Computational Mean-field information dynamics associated with Reaction diffusion equations

Wuchen Li; Wonjun Lee; Stanley Osher

doi:10.1016/j.jcp.2022.111409

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arXiv · 2107.11501

Computational Mean-field information dynamics associated with Reaction diffusion equations

Wuchen Li·Wonjun Lee·Stanley Osher

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Abstract

We formulate and compute a class of mean-field information dynamics for reaction-diffusion equations. Given a class of nonlinear reaction-diffusion equations and entropy type Lyapunov functionals, we study their gradient flows formulations with generalized optimal transport metrics and mean-field control problems. We apply the primal-dual hybrid gradient algorithm to compute the mean-field control problems with potential energies. A byproduct of the proposed method contains a new and efficient variational scheme for solving implicit in time schemes of mean-field control problems. Several numerical examples demonstrate the solutions of mean-field control problems.

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BibTeX RIS

Wuchen Li, Wonjun Lee, Stanley Osher. 2021-07-24. Computational Mean-field information dynamics associated with Reaction diffusion equations. https://doi.org/10.1016/j.jcp.2022.111409

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