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

TL;DR

This paper introduces MIONet, a physics-informed operator learning model that predicts dynamic structural responses continuously over space and time, offering high accuracy and efficiency for real-time structural analysis.

Contribution

The work develops a novel Multiple Input Operator Network with physics-informed loss and Schur complement formulation, enabling continuous, accurate, and fast dynamic response prediction without solving PDEs.

Findings

Achieves FEM-level accuracy in seconds.

Over 100 times faster inference than GRU-based DeepONet.

Effective in modeling responses of both simple beams and complex bridges.

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.