notes & Slides	Topics
April 23, 2025	lecture_01, introduction slides	ODEs and Gaussian variables
April 30, 2025	lecture_02, slides_02	Ito integral, Ito's lemma, and Fokker-Planck equation
May 07, 2025	1. lecture_03, slides_03 2. slides_03-DL	1. Feynman-Kac, invariant distribution, Brownian and Langevin dynamics; 2. short introduction to ML/DL
May 14, 2025	lecture_04	eigenvalues, convergence to equilibrium, and Markov chains
May 21, 2025	1. lecture_05 2. slides_05	1. Markov state models and variational principle 2. PyTorch tutorial
May 28, 2025	lecture_06, slides_06	score-based diffusion models
June 11, 2025	lecture_07, slides_07	Dirac delta function, conditional expectation, flow-based generative models