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.

翻译：我们提出一种通用的、数据驱动的单组分等离子体碰撞算子，该算子基于分子动力学模拟学习得到，旨在将动理学碰撞模型拓展至弱耦合区域之外。该算子具有各向异性非定常碰撞核，能够计入经典Landau公式中通常忽略的粒子关联效应。为高效实现数值计算，我们发展了一种快速谱分离方法，将碰撞核表示为单变量基函数的低秩张量积形式。该公式通过快速傅里叶变换实现O(N log N)算法，并通过保持结构的中心差分离散化方法，保留了关键物理性质，包括离散守恒律和H定理。数值实验表明，所提模型在标准Landau模型之外的适度耦合区域中能准确捕捉等离子体动力学行为，同时保持高计算效率与结构保持特性。