Control of Fokker-Plack equation

In this paper, we present a spectral optimal control framework for Fokker-Planck equations based on the standard ground state transformation that maps the Fokker-Planck operator to a Schrodinger operator. Our primary objective is to accelerate convergence toward the (unique) steady state. To fulfill this objective, a gradient-based iterative algorithm with Pontryagin’s maximum principle and Barzilai-Borwein update is developed to compute time-dependent controls. Numerical experiments on two-dimensional ill-conditioned normal distributions and double-well potentials demonstrate that our approach effectively targets slow-decaying modes, thus increasing the spectral gap.

Check the preprint here: https://arxiv.org/abs/2503.15125.