Physics-informed Multiple-Input Operators for efficient dynamic response prediction of structures

TL;DR

This work introduces MIONet, a physics-informed, dual-trunk neural operator designed for continuous, full-field predictions of structural responses under moving loads. By separating spatial and temporal dynamics into two trunk networks and using a single branch to encode inputs, the method yields continuous space-time predictions with FEM-level accuracy and real-time inference speeds. It couples data-driven learning with dynamic-equilibrium constraints based on mass, damping, and stiffness matrices, and leverages Schur complement reductions to drastically lower training costs without sacrificing accuracy. Validation on a 2D beam and the KW-51 bridge demonstrates high fidelity and substantial speedups over conventional FEM, with a practical pathway for digital twins and real-time structural health monitoring. The study highlights a trade-off between full-domain physics enforcement and computational feasibility, proposing a hybrid DD-Schur approach that maintains physics-consistency while enabling efficient large-scale deployment.

Abstract

Finite element (FE) modeling is essential for structural analysis but remains computationally intensive, especially under dynamic loading. While operator learning models have shown promise in replicating static structural responses at FEM level accuracy, modeling dynamic behavior remains more challenging. This work presents a Multiple Input Operator Network (MIONet) that incorporates a second trunk network to explicitly encode temporal dynamics, enabling accurate prediction of structural responses under moving loads. Traditional DeepONet architectures using recurrent neural networks (RNNs) are limited by fixed time discretization and struggle to capture continuous dynamics. In contrast, MIONet predicts responses continuously over both space and time, removing the need for step wise modeling. It maps scalar inputs including load type, velocity, spatial mesh, and time steps to full field structural responses. To improve efficiency and enforce physical consistency, we introduce a physics informed loss based on dynamic equilibrium using precomputed mass, damping, and stiffness matrices, without solving the governing PDEs directly. Further, a Schur complement formulation reduces the training domain, significantly cutting computational costs while preserving global accuracy. The model is validated on both a simple beam and the KW-51 bridge, achieving FEM level accuracy within seconds. Compared to GRU based DeepONet, our model offers comparable accuracy with improved temporal continuity and over 100 times faster inference, making it well suited for real-time structural monitoring and digital twin applications.

Figures (22)

• Figure 1: Flowchart illustrating the proposed methodology
• Figure 2: Architecture of the proposed MIONet, incorporating two trunk networks and a single branch network based on MLPs
• Figure 3: Flowchart for integrating the Schur-based loss function in the network training process
• Figure 4: Illustration of the Schur Complement to reduce the size of the system: A. Total nodes in the structural domain, B. Picked nodes by applying Schur complement, C. The remaining nodes solution obtained by using post-processing (Eq. \ref{['u_N']})
• Figure 5: Schematic representation of the 2D beam structure with a single moving load