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

Mengwu Guo*, Ehsan Haghighat

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)
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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.
Original languageEnglish
Article number04022038
JournalJournal of Engineering Mechanics
Issue number8
Early online date23 May 2022
Publication statusPublished - Aug 2022


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