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arXiv · 2503.15125

A Spectral Approach to Optimal Control of the Fokker-Planck Equation

Dante Kalise·Lucas M. Moschen·Grigorios A. Pavliotis·Urbain Vaes
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Abstract

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 the 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.

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Dante Kalise, Lucas M. Moschen, Grigorios A. Pavliotis, Urbain Vaes. 2025-03-19. A Spectral Approach to Optimal Control of the Fokker-Planck Equation. https://doi.org/10.1109/lcsys.2025.3573604

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