发表机构
Michigan State University（密歇根州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究从分子动力学出发，构建保结构的多物种碰撞算子，推导其可容许条件，通过低秩张量表示学习广义数据驱动算子，实验显示其能准确预测输运系数并捕捉中等耦合区等离子体动力学。
AI 中文摘要
我们从分子动力学（MD）出发，为空间均匀的多物种动力学系统构建了一种保结构、数据驱动的碰撞算子。该算子由对角自碰撞块与有序非对角跨物种块组成，用于描述物种内部及物种间的动量与能量交换。在局部且逐点可识别的核类中，我们推导了可容许核类满足守恒律、H定理及框架无差别的充要条件。与经典朗道（Landau）算子不同，非对角核不受限于两个速度变量置换下的对称性，这种独特的结构自由度可捕捉不同物种对未 resolves 的关联及微观粒子相互作用产生的多体效应的不同响应。等价的可参数化核形式使我们能直接从MD学习广义数据驱动碰撞算子，其中低秩张量表示与随机采样用于实现高效的核训练与数值模拟。数值实验表明，学习得到的算子能准确预测输运系数与非平衡弛豫，同时保持离散守恒与熵产生，尤其能捕捉中等耦合区的等离子体动力学，而朗道算子及受限于速度置换对称性的数据驱动模型的预测则存在显著偏差。
英文摘要
We develop a structure-preserving, data-driven collision operator for spatially homogeneous multi-species kinetic systems from molecular dynamics (MD). The operator consists of diagonal self-collision blocks and ordered off-diagonal cross-species blocks to describe intra- and inter-species momentum and energy exchange. Within a local and point-wise identifiable kernel class, we develop the necessary and sufficient condition for the admissible kernel class satisfying the conservation laws, the H-theorem, and the frame indifference. Unlike the classical Landau operator, the off-diagonal kernels are not restricted to be symmetric under permutation of the two velocity variables. This unique structural freedom captures the distinct responses of different species to unresolved correlations and many-body effects arising from micro-scale particle interactions. The equivalent parameterizable kernel formalization enables us to learn a generalized data-driven collision operator directly from MD, where the low-rank tensor representations and random sampling are used to achieve efficient kernel training and numerical simulation. Numerical experiments show that the learned operator accurately predicts transport coefficients and the non-equilibrium relaxation, while retaining discrete conservation and entropy production. In particular, it captures plasma kinetics in the moderately coupled regime, where the predictions of both the Landau and the data-driven model restricted to velocity-permutation symmetry show significant discrepancies.
