Energy-based error bound of physics-informed neural network solutions in elasticity
This work addresses the need for reliable error estimation in PINNs for elasticity, which is important for engineers and computational scientists, though it appears incremental as it builds on existing mixed-form PINN approaches.
The authors tackled the problem of quantifying the error in physics-informed neural network (PINN) solutions for elasticity problems by proposing an energy-based a posteriori error bound, which provides an upper bound on the global discretization error, as demonstrated in an example.
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 demonstrating example.