Webrelaunch 2020

Deep neural network approximations for high dimensional Kolmogorov PDEs

  • Speaker: JProf. Dr. Diyora Salimova
  • Place: 1.067
  • Time: 16.5.2024, 14:00
  • Invited by: Prof. Dr. Dorothee Frey

Abstract

Most of the numerical approximation methods for PDEs in the scientific literature suffer from the so-called curse of dimensionality (CoD) in the sense that the number of computational operations and/or the number of parameters employed in the corresponding approximation scheme grows exponentially in the PDE dimension and/or the reciprocal of the desired approximation precision. In the recent years certain deep learning-based approximation methods for PDEs have been proposed and various numerical simulations for such methods suggest that they might have the capacity to indeed overcome the CoD in the sense that the number of real parameters used to describe the approximating neural networks grows at most polynomially in both the PDE dimension and the reciprocal of the prescribed approximation accuracy. In this talk I will show some theoretical results which state that this is indeed the case for suitable Kolmogorov PDEs.