Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Yue Zhao, Guosheng Fu, Huan Lei

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.

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

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 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.

Paper Structure

This paper contains 17 sections, 3 theorems, 58 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Inhomogeneous metriplectic collision operator
  4. Data-driven construction from molecular dynamics
  5. Numerical scheme
  6. Advection
  7. Collision
  8. Numerical results
  9. Summary
  10. Momentum conservation numerical scheme
  11. Mass conservation
  12. Momentum conservation
  13. Energy change
  14. Properties and construction of the inhomogeneous collision kernel
  15. Comparison with homogeneous kernel
  16. ...and 2 more sections

Key Result

Proposition 1

The Ampère solver iteratively updates the electric field $E^{n}$ instead of recalculating it from the density distribution, which ensures the conservation of total energy $\mathcal{E}$.

Figures (8)

  • Figure 1: Comparison of the diffusion and viscosity coefficients predicted from MD, Landau equation and DDCO models under different temperatures $T_0$ and densities $\rho = m_0 n$ with number density $n_{1}=10^{21}~{\rm m}^{-3}$ and $n_{2}=10^{24}~{\rm m}^{-3}$.
  • Figure 2: Comparison of the instantaneous velocity distribution on the $v_x$-$v_y$ plane at $t=0.4~t_{0}$ (up) and $0.8~t_{0}$ (bottom) with the initial symmetric double-well distribution. "DDCO" represents our model with the data-driven collision operator.
  • Figure 3: Comparison of the instantaneous velocity distribution on the $v_x$-$v_y$ plane at $t=0.4~t_{0}$ (up) and $0.8~t_{0}$ (bottom) with the initial asymmetric double-well distribution.
  • Figure 4: Comparison of the instantaneous velocity distribution on the $x$-$v_{x}$ plane at $t=0.4~t_{0}$ (left) and $0.6~t_{0}$ (right) with the initial symmetric double-well distribution.
  • Figure 5: Comparison of the instantaneous velocity distribution on the $x$-$v_{x}$ plane at $t=0.4~t_{0}$ (left) and $0.6~t_{0}$ (right) with the initial asymmetric double-well distribution.
  • ...and 3 more figures

Theorems & Definitions (7)

  • Proposition 1
  • proof
  • Remark 1
  • Proposition 2
  • proof
  • Proposition 3
  • proof