Parametric Neural Networks as Full-Field Surrogates for Material Model Calibration

Abstract

The identification of material parameters occurring in material models is essential for structural health monitoring. Due to chemical and physical processes, building structures and materials age during their service life. This, in turn, leads to a deterioration in both the reliability and quality of the structures. Knowing the current condition of the building structures can help prevent disasters and extend service life. We developed a physics-informed neural network (PINN) [1] for the calibration of the linear-elastic material model from full-field displacement data measured by digital image correlation. In an offline-phase, the PINN is trained to learn a parameterized solution of the underlying parametric partial differential equation without the need for training data [2]. We demonstrate the ability of the parametric PINN to act as a surrogate in a least-squares based material model calibration. In order to quantify the uncertainty, we further use the parametric PINN with Markov Chain Monte Carlo based Bayesian inference. Even with artificially noisy data, the calibration produces good results for reasonable material parameter ranges. Especially in sampling based methods, parametric PINNs have the advantage that model evaluation is very cheap compared to, e.g., the Finite Element Method. Thus, information on the material condition can be provided in near real-time in the online-phase. Moreover, PINNs use a continuous ansatz and thereby avoid the need to interpolate sensor locations to the simulation domain. In our ongoing work, we plan to apply the parametric PINN to more complex material models, such as those for elasto-plastic materials. We also investigate the extension of the proposed method to more complex geometries. [1] M. Raissi et al.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Journal of Computational Physics 378, 686-707 (2019). [2] A. Beltrán-Pulido et al.: Physics-Informed Neural Networks for Solving Parametric Magnetostatic Problems, IEEE Transactions on Energy Conversion 37(4), 2678-2689 (2022).