Extensions of the deep Galerkin method
作者：
Highlights：
• An extension of the deep Galerkin method (DGM) to solve Fokker–Planck PDEs keeping the probability density constraints automatically satisfied.
• A novel application of the policy iteration algorithm (PIA) together with the DGM to solve HJB equations.
• Additional applications to system of coupled HJB equations (arising from stochastic games) and mean-field Game system of PDE (coupled HJB and Fokker Planck).
• Both extensions are applicable to multidimensional PDEs.
摘要
•An extension of the deep Galerkin method (DGM) to solve Fokker–Planck PDEs keeping the probability density constraints automatically satisfied.•A novel application of the policy iteration algorithm (PIA) together with the DGM to solve HJB equations.•Additional applications to system of coupled HJB equations (arising from stochastic games) and mean-field Game system of PDE (coupled HJB and Fokker Planck).•Both extensions are applicable to multidimensional PDEs.
论文关键词：Partial differential equations,Stochastic control,Hamilton–Jacobi–Bellman equations,Deep Galerkin method,Neural networks,Policy improvement
论文评审过程：Received 20 April 2021, Revised 21 May 2022, Accepted 24 May 2022, Available online 5 June 2022, Version of Record 5 June 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.127287
