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

The identification of material parameters occurring in constitutive models has a wide range of applications in practice. One of these applications is the monitoring and assessment of the actual condition of infrastructure buildings, as the material parameters directly reflect the resistance of the structures to external impacts. Physics-informed neural networks (PINNs) have recently emerged as a suitable method for solving inverse problems. The advantages of this method are a straightforward inclusion of observation data. Unlike grid-based methods, such as the least square finite element method (LS-FEM) approach, no computational grid and no interpolation of the data is required. In the current work, we propose PINNs for the calibration of constitutive models from full-field displacement and global force data in a realistic regime on the example of linear elasticity. We show that conditioning and reformulation of the optimization problem play a crucial role in real-world applications. Therefore, among others, we identify the material parameters from initial estimates and balance the individual terms in the loss function. In order to reduce the dependency of the identified material parameters on local errors in the displacement approximation, we base the identification not on the stress boundary conditions but instead on the global balance of internal and external work. We demonstrate that the enhanced PINNs are capable of identifying material parameters from both experimental one-dimensional data and synthetic full-field displacement data in a realistic regime. Since displacement data measured by, e.g., a digital image correlation (DIC) system is noisy, we additionally investigate the robustness of the method to different levels of noise.