Physics-informed Multiple-Input Operators for efficient dynamic response prediction of structures
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 28 of its 85 references that are in the map. First posted on arXiv 11 May 2025.
Builds on
28 of 85 references.
References · 28
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- 2016WaveNet: A Generative Model for Raw Audiocited by 1,722
- 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
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- 2020Physics informed deep learning for computational elastodynamics without labeled datacited by 80
16 more
- 2019Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transportcited by 61
- 2020Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacturecited by 48
- 2022Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problemscited by 48
- 2023Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loadscited by 47
- 2021Physics informed neural networks for continuum micromechanicscited by 46
- 2023Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loadscited by 33
- 2023Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networkscited by 32
- 2021DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networkscited by 28
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- 2021Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEscited by 22
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- 2020Digital twin, physics-based model, and machine learning applied to damage detection in structurescited by 17
- 2023Predictions of Transient Vector Solution Fields with Sequential Deep Operator Networkcited by 9
- 2024Damage identification for bridges using machine learning: Development and application to KW51 bridgecited by 2
- 2023B-LSTM-MIONet: Bayesian LSTM-based Neural Operators for Learning the Response of Complex Dynamical Systems to Length-Variant Multiple Input Functionscited by 1
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