Low rankness in forward and inverse kinetic theory
Multi-scale kinetic equations can be compressed: in certain regimes, the Boltzmann equation is asymptotically equivalent to the Euler equations, and the radiative transfer equation is asymptotically equivalent to the diffusion equation. A lot of detailed information is lost when the system passes to the limit. In linear algebra, it is equivalent to being of low rank. I will discuss such transition and how it affects the computation: mainly, in the forward regime, inserting low-rankness could greatly advances the computation, while in the inverse regime, the system being of low rank typically makes the problems significantly harder.