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

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. (C) 2022 American Society of Civil Engineers.

Automated summary

An energy-based a posteriori error bound is proposed for the physics-informed neural network solutions of elasticity problems. The error bound is formulated as the constitutive relation error defined by the solution pair. It provides an upper bound of the global error of neural network discretization and studies the bounding property and asymptotic behavior of the physics-informed neural network solutions.