A Spectral Approach to Optimal Control of the Fokker-Planck Equation
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910970224312320 |
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| author | Kalise, Dante Moschen, Lucas M. Pavliotis, Grigorios A. Vaes, Urbain |
| author_facet | Kalise, Dante Moschen, Lucas M. Pavliotis, Grigorios A. Vaes, Urbain |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_15125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Spectral Approach to Optimal Control of the Fokker-Planck Equation Kalise, Dante Moschen, Lucas M. Pavliotis, Grigorios A. Vaes, Urbain Optimization and Control Numerical Analysis 49M41, 35Q84, 65M70 G.1.6; G.1.8 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. |
| title | A Spectral Approach to Optimal Control of the Fokker-Planck Equation |
| topic | Optimization and Control Numerical Analysis 49M41, 35Q84, 65M70 G.1.6; G.1.8 |
| url | https://arxiv.org/abs/2503.15125 |