  The calibration of constitutive models from full-field data has recently
gained increasing interest due to improvements in full-field measurement
capabilities. In addition to the experimental characterization of novel
materials, continuous structural health monitoring is another application that
is of great interest. However, monitoring is usually associated with severe
time constraints, difficult to meet with standard numerical approaches.
Therefore, parametric physics-informed neural networks (PINNs) for constitutive
model calibration from full-field displacement data are investigated. In an
offline stage, a parametric PINN can be trained to learn a parameterized
solution of the underlying partial differential equation. In the subsequent
online stage, the parametric PINN then acts as a surrogate for the
parameters-to-state map in calibration. We test the proposed approach for the
deterministic least-squares calibration of a linear elastic as well as a
hyperelastic constitutive model from noisy synthetic displacement data. We
further carry out Markov chain Monte Carlo-based Bayesian inference to quantify
the uncertainty. A proper statistical evaluation of the results underlines the
high accuracy of the deterministic calibration and that the estimated
uncertainty is valid. Finally, we consider experimental data and show that the
results are in good agreement with a Finite Element Method-based calibration.
Due to the fast evaluation of PINNs, calibration can be performed in near
real-time. This advantage is particularly evident in many-query applications
such as Markov chain Monte Carlo-based Bayesian inference.
