  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.
