Energy-Based Error Bound of Physics-Informed Neural Network Solutions in Elasticity
(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.
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https://lup.lub.lu.se/record/ee4929cc-67ae-4f28-8b0b-a77d8692e250
- author
- Guo, Mengwu LU and Haghighat, Ehsan
- publishing date
- 2022-08-01
- 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}}, }