Sparse and low-rank kinetic distribution estimation

arXiv (Cornell University)

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.

Authors 5

1. Georgii Oblapenko Aachen Applied and Computational Mathematics

   RWTH Aachen University

   Affiliation as printed

   Applied and Computational Mathematics , RWTH Aachen , Schinkelstraße 2 , Aachen , 52062 , Germany

2. Lambert Theisen Aachen Applied and Computational Mathematics

   RWTH Aachen University

   Affiliation as printed

   Applied and Computational Mathematics , RWTH Aachen , Schinkelstraße 2 , Aachen , 52062 , Germany

3. Rostislav‐Paul Wilhelm

   KU Leuven

   Affiliation as printed

   Centre for mathematical Plasma Astrophysics , KU Leuven , Celestijnenlaan 200b , Leuven , 3001 , Belgium

4. Michael Herty Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und praktische Mathematik , RWTH Aachen , Templergraben 55 , Aachen , 52062 , Germany

5. Manuel Torrilhon Aachen Applied and Computational Mathematics

   RWTH Aachen University

   Affiliation as printed

   Applied and Computational Mathematics , RWTH Aachen , Schinkelstraße 2 , Aachen , 52062 , Germany