  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.
