计算与应用讨论班

报告题目：From Micro-physics to Stable Macro-models: Variational Learning for Collisional Kinetic Equations

报告人：雷欢( Michigan State University )

时  间：2026年7月3日（星期五），上午10:30-12:00

地  点：海纳苑2幢203

摘  要：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 preserve the    frame-indifference, conservation laws, and physical constraints such as 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. If time permitted, I will discuss a second example on variational learning of non-Newtonian hydrodynamic model from micro-model.

报告人简介：Dr. Huan Lei got his Ph.D. in applied mathematics at Brown University. Prior to that, he obtained his B.S. from University of Science and Technology of China. He is currently an associate professor in the Department of Computational Mathematics, Science and Engineering at Michigan State University. His research mainly focuses on developing physics interpretable and structure preserving machine-learning methods for computational modeling of multiscale problems. He is the recipient of the National Science Foundation (NSF) CAREER award.