An efficient data-driven solver for Fokker-Planck equations: algorithm and analysis
Numerical Analysis
2024-09-23 v1 Numerical Analysis
Dynamical Systems
Abstract
Computing the invariant probability measure of a randomly perturbed dynamical system usually means solving the stationary Fokker-Planck equation. This paper studies several key properties of a novel data-driven solver for low-dimensional Fokker-Planck equations proposed in [15]. Based on these results, we propose a new `block solver' for the stationary Fokker-Planck equation, which significantly improves the performance of the original algorithm. Some possible ways of reducing numerical artifacts caused by the block solver are discussed and tested with examples.
Cite
@article{arxiv.1906.02600,
title = {An efficient data-driven solver for Fokker-Planck equations: algorithm and analysis},
author = {Matthew Dobson and Yao Li and Jiayu Zhai},
journal= {arXiv preprint arXiv:1906.02600},
year = {2024}
}