Course Material

Charalambos Makridakis: Approximations of Nonlinear Problems: Adaptive Algorithms and Analysis

  • Slides and papers are available here
Grigorios Pavliotis: Sampling from probability measures using stochastic differential equations
  • Lecture 1: Stochastic differential equations and the backward and forward Kolmogorov equations
  • Lecture 2: Ergodic properties of SDEs and SDE-based sampling schemes for sampling from high dimensional distributions.
  • Lecture 3: Numerical methods for SDEs, long time behaviour of numerical schemes.
  • Lecture 4: Optimal SDE-based samplers.

Daniel Peterseim: Numerical homogenization beyond periodicity and scale separation

  • Lecture notes: PDF
  • Tutorials offered by Roland Maier
Evangelia Kalligiannaki: Indirect inference for probabilistic wind power forecast models with Itô stochastic differential equations
  • Abstract: PDF
Konstantinos Spiliopoulos: Stochastic gradient descent in continuous time and deep learning for PDEs
  • Abstract: PDF