# A physics-informed U-Net-LSTM network for nonlinear structural response under seismic excitation

arXiv: https://arxiv.org/abs/2511.21276 · HTML: https://mlsanity.com/paper/2511.21276/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 57 references that are in the map.
- First posted on arXiv 26 Nov 2025.

## Builds on (most cited first, 12 of 12)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [U-Net and its variants for medical image segmentation: theory and applications](https://mlsanity.com/paper/2011.01118/) (2020)
- [Learning Longer-term Dependencies in RNNs with Auxiliary Losses](https://mlsanity.com/paper/1803.00144/) (2018)
- [Physics-Informed Multi-LSTM Networks for Metamodeling of Nonlinear Structures](https://mlsanity.com/paper/2002.10253/) (2020)
- [Physics-guided Convolutional Neural Network (PhyCNN) for Data-driven Seismic Response Modeling](https://mlsanity.com/paper/1909.08118/) (2019)
- [Seq-U-Net: A One-Dimensional Causal U-Net for Efficient Sequence Modelling](https://mlsanity.com/paper/1911.06393/) (2019)
- [Integrated Finite Element Neural Network (I-FENN) for non-local continuum damage mechanics](https://mlsanity.com/paper/2207.09908/) (2022)
- [I-FENN with Temporal Convolutional Networks: expediting the load-history analysis of non-local gradient damage propagation](https://mlsanity.com/paper/2402.05460/) (2024)

## Abstract (arXiv)

Accurate and efficient seismic response prediction is essential for the design of resilient structures. While the Finite Element Method (FEM) remains the standard for nonlinear seismic analysis, its high computational demands limit its scalability and real-time applicability. Recent developments in deep learning - particularly Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), and Long Short-Term Memory (LSTM) models - have shown promise in reducing the computational cost of the nonlinear seismic analysis of structures. However, these data-driven models often struggle to generalize and capture the underlying physics, leading to reduced reliability. We propose a novel Physics-Informed U-Net-LSTM framework that integrates physical laws with deep learning to enhance both accuracy and efficiency. The proposed 1D U-Net captures the underlying latent features of the long-term input sequences. By embedding domain-specific constraints into the learning process, the proposed model achieves improved predictive performance over conventional Machine Learning (ML) architectures. This approach bridges the gap between purely data-driven methods and physics-based modeling, offering a robust and computationally efficient alternative for predicting the seismic response of structures.