FBSDE based neural network algorithms for high-dimensional quasilinear parabolic PDEs

DOI10.1016/J.JCP.2022.111557OpenAlexW3110941460WikidataQ114163188 ScholiaQ114163188MaRDI QIDQ2083635

Wei Cai, Wenzhong Zhang

Publication date: 11 October 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.07924

zbMATH Keywords

quasilinear parabolic equationsFeynman-Kac formulaforward and backward SDEsmulti-scale deep neural networkPardoux-Peng theory

Mathematics Subject Classification ID

Stochastic analysis (60Hxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Partial differential equations of mathematical physics and other areas of application (35Qxx)

Related Items (1)

Linearized Learning with Multiscale Deep Neural Networks for Stationary Navier-Stokes Equations with Oscillatory Solutions

Cites Work

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• Convergence of the deep BSDE method for coupled FBSDEs
• An Introduction to Deep Reinforcement Learning
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• Solving high-dimensional partial differential equations using deep learning
• Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
• Multiscale Methods
• Stochastic differential equations. An introduction with applications.

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