Score-based transport modeling for mean-field Fokker-Planck equations

• Published in: Journal of computational physics Vol. 503; p. 112859
• Main Authors: Lu, Jianfeng, Wu, Yue, Xiang, Yang
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.04.2024
• Subjects: Fokker-Planck equation; Mean field interaction; Scored-based modeling; Mean field interaction; Scored-based modeling; Fokker-Planck equation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2024.112859

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 three 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. •Propose a score-based transport modeling, MSBTM, for solving mean-field Fokker-Planck equations.•The MSBTM algorithm is efficient for simulations of interacting particle systems.•Establish an upper bound on time derivative of the KL divergence to MSBTM solution from the exact one.•Perform error analysis of the MSBTM algorithm.•The MSBTM algorithm is numerically validated through comparison with results of the associated SDEs and analytical solutions.