We propose a particle method for numerically solving the Landau equation, inspired by the score-based transport modeling (SBTM) method for the Fokker-Planck equation. This method can preserve some important physical properties of the Landau equation, such as the conservation of mass, momentum, and energy, and decay of estimated entropy. We prove that matching the gradient of the logarithm of the approximate solution is enough to recover the true solution to the Landau equation with Maxwellian molecules. Several numerical experiments in low and moderately high dimensions are performed, with particular emphasis on comparing the proposed method with the traditional particle or blob method.

翻译：受Fokker-Planck方程的基于分数传输建模（SBTM）方法启发，我们提出了一种数值求解Landau方程的粒子方法。该方法能够保持Landau方程的一些重要物理性质，例如质量、动量和能量的守恒，以及估计熵的衰减。我们证明，匹配近似解对数梯度的条件足以恢复具有麦克斯韦分子的Landau方程的真实解。在低维和中等高维条件下进行了多项数值实验，重点比较了所提方法与传统的粒子或团块方法。