Computational Mean-field information dynamics associated with Reaction diffusion equations
arXiv:2107.11501 · doi:10.1016/j.jcp.2022.111409
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.
arXiv comment38 pages
References in corpus (11)
- Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm
- Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures
- A new class of transport distances
- Cahn-Hilliard and Thin Film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics
- Unnormalized Optimal Transport
- A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility
- Transport information geometry I: Riemannian calculus on probability simplex
- Modeling of chemical reaction systems with detailed balance using gradient structures
- A JKO splitting scheme for Kantorovich-Fisher-Rao gradient flows
- Generalized Unnormalized Optimal Transport and its fast algorithms
- Hessian metric via transport information geometry