  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. The performance of our
method shows promising results, with more accurate and less fluctuating
statistics compared to direct stochastic simulations of comparable particle
number. Taken together, our framework allows for effortless and reliable
particle-based simulations of Fokker-Planck equations in low and moderate
dimensions. The proposed gradient-log-density estimator is also of independent
interest, for example, in the context of optimal control.
