Implicit Runge Kutta physics informed neural network for parameter identification of structural systems
Résumé
System identification (SI) is essential for ensuring the reliability of structural and mechanical components across engineering applications. Traditional model-based SI methods often struggle with complex systems due to modeling uncertainties and the limited availability of accurate physical models. In contrast, datadriven approaches are computationally efficient but typically lack physical interpretability. Physics-informed neural networks (PINNs) have recently emerged as a promising alternative by combining data with physical laws. However, conventional PINNs are computationally expensive for parameter identification due to collocation-based physics enforcement and multi-objective loss optimization. To overcome these challenges, this study proposes an implicit Runge-Kutta physics-informed neural network based on the Radau IIA discretization scheme, termed as Radau IIA PINN. In the proposed framework, physical laws are embedded directly into the architecture of a recurrent neural network through physics-based time integration, eliminating the need for collocation points and complex regressor construction. A comprehensive comparison with state-of-the-art approaches, including Parallel PINNs, IPEnKF, Physics-Informed LSTM, and an explicit fourth-order Runge-Kutta PINN, demonstrates superior robustness, numerical stability, and accuracy under sparse and noisy measurements. Numerical simulations on various structural systems further confirm faster convergence and reliable identification of localized structural deterioration, highlighting the method's potential for practical system identification.