Project start: 1.10.2025.

The research examines the application of physics-informed neural networks (PINNs) in mechanics. Although this field has seen significant development in recent years, many problems remain unsolved. This study focuses on two open questions: the nonlocal behavior of beam structures and the difficulties in applying PINNs to experimentally acquired data in mechanics.

For problems involving beam structures, PINNs will serve as a surrogate for the partial differential equation that governs beam bending. The loss function will be augmented with terms that enforce boundary conditions. A multi-level approach will be employed, decomposing the problem into multiple PINNs that involve only first- or at most second-order derivatives, thereby preventing numerical instabilities. Since no nonlocal PINN formulation currently exists for beam structures, the significance of this research is clear.

The application of physical constraints significantly reduces the amount of training data required for PINNs. However, in some cases, it may lead to overly restrictive formulations, making it difficult to accurately capture experimental observations. To mitigate this, the study will explore methods for relaxing physical constraints. Additionally, recently introduced PINNs based on principal values rather than invariants may offer a complete solution to this issue. This research will determine which of these approaches is more effective.

The results will be validated using data collected in this study through experiments on 3D-printed structures. The PINNs developed in this research will be robust enough for practical industrial applications.