Sponsor
G. Fu's work is supported by NSF grant DMS-2012031. S. Osher's work is supported in part by AFOSR MURI FP 9550-18-1-502 and ONR grants: N00014-20-1-2093 and N00014-20-1-2787. W. Pazner acknowledges the support of NSF RTG DMS-2136228. W. Li's work is supported by AFOSR MURI FP 9550-18-1-502, AFOSR YIP award No. FA9550-23-1-0087, NSF DMS-2245097, and NSF RTG: 2038080.
Published In
Journal of Computational Physics
Document Type
Pre-Print
Publication Date
7-1-2024
Subjects
Computer science -- reaction-diffusion systems
Abstract
We design and compute a class of optimal control problems for reaction-diffusion systems. They form mean field control problems related to multi-density reaction-diffusion systems. To solve proposed optimal control problems numerically, we first apply high-order finite element methods to discretize the space-time domain and then solve the optimal control problem using augmented Lagrangian methods (ALG2). Numerical examples, including generalized optimal transport and mean field control problems between Gaussian distributions and image densities, demonstrate the effectiveness of the proposed modeling and computational methods for mean field control problems involving reaction-diffusion equations/systems.
Rights
© Copyright the author(s) 2024
Locate the Document
DOI
10.1016/j.jcp.2024.112994
Persistent Identifier
https://archives.pdx.edu/ds/psu/41971
Citation Details
Published as: Fu, G., Osher, S., Pazner, W., & Li, W. (2024). Generalized optimal transport and mean field control problems for reaction-diffusion systems with high-order finite element computation. Journal of Computational Physics, 508, 112994.
Description
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as: Generalized optimal transport and mean field control problems for reaction-diffusion systems with high-order finite element computation. Journal of Computational Physics, 508.