DGM: A deep learning algorithm for solving partial differential equations

High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial condition, and boundary conditions. Our algorithm is meshfree, whi...

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Bibliographic Details
Published in:	Journal of computational physics Vol. 375; pp. 1339 - 1364
Main Authors:	Sirignano, Justin, Spiliopoulos, Konstantinos
Format:	Journal Article
Language:	English
Published:	Cambridge Elsevier Inc 15.12.2018 Elsevier Science Ltd
Subjects:	Algorithms Approximation Artificial intelligence Artificial neural networks Basis functions Boundary conditions Burgers equation Computational physics Deep learning Free boundaries Galerkin method High-dimensional partial differential equations Machine learning Meshless methods Neural networks Operators (mathematics) Parabolic differential equations Partial differential equations Deep learning High-dimensional partial differential equations Partial differential equations Machine learning
ISSN:	0021-9991, 1090-2716
Online Access:	Get full text
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