Sparse and low-rank kinetic distribution estimation

Abstract

In this paper, we consider methods that allow for memory-efficient storage of high-dimensional distributions and retain certain key features thereof, specifically in a kinetic theory context. We propose an extension to the entropic quadrature method that allows for enforcing sparsity, and propose a new low-rank decomposition approach that ensures preservation of moment information. The methods are applied to several model kinetic distributions, as well as to distributions obtained from high-resolution kinetic simulations of the Vlasov--Maxwell system.