Energy-Based Error Bound of Physics-Informed Neural Network Solutions in Elasticity
Publication: Journal of Engineering Mechanics
Volume 148, Issue 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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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
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© 2022 American Society of Civil Engineers.
History
Received: Oct 22, 2021
Accepted: Mar 15, 2022
Published online: May 23, 2022
Published in print: Aug 1, 2022
Discussion open until: Oct 23, 2022
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