Deep Kinetic JKO schemes for Vlasov-Fokker-Planck Equations
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| Format: | Preprint |
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2026
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| _version_ | 1866910070692904960 |
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| author | Lee, Wonjun Wang, Li Li, Wuchen |
| author_facet | Lee, Wonjun Wang, Li Li, Wuchen |
| contents | We introduce a deep neural network-based numerical method for solving kinetic Fokker Planck equations, including both linear and nonlinear cases. Building upon the conservative dissipative structure of Vlasov-type equations, we formulate a class of generalized minimizing movement schemes as iterative constrained minimization problems: the conservative part determines the constraint set, while the dissipative part defines the objective functional. This leads to an analog of the classical Jordan-Kinderlehrer-Otto (JKO) scheme for Wasserstein gradient flows, and we refer to it as the kinetic JKO scheme. To compute each step of the kinetic JKO iteration, we introduce a particle-based approximation in which the velocity field is parameterized by deep neural networks. The resulting algorithm can be interpreted as a kinetic-oriented neural differential equation that enables the representation of high-dimensional kinetic dynamics while preserving the essential variational and structural properties of the underlying PDE. We validate the method with extensive numerical experiments and demonstrate that the proposed kinetic JKO-neural ODE framework is effective for high-dimensional numerical simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_23901 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deep Kinetic JKO schemes for Vlasov-Fokker-Planck Equations Lee, Wonjun Wang, Li Li, Wuchen Numerical Analysis Mathematical Physics We introduce a deep neural network-based numerical method for solving kinetic Fokker Planck equations, including both linear and nonlinear cases. Building upon the conservative dissipative structure of Vlasov-type equations, we formulate a class of generalized minimizing movement schemes as iterative constrained minimization problems: the conservative part determines the constraint set, while the dissipative part defines the objective functional. This leads to an analog of the classical Jordan-Kinderlehrer-Otto (JKO) scheme for Wasserstein gradient flows, and we refer to it as the kinetic JKO scheme. To compute each step of the kinetic JKO iteration, we introduce a particle-based approximation in which the velocity field is parameterized by deep neural networks. The resulting algorithm can be interpreted as a kinetic-oriented neural differential equation that enables the representation of high-dimensional kinetic dynamics while preserving the essential variational and structural properties of the underlying PDE. We validate the method with extensive numerical experiments and demonstrate that the proposed kinetic JKO-neural ODE framework is effective for high-dimensional numerical simulations. |
| title | Deep Kinetic JKO schemes for Vlasov-Fokker-Planck Equations |
| topic | Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2603.23901 |