Physics-Informed Multi-LSTM Networks for Metamodeling of Nonlinear Structures
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Abstract (arXiv)
This paper introduces an innovative physics-informed deep learning framework for metamodeling of nonlinear structural systems with scarce data. The basic concept is to incorporate physics knowledge (e.g., laws of physics, scientific principles) into deep long short-term memory (LSTM) networks, which boosts the learning within a feasible solution space. The physics constraints are embedded in the loss function to enforce the model training which can accurately capture latent system nonlinearity even with very limited available training datasets. Specifically for dynamic structures, physical laws of equation of motion, state dependency and hysteretic constitutive relationship are considered to construct the physics loss. In particular, two physics-informed multi-LSTM network architectures are proposed for structural metamodeling. The satisfactory performance of the proposed framework is successfully demonstrated through two illustrative examples (e.g., nonlinear structures subjected to ground motion excitation). It turns out that the embedded physics can alleviate overfitting issues, reduce the need of big training datasets, and improve the robustness of the trained model for more reliable prediction. As a result, the physics-informed deep learning paradigm outperforms classical non-physics-guided data-driven neural networks.
Key facts. Cited by 52 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Feb 2020.
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Citing papers per year: 2021: 6; 2022: 10; 2023: 9; 2024: 12; 2025: 11; 2026: 4.
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- 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
- 2021PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEscited by 97
- 2021CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Methodcited by 93
- 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
- 2023PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEscited by 84
- 2022Predicting Physics in Mesh-reduced Space with Temporal Attentioncited by 82
- 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
- 2021Encoding physics to learn reaction-diffusion processescited by 61
- 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
- 2022Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamicscited by 44
- 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 37
- 2023Deep Learning in Deterministic Computational Mechanicscited by 21
38 more
- 2022SeismicNet: Physics-informed neural networks for seismic wave modeling in semi-infinite domaincited by 16
- 2022Finite Element Method-enhanced Neural Network for Forward and Inverse Problemscited by 13
- 2024P2C2Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamicscited by 13
- 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunitiescited by 10
- 2022Physics-informed Deep Super-resolution for Spatiotemporal Datacited by 9
- 2024Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)cited by 9
- 2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacousticcited by 7
- 2022An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operatorcited by 7
- 2022AutoKE: An automatic knowledge embedding framework for scientific machine learningcited by 6
- 2023Efficient Surrogate Models for Materials Science Simulations: Machine Learning-based Prediction of Microstructure Propertiescited by 6
- 2024Generative Learning for Forecasting the Dynamics of Complex Systemscited by 6
- 2025Neural Operators for Stochastic Modeling of Nonlinear Structural System Response to Natural Hazardscited by 6
- 2023Neural-Integrated Meshfree (NIM) Method: A differentiable programming-based hybrid solver for computational mechanicscited by 4
- 2024PAPM: A Physics-aware Proxy Model for Process Systemscited by 4
- 2024Conservation-informed Graph Learning for Spatiotemporal Dynamics Predictioncited by 4
- 2025RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equationscited by 4
- 2023Temporal Consistency Loss for Physics-Informed Neural Networkscited by 3
- 2023Physics-Informed Long Short-Term Memory for Forecasting and Reconstruction of Chaoscited by 3
- 2025DGNN: A Neural PDE Solver Induced by Discontinuous Galerkin Methodscited by 3
- 2023Physics-Informed Machine Learning of Argon Gas-Driven Melt Pool Dynamicscited by 2
- 2024Wasserstein Distributionally Robust Shallow Convex Neural Networkscited by 2
- 2023Physics-informed Neural Network: The Effect of Reparameterization in Solving Differential Equationscited by 1
- 2024Kolmogorov n-Widths for Multitask Physics-Informed Machine Learning (PIML) Methods: Towards Robust Metricscited by 1
- 2025Learnable-Differentiable Finite Volume Solver for Accelerated Simulation of Flowscited by 1
- 2025Adaptive Machine Learning-Driven Multi-Fidelity Stratified Sampling for Failure Analysis of Nonlinear Stochastic Systemscited by 1
- 2021Condition Assessment of Stay Cables through Enhanced Time Series Classification Using a Deep Learning Approachcited by 0
- 2021Long short-term relevance learningcited by 0
- 2023Physics Informed Recurrent Neural Networks for Seismic Response Evaluation of Nonlinear Systemscited by 0
- 2024Physics-Informed Machine Learning for Seismic Response Prediction OF Nonlinear Steel Moment Resisting Frame Structurescited by 0
- 2024Deep Learning in Earthquake Engineering: A Comprehensive Reviewcited by 0
- 2024Parametric Taylor series based latent dynamics identification neural networkscited by 0
- 2025MC-GRU:a Multi-Channel GRU network for generalized nonlinear structural response prediction across structurescited by 0
- 2025Over-PINNs: Enhancing Physics-Informed Neural Networks via Higher-Order Partial Derivative Overdetermination of PDEscited by 0
- 2025Structural System Identification via Validation and Adaptationcited by 0
- 2025A physics-informed U-Net-LSTM network for nonlinear structural response under seismic excitationcited by 0
- 2025A Novel Deep Neural Network Architecture for Real-Time Water Demand Forecastingcited by 0
- 2026Deep Learning-Based Metamodeling of Nonlinear Stochastic Dynamic Systems under Parametric and Predictive Uncertaintycited by 0
- 2026Variational LSTM with Augmented Inputs: Nonlinear Response History Metamodeling with Aleatoric and Epistemic Uncertaintycited by 0
50 most cited of 52 All 52 (JSON)
- 2026Physical knowledge on historical data matters more than enforcing physical constraints on the forecast17 Sep 2026
- 2026Development and Validation of a Physics-Guided Machine Learning Extrapolation Framework Using a Classical Transient Diffusion Benchmark9 Sep 2026
- 2026Variational LSTM with Augmented Inputs: Nonlinear Response History Metamodeling with Aleatoric and Epistemic Uncertainty2 Apr 2026
- 2026Deep Learning-Based Metamodeling of Nonlinear Stochastic Dynamic Systems under Parametric and Predictive Uncertainty12 Mar 2026
- 2025A Novel Deep Neural Network Architecture for Real-Time Water Demand Forecasting7 Dec 2025
- 2025A physics-informed U-Net-LSTM network for nonlinear structural response under seismic excitation26 Nov 2025
- 2025RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations1 Sep 2025
- 2025Adaptive Machine Learning-Driven Multi-Fidelity Stratified Sampling for Failure Analysis of Nonlinear Stochastic Systems1 Aug 2025
- 2025Structural System Identification via Validation and Adaptation25 Jun 2025
- 2025Learnable-Differentiable Finite Volume Solver for Accelerated Simulation of Flows23 Jun 2025
- 2025Over-PINNs: Enhancing Physics-Informed Neural Networks via Higher-Order Partial Derivative Overdetermination of PDEs6 Jun 2025
- 2025DGNN: A Neural PDE Solver Induced by Discontinuous Galerkin Methods13 Mar 2025
38 more
- 2025MC-GRU:a Multi-Channel GRU network for generalized nonlinear structural response prediction across structures10 Mar 2025
- 2025Neural Operators for Stochastic Modeling of Nonlinear Structural System Response to Natural Hazards16 Feb 2025
- 2025Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities11 Jan 2025
- 2024Conservation-informed Graph Learning for Spatiotemporal Dynamics Prediction30 Dec 2024
- 2024P2C2Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics29 Oct 2024
- 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning17 Oct 2024
- 2024Parametric Taylor series based latent dynamics identification neural networks5 Oct 2024
- 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks24 Jul 2024
- 2024Wasserstein Distributionally Robust Shallow Convex Neural Networks23 Jul 2024
- 2024PAPM: A Physics-aware Proxy Model for Process Systems7 Jul 2024
- 2024Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)5 Jun 2024
- 2024Deep Learning in Earthquake Engineering: A Comprehensive Review15 May 2024
- 2024Physics-Informed Machine Learning for Seismic Response Prediction OF Nonlinear Steel Moment Resisting Frame Structures28 Feb 2024
- 2024Generative Learning for Forecasting the Dynamics of Complex Systems27 Feb 2024
- 2024Kolmogorov n-Widths for Multitask Physics-Informed Machine Learning (PIML) Methods: Towards Robust Metrics16 Feb 2024
- 2023Neural-Integrated Meshfree (NIM) Method: A differentiable programming-based hybrid solver for computational mechanics21 Nov 2023
- 2023Deep Learning in Deterministic Computational Mechanics27 Sep 2023
- 2023Efficient Surrogate Models for Materials Science Simulations: Machine Learning-based Prediction of Microstructure Properties1 Sep 2023
- 2023Physics Informed Recurrent Neural Networks for Seismic Response Evaluation of Nonlinear Systems16 Aug 2023
- 2023Physics-Informed Machine Learning of Argon Gas-Driven Melt Pool Dynamics23 Jul 2023
- 2023PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs15 Jun 2023
- 2023Physics-Informed Long Short-Term Memory for Forecasting and Reconstruction of Chaos3 Feb 2023
- 2023Temporal Consistency Loss for Physics-Informed Neural Networks30 Jan 2023
- 2023Physics-informed Neural Network: The Effect of Reparameterization in Solving Differential Equations28 Jan 2023
- 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications15 Nov 2022
- 2022SeismicNet: Physics-informed neural networks for seismic wave modeling in semi-infinite domain25 Oct 2022
- 2022An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator21 Oct 2022
- 2022Physics-informed Deep Super-resolution for Spatiotemporal Data2 Aug 2022
- 2022Finite Element Method-enhanced Neural Network for Forward and Inverse Problems17 May 2022
- 2022AutoKE: An automatic knowledge embedding framework for scientific machine learning11 May 2022
- 2022Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics9 May 2022
- 2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic13 Apr 2022
- 2022Predicting Physics in Mesh-reduced Space with Temporal Attention22 Jan 2022
- 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next14 Jan 2022
- 2021CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method29 Oct 2021
- 2021One-Shot Transfer Learning of Physics-Informed Neural Networks21 Oct 2021
- 2021PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs26 Jun 2021
- 2021Long short-term relevance learning21 Jun 2021
50 newest of 52 All 52 (JSON)
- 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
- 2021PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEscited by 97
- 2021CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Methodcited by 93
- 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
- 2023PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEscited by 84
- 2022Predicting Physics in Mesh-reduced Space with Temporal Attentioncited by 82
- 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
- 2021Encoding physics to learn reaction-diffusion processescited by 61
- 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
- 2022Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamicscited by 44
- 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 37
- 2023Deep Learning in Deterministic Computational Mechanicscited by 21
12 most cited of 52 All 52 (JSON)
- 2026Physical knowledge on historical data matters more than enforcing physical constraints on the forecast17 Sep 2026
- 2026Development and Validation of a Physics-Guided Machine Learning Extrapolation Framework Using a Classical Transient Diffusion Benchmark9 Sep 2026
- 2026Variational LSTM with Augmented Inputs: Nonlinear Response History Metamodeling with Aleatoric and Epistemic Uncertainty2 Apr 2026
- 2026Deep Learning-Based Metamodeling of Nonlinear Stochastic Dynamic Systems under Parametric and Predictive Uncertainty12 Mar 2026
- 2025A Novel Deep Neural Network Architecture for Real-Time Water Demand Forecasting7 Dec 2025
- 2025A physics-informed U-Net-LSTM network for nonlinear structural response under seismic excitation26 Nov 2025
- 2025RAMS: Residual-based adversarial-gradient moving sample method for scientific machine learning in solving partial differential equations1 Sep 2025
- 2025Adaptive Machine Learning-Driven Multi-Fidelity Stratified Sampling for Failure Analysis of Nonlinear Stochastic Systems1 Aug 2025
- 2025Structural System Identification via Validation and Adaptation25 Jun 2025
- 2025Learnable-Differentiable Finite Volume Solver for Accelerated Simulation of Flows23 Jun 2025
- 2025Over-PINNs: Enhancing Physics-Informed Neural Networks via Higher-Order Partial Derivative Overdetermination of PDEs6 Jun 2025
- 2025DGNN: A Neural PDE Solver Induced by Discontinuous Galerkin Methods13 Mar 2025
12 newest of 52 All 52 (JSON)