Physics-informed neural networks (PINNs) for numerical model error approximation and superresolution for structures

Abstract Numerical modeling errors exist when conducting low-fidelity and high-fidelity modeling in finite element analysis. The presence of model errors reflects both model accuracy and uncertainty for structural engineering problems. To date, there have been few methods for explicitly quantifying errors at points of interest (e.g. at finite element nodes) in finite element models. The lack of explicit model error approximators has been addressed recently with the emergence of machine learning (ML), which closes the loop between numerical model features/solutions and explicit model error approximations. In this paper, physics-informed neural networks (PINNs) are proposed for simultaneous numerical model error approximation and superresolution. To test the proposed approach, numerical data was generated using finite element simulations on a two-dimensional elastic plate with a central opening and a cantilever beam. Four- and eight-node quadrilateral elements were used in the discretization to represent the reduced-order and higher-order models, respectively. It was found that the developed PINNs effectively predict model errors in both x and y displacement fields with small differences to the ground truth. The findings demonstrate that the integration of physics-informed loss functions enables neural networks (NNs) to outperform a purely data-driven approach for approximating model errors in structural engineering.