Three ways to solve partial differential equations with neural networks — A review

DOI10.1002/gamm.202100006zbMath1530.65137arXiv2102.11802OpenAlexW3171202467WikidataQ115406123 ScholiaQ115406123MaRDI QIDQ6068232

Jan Blechschmidt, Oliver G. Ernst

Publication date: 15 December 2023

Published in: GAMM-Mitteilungen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.11802

zbMATH Keywords

neural networksstochastic processpartial differential equationHamilton-Jacobi-Bellman equationscurse of dimensionalityFeynman-Kacbackward differential equationPINN

Mathematics Subject Classification ID

Computational learning theory (68Q32) Artificial neural networks and deep learning (68T07) Optimal stochastic control (93E20) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) PDEs with randomness, stochastic partial differential equations (35R60) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Second-order parabolic equations (35K10)

Related Items (5)

A decoupled physics-informed neural network for recovering a space-dependent force function in the wave equation from integral overdetermination data ⋮ An introduction to kernel and operator learning methods for homogenization by self-consistent clustering analysis ⋮ Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing ⋮ Physics-informed ConvNet: learning physical field from a shallow neural network ⋮ Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions

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