A score-based particle method for homogeneous Landau equation

arXiv:2405.05187v1 Announce Type: cross
Abstract: We propose a novel score-based particle method for solving the Landau equation in plasmas, that seamlessly integrates learning with structure-preserving particle methods [arXiv:1910.03080]. Building upon the Lagrangian viewpoint of the Landau equation, a central challenge stems from the nonlinear dependence of the velocity field on the density. Our primary innovation lies in recognizing that this nonlinearity is in the form of the score function, which can be approximated dynamically via techniques from score-matching. The resulting …

abstract arxiv building challenge cs.lg cs.na equation math.na novel particle type