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

2025-05-11

AI Summary

Predicting structural responses under dynamic loading via finite element methods (FEM) incurs prohibitive computational cost, while conventional RNN-based DeepONets struggle to capture continuous-time dynamical behavior. Method: We propose the Multi-Input Operator Network (MIONet), featuring a dual-branch architecture that explicitly encodes spatially discretized meshes and continuous temporal evolution; incorporates mass, damping, and stiffness matrices to embed physical priors; enforces physics-informed constraints derived from dynamic equilibrium equations; and employs Schur complement-based dimensionality reduction for efficient training-domain compression. Contribution/Results: On benchmark cases—simply supported beams and the KW-51 bridge—MIONet achieves FEM-level accuracy with sub-second inference time per query, accelerating predictions by over two orders of magnitude relative to GRU-DeepONet. This enables real-time structural health monitoring and high-fidelity digital twin deployment.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• Efficient dynamic response prediction of structures under moving loads
• Overcoming computational intensity of traditional finite element modeling
• Ensuring physical consistency without solving PDEs directly

Innovation

• MIONet encodes temporal dynamics with second trunk network
• Physics-informed loss enforces dynamic equilibrium without PDEs
• Schur complement reduces training domain, cuts computational costs