Title

Kinetic equations and high-dimensional scientific computing

Abstract

In this talk, I will overview kinetic equations, which are fundamental models in mathematical physics. The understanding and numerical simulations of kinetic equations are critical for the understanding of nuclear fusion and many other important areas. 

Deterministic simulations of kinetic models are challenging due to the high dimensionality of the model. In the second part of the talk, I will give an overview of some efforts in high-dimensional scientific computing, touching upon techniques in sparse grid, low-rank and machine learning. Those techniques are essential in modern scientific computing to tackle curse of dimensions in challenging physic simulations of various kinds.