Parametric Physics-Informed Neural Networks for Material Model Calibration from Full-Field Displacement Data

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. The material parameters indicate possible damage and material degradation, as they directly reflect the resistance of the structure to external impacts. We further developed physics-informed neural networks (PINNs) [1] for the calibration of the linear-elastic material model from full-field displacement data and global force data in a realistic regime [2]. For a realistic data regime, the optimization problem had to be conditioned. The advantage of this method is a straightforward inclusion of observation data. Unlike grid-based methods, such as the least square finite element method approach, no computational grid and no interpolation of the data are required. However, directly solving inverse problems using PINNs is computationally expensive and prone to realistic noise levels in the measurement data. Moreover, the PINN must be trained completely from scratch for each new full-field displacement measurement, even if the geometry and material of the structure remain unchanged. In our ongoing work, we are therefore focusing on learning parameterized solutions of parametric partial differential equations using PINNs, such as [3]. We further investigate the ability of parametric PINNs to act as a surrogate for the identification of material parameters from full-field displacement data. By learning parameterized solutions, the PINN does not need to be completely re-trained for each full-field displacement measurement. The calibration of the material model can thus be drastically accelerated, and information about the material condition can be provided near real-time. Furthermore, we also plan to apply the parametric PINN to more complex material models, such as those for hyper-elastic and elasto-plastic materials.