FE reduced-order model-informed neural operator for structural dynamic response prediction

Physics-Informed Neural Networks (PINN) have achieved remarkable advancements in recent years and have been extensively used in solving differential equations across various disciplines. However, when predicting structural dynamic responses, directly applying them to solve partial differential equations of structural dynamic models encounters challenges like inadequate result accuracy, inefficient training processes, and limited versatility. Furthermore, embedding large-scale structural dynamic models as physical constraints for neural networks can lead to poor trainability and low precision accuracy. To address the above issues, in this paper, we propose a novel FE reduced-order model-informed neural operator (FRINO) for structural dynamic response prediction with high precision, low computational cost, and broad versatility. Specifically, the Fourier neural operator (FNO) is employed to capture the dominant features of structural dynamic responses in the frequency domain, facilitating accurate and efficient solutions. Additionally, a reduced-order model derived using proper orthogonal decomposition is integrated to constrain the FNO. This ensures that the predicted solutions conform to physical differential equations, while also mitigating the high computational costs typically associated with large-dimensional physical equations. Special cantilever beam cases are designed to validate and evaluate the performance of the proposed FRINO. The comparative results demonstrate that FRINO can learn not only the responses of structural dynamic models but also the inherent dynamic characteristics of mechanical structure, allowing for precise predictions of structural responses under diverse unknown excitations. The results demonstrate that, compared with the PINN method, FRINO enhances prediction accuracy by up to two orders of magnitude and computation speed by up to three orders of magnitude. Besides, for practical use of FRINO, one should comprehensively consider the factors such as physical loss, training data resolution, and network width to obtain optimal performance of FRINO.