# Computational Mean-field information dynamics associated with Reaction diffusion equations

arXiv: https://arxiv.org/abs/2107.11501 · HTML: https://mlsanity.com/paper/2107.11501/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2021.

## Built on by (most cited first, 1 of 1)

- [A deep learning framework for geodesics under spherical Wasserstein-Fisher-Rao metric and its application for weighted sample generation](https://mlsanity.com/paper/2208.12145/) (2022)

## Abstract (arXiv)

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.