Computational mean-field information dynamics associated with reaction-diffusion equations

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 co...

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Bibliographic Details
Published in:Journal of computational physics Vol. 466; p. 111409
Main Authors: Li, Wuchen, Lee, Wonjun, Osher, Stanley
Format: Journal Article
Language:English
Published: Cambridge Elsevier Science Ltd 01.10.2022
Subjects:
Algorithms
Computational physics
Diffusion
Entropy of reaction
Gradient flow
Reaction-diffusion equations
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary: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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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2022.111409