Score-based Transport Modeling for Mean-Field Fokker-Planck Equations
This work addresses computational challenges in modeling interacting particle systems, but it appears incremental as it applies an existing score-based method to a specific class of equations.
The paper tackled solving mean-field Fokker-Planck equations using a score-based transport modeling method (MSBTM), establishing an upper bound on the KL divergence time derivative and validating the approach through numerical experiments with qualitative and quantitative comparisons.
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.