| Abstract: |
| We introduce a data-driven approach to learn generalized collision operators from molecular dynamics. Unlike conventional models (e.g., Landau), the present operator takes a symmetry-breaking non-stationary form that depends not only on the relative velocity but also on the average velocity of the collision pair, capturing heterogeneous energy transfer arising from collective interactions with the environment. The constructed model strictly preserves the frame-indifference, conservation laws, and physical constraints such as the H-theorem. 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 and structure-preserving discretization. Numerical results 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. |
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