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Energy-Based Error Bound of Physics-Informed Neural Network Solutions in Elasticity

Guo, Mengwu LU and Haghighat, Ehsan (2022) In Journal of Engineering Mechanics 148(8).
Abstract

An energy-based a posteriori error bound is proposed for the physics-informed neural network solutions of elasticity problems. An admissible displacement-stress solution pair is obtained from a mixed form of physics-informed neural networks, and the proposed error bound is formulated as the constitutive relation error defined by the solution pair. Such an error estimator provides an upper bound of the global error of neural network discretization. The bounding property, as well as the asymptotic behavior of the physics-informed neural network solutions, are studied in a demonstration example.

Please use this url to cite or link to this publication:
author
and
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Engineering Mechanics
volume
148
issue
8
article number
04022038
publisher
American Society of Civil Engineers (ASCE)
external identifiers
  • scopus:85130772342
ISSN
0733-9399
DOI
10.1061/(ASCE)EM.1943-7889.0002121
language
English
LU publication?
no
additional info
Publisher Copyright: © 2022 American Society of Civil Engineers.
id
ee4929cc-67ae-4f28-8b0b-a77d8692e250
date added to LUP
2024-03-19 12:17:25
date last changed
2024-04-17 14:31:16
@article{ee4929cc-67ae-4f28-8b0b-a77d8692e250,
  abstract     = {{<p>An energy-based a posteriori error bound is proposed for the physics-informed neural network solutions of elasticity problems. An admissible displacement-stress solution pair is obtained from a mixed form of physics-informed neural networks, and the proposed error bound is formulated as the constitutive relation error defined by the solution pair. Such an error estimator provides an upper bound of the global error of neural network discretization. The bounding property, as well as the asymptotic behavior of the physics-informed neural network solutions, are studied in a demonstration example.</p>}},
  author       = {{Guo, Mengwu and Haghighat, Ehsan}},
  issn         = {{0733-9399}},
  language     = {{eng}},
  month        = {{08}},
  number       = {{8}},
  publisher    = {{American Society of Civil Engineers (ASCE)}},
  series       = {{Journal of Engineering Mechanics}},
  title        = {{Energy-Based Error Bound of Physics-Informed Neural Network Solutions in Elasticity}},
  url          = {{http://dx.doi.org/10.1061/(ASCE)EM.1943-7889.0002121}},
  doi          = {{10.1061/(ASCE)EM.1943-7889.0002121}},
  volume       = {{148}},
  year         = {{2022}},
}