From molecular dynamics to kinetic models: data-driven generalized collision operators in 1D3V plasmas

TL;DR

This paper introduces a data-driven kinetic model for 1D3V plasmas that learns from molecular dynamics, capturing complex collisional effects more accurately than traditional models.

Contribution

It develops a novel anisotropic, non-stationary collision operator learned from MD data, with efficient computation and strict conservation properties.

Findings

Accurately predicts transport coefficients and kinetic processes.

Maintains conservation laws and physical constraints.

Works across a broad range of plasma conditions.

Abstract

We present a data-driven approach for constructing generalized collisional kinetic models for inhomogeneous plasmas in one-dimensional physical space and three-dimensional velocity space (1D-3V). The collision operator is directly learned from micro-scale molecular dynamics (MD) and accurately accounts for the unresolved particle interactions over a broad range of plasma conditions. Unlike the standard Landau operator, the present operator takes an anisotropic, non-stationary form that captures the heterogeneous collisional energy transfer arising from the many-body interactions, which is crucial for plasma kinetics beyond the weakly coupled regime. Efficient numerical evaluation is achieved through a low-rank tensor representation with $O(N \log N)$ computational complexity. The constructed kinetic equation strictly preserves conservation laws and physical constraints and therefore, enables us to develop an explicit second-order, energy-conserving scheme that ensures fully discrete conservation of mass and total energy. Numerical results demonstrate that the present model accurately predicts both transport coefficients and several 1D-3V kinetic processes compared with MD simulations across a broad range of densities and temperatures in spatially inhomogeneous settings. This work provides a systematic pathway for bridging micro-scale MD and inhomogeneous plasma kinetic descriptions where empirical models show limitation.