Error bound, an inherent property of an optimization problem, has recently revived in the development of algorithms with improved global convergence without strong convexity. The most studied error bound is the quadratic error bound, which generalizes strong convexity and is satisfied by a large family of machine learning problems. Quadratic error bound have been leveraged to achieve linear con...

An energy-based a posteriori error bound is proposed for the physics-informed neural network solutions of elasticity problems. admissible displacement-stress solution pair obtained from mixed form networks, and formulated as constitutive relation defined by pair. Such an estimator provides upper global discretization. The bounding property, well asymptotic behavior solutions, are studied in dem...