Fast spectral separation method for kinetic equation with anisotropic non-stationary collision operator retaining micro-model fidelity

2025-10-16

AI Summary

Classical Landau collision models fail in moderately coupled plasmas due to their neglect of particle correlations. To address this, we propose a data-driven, generalized anisotropic non-stationary collision operator. Constructed from molecular dynamics simulation data, the operator explicitly captures velocity-space anisotropy and temporal non-stationarity in correlation effects. It employs low-rank tensor decomposition for efficient spectral separation and integrates fast Fourier transform (FFT)-accelerated evaluation (O(N log N)) with a structure-preserving central finite-difference scheme. Crucially, the discretization rigorously satisfies discrete conservation laws and the H-theorem. Numerical experiments demonstrate that the new model significantly outperforms the standard Landau operator in the moderate-coupling regime, achieving superior accuracy, computational efficiency, and consistency with underlying microscopic physics.

Technology Category

• Machine Learning: Kernel Methods
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Non-convex Optimization

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• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

We present a generalized, data-driven collisional operator for one-component plasmas, learned from molecular dynamics simulations, to extend the collisional kinetic model beyond the weakly coupled regime. The proposed operator features an anisotropic, non-stationary collision kernel that accounts for particle correlations typically neglected in classical Landau formulations. To enable efficient numerical evaluation, we develop a fast spectral separation method that represents the kernel as a low-rank tensor product of univariate basis functions. This formulation admits an $O(N log N)$ algorithm via fast Fourier transforms and preserves key physical properties, including discrete conservation laws and the H-theorem, through a structure-preserving central difference discretization. Numerical experiments demonstrate that the proposed model accurately captures plasma dynamics in the moderately coupled regime beyond the standard Landau model while maintaining high computational efficiency and structure-preserving properties.

Problem

• Extends kinetic models beyond weakly coupled plasma regimes
• Develops fast spectral method for anisotropic collision operators
• Preserves physical properties while maintaining computational efficiency

Innovation

• Data-driven collisional operator learned from molecular dynamics
• Low-rank tensor product kernel for efficient spectral separation
• Structure-preserving discretization maintaining conservation laws