A deep learning method for solving Fokker-Planck equations

被引:0
|
作者
Zhai, Jiayu [1 ]
Dobson, Matthew [1 ]
Li, Yao [1 ]
机构
[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01002 USA
来源
MATHEMATICAL AND SCIENTIFIC MACHINE LEARNING, VOL 145 | 2021年 / 145卷
关键词
Stochastic differential equation; Monte Carlo simulation; invariant measure; coupling method; data-driven and machine learning methods; APPROXIMATION; ALGORITHMS;
D O I
暂无
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
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 Li (2019), 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 demand of data in the training process. Several high dimensional numerical examples are demonstrated.
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页码:568 / 597
页数:30
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