Real-time full-field inference of displacement and stress from sparse local measurements using physics-informed neural networks

In this study, we propose a method to infer the displacement and stress of the entire domain using physics-informed neural networks (PINNs), utilizing locally measured strain data from strain sensors. To achieve this, we employed PINNs to constrain the solution field, ensuring that the solutions satisfy the laws of physics, including the force equilibrium equation, strain-displacement relationship, constitutive equation, and displacement and traction boundary conditions into the loss function of PINNs, as well as the loss functions of measurement data. The PINNs were trained with input features in terms of coordinates and measured strain data and corresponding output features in terms of displacement and stress associated with the strain. Finally, by plugging the measured strain data at specific points into the trained PINN model, the full-field displacement and stress can be inferred in real time at the millisecond level without retraining, even for arbitrary measured strain data. To demonstrate the superiority of the proposed method, we analyzed linear elastic problems involving a two-dimensional rectangular plate with a hole and a center-cracked plate. As a result, it has been confirmed that the proposed method allows for accurate inference of the displacement and stress of the entire domain in real time from a limited set of measured strain data. Furthermore, it is noted that the unknown applied load was accurately predicted through integration of the inferred stress field.