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

Finite element (FE) modeling is crucial for structural analysis but remains expensive, particularly under dynamic loading. Recently, operator learning models have replicated structural responses at the FE level under static loading; however, modeling dynamic behavior remains challenging. In this work, we address this by developing a modified multiple-input operator network (MIONet) that incorporates a second trunk network to explicitly encode temporal dynamics, enabling accurate prediction of responses under moving loads. Traditional Deep Operator Networks (DeepONet), especially those using recurrent neural networks (RNNs), rely on fixed-time discretization, limiting their ability to capture continuous dynamics in real structures. In contrast, the proposed MIONet enables seamless prediction across space and time, eliminating the need for step-wise modeling. It maps scalar inputs, including moving load parameters, velocity, spatial discretization, and time, to a continuous response. To improve efficiency and consistency, we introduce physics-informed learning that leverages precomputed mass, damping, and stiffness matrices to enforce dynamic equilibrium without explicitly solving governing equations. Additionally, a Schur complement approach reduces computational cost by training the model in a reduced domain while maintaining accuracy across the full structure. The method is validated on a simple beam and the real-world KW-51 bridge, demonstrating its ability to produce FE-level accurate predictions, making it suitable for real-time applications such as digital twins and structural monitoring, where updates are required faster than conventional FE simulations. Comparative studies with Gated Recurrent Unit (GRU) DeepONet show that our approach achieves similar accuracy, ensures temporal continuity, and delivers over 100-fold faster computation than FE modeling. • Proposed MIONet for real-time structural response prediction under dynamic loading. • Outperforms GRU-based DeepONet in capturing continuous temporal dynamics. • Enforces physics via dynamic equilibrium matrix constraints. • Achieves accuracy > 95 % and 100 × speedup in dynamic response prediction.