Title: Fast spectral separation method for kinetic equation with anisotropic non-stationary collision operator retaining micro-model fidelity Show Chinese title

Title: 用于各向异性非稳态碰撞算子的快速谱分离方法，保留微观模型保真度

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. Show Chinese abstract

Abstract: 我们提出了一种广义的、数据驱动的碰撞算子，用于单组分等离子体，该算子通过分子动力学模拟学习得到，以将碰撞动力学模型扩展到弱耦合区域之外。 所提出的算子具有各向异性、非平稳的碰撞核，能够考虑经典Landau公式中通常被忽略的粒子相关性。 为了实现高效的数值计算，我们开发了一种快速谱分离方法，将核表示为一元基函数的低秩张量积。 该公式通过快速傅里叶变换实现了$O(N \log N)$算法，并通过保持结构的中心差分离散化保留了关键的物理特性，包括离散守恒定律和H定理。 数值实验表明，所提出的模型在中等耦合区域准确捕捉了等离子体动力学，超越了标准Landau模型，同时保持了高计算效率和结构保持特性。