hp-VPINNs: Variational physics-informed neural networks with domain decomposition

We formulate a general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-refinement via domain decomposition and projection onto the space of high-order polynomials. The trial space is the space o...

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Bibliographic Details
Published in:	Computer methods in applied mechanics and engineering Vol. 374; no. C; p. 113547
Main Authors:	Kharazmi, Ehsan, Zhang, Zhongqiang, Karniadakis, George E.M.
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01.02.2021 Elsevier BV Elsevier
Subjects:	Algorithms Approximation Artificial neural networks Automatic differentiation Differential equations Domain decomposition Domain decomposition methods hp-refinement Machine learning Neural networks Optimization Partial differential equations Physics-informed learning Polynomials Variational neural network VPINNs Partial differential equations Variational neural network hp-refinement Physics-informed learning Domain decomposition VPINNs Automatic differentiation
ISSN:	0045-7825, 1879-2138
Online Access:	Get full text
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