A deep learning method for solving Fokker-Planck equations
Numerical Analysis
2020-12-22 v1 Numerical Analysis
Abstract
The time evolution of the probability distribution of a stochastic differential equation follows the Fokker-Planck equation, which usually has an unbounded, high-dimensional domain. Inspired by our early study in \cite{li2018data}, we propose a mesh-free Fokker-Planck solver, in which the solution to the Fokker-Planck equation is now represented by a neural network. The presence of the differential operator in the loss function improves the accuracy of the neural network representation and reduces the the demand of data in the training process. Several high dimensional numerical examples are demonstrated.
Cite
@article{arxiv.2012.10696,
title = {A deep learning method for solving Fokker-Planck equations},
author = {Jiayu Zhai and Matthew Dobson and Yao Li},
journal= {arXiv preprint arXiv:2012.10696},
year = {2020}
}