Young Researchers Workshop: Kinetic descriptions in theory and applications

Low rankness in forward and inverse kinetic theory

Qin Li

University of Wisconsin-Madison

Multi-scale kinetic equations can be compressed: in certain regimes, the Boltzmann equation is close to the Euler, and the radiative transfer equation is close to the diffusion equation. While passing to the limits, a lot of detailed information is lost. In linear algebra language it is equivalent to low-rankness. I will discuss such transition and how it affects the computation: mainly, it greatly advances the forward solvers, but the inverse problem is significantly harder. I invite discussions and suggestions.