Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation

Understand

Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions.

• Although broadly used, they allow for analytical treatment only in limited settings, and often is inevitable to resort to numerical solutions.
• Here, we develop a computational approach for simulating the time evolution of Fokker-Planck solutions in terms of a mean field limit of an interacting particle system.
• The interactions between particles are determined by the gradient of the logarithm of the particle density, approximated here by a novel statistical estimator.