Score-based Transport Modeling for Mean-Field Fokker-Planck Equations. (arXiv:2305.03729v1 [math.NA])

We use the score-based transport modeling method to solve the mean-field
Fokker-Planck equations, which we call MSBTM. We establish an upper bound on
the time derivative of the Kullback-Leibler (KL) divergence to MSBTM numerical
estimation from the exact solution, thus validates the MSBTM approach. Besides,
we provide an error analysis for the algorithm. In numerical experiments, we
study two types of mean-field Fokker-Planck equation and their corresponding
dynamics of particles in interacting systems. The MSBTM algorithm is
numerically validated through qualitative and quantitative comparison between
the MSBTM solutions, the results of integrating the associated stochastic
differential equation and the analytical solutions if available.