Structure-Preserving Learning of Kinetic Collision Operators from Molecular Dynamics

Data Science Seminar

Huan Lei
Michigan State University

Abstract

We develop a structure-preserving, data-driven framework for constructing generalized collision operators for kinetic equations directly from molecular dynamics simulations. Within a pairwise quadratic dissipative framework, we establish necessary and sufficient conditions for admissible collision kernels that preserve frame indifference, conservation of mass, momentum, and energy, and the H-theorem. These conditions lead to an equivalent parameterization of anisotropic, non-stationary collision kernels that extends the classical Landau operator while preserving the underlying variational structure. The kernel is represented by a low-rank spectral separation that admits an O(N log N) computational complexity and structure-preserving discretization, and can be efficiently learned from microscopic MD data in a weak-form formulation with a random batch sampling method. Numerical results demonstrate the accuracy and computational efficiency of the constructed collision operator in predicting non-equilibrium plasma kinetics in the moderately coupled regime, where classical collision models show limitations.