Using Deep Operators to Create Spatio-temporal Surrogates for Dynamical Systems under Uncertainty

• URL: http://arxiv.org/abs/2506.11761v1
• Date: Fri, 13 Jun 2025 13:16:09 GMT
• Title: Using Deep Operators to Create Spatio-temporal Surrogates for Dynamical Systems under Uncertainty
• Authors: Jichuan Tang, Patrick T. Brewick, Ryan G. McClarren, Christopher Sweet,
• Abstract summary: This study proposes a novel variant of deep operator networks (DeepONets), namely the full-field Extended DeepONet (FExD), to serve as a spatial-temporal surrogate.<n>The proposed FExD can achieve both superior accuracy and computational efficiency, representing a significant advancement in operator learning for structural dynamics applications.
• Score: 0.4499833362998487
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Spatio-temporal data, which consists of responses or measurements gathered at different times and positions, is ubiquitous across diverse applications of civil infrastructure. While SciML methods have made significant progress in tackling the issue of response prediction for individual time histories, creating a full spatial-temporal surrogate remains a challenge. This study proposes a novel variant of deep operator networks (DeepONets), namely the full-field Extended DeepONet (FExD), to serve as a spatial-temporal surrogate that provides multi-output response predictions for dynamical systems. The proposed FExD surrogate model effectively learns the full solution operator across multiple degrees of freedom by enhancing the expressiveness of the branch network and expanding the predictive capabilities of the trunk network. The proposed FExD surrogate is deployed to simultaneously capture the dynamics at several sensing locations along a testbed model of a cable-stayed bridge subjected to stochastic ground motions. The ensuing response predictions from the FExD are comprehensively compared against both a vanilla DeepONet and a modified spatio-temporal Extended DeepONet. The results demonstrate the proposed FExD can achieve both superior accuracy and computational efficiency, representing a significant advancement in operator learning for structural dynamics applications.

Related papers

• A Wireless Foundation Model for Multi-Task Prediction [50.21098141769079]
  We propose a unified foundation model for multi-task prediction in wireless networks that supports diverse prediction intervals.<n>After trained on large-scale datasets, the proposed foundation model demonstrates strong generalization to unseen scenarios and zero-shot performance on new tasks.
  arXiv  Detail & Related papers  (2025-07-08T12:37:55Z)
• Multivariate Long-term Time Series Forecasting with Fourier Neural Filter [55.09326865401653]
  We introduce FNF as the backbone and DBD as architecture to provide excellent learning capabilities and optimal learning pathways for spatial-temporal modeling.<n>We show that FNF unifies local time-domain and global frequency-domain information processing within a single backbone that extends naturally to spatial modeling.
  arXiv  Detail & Related papers  (2025-06-10T18:40:20Z)
• PMNO: A novel physics guided multi-step neural operator predictor for partial differential equations [23.04840527974364]
  We propose a novel physics guided multi-step neural operator (PMNO) architecture to address challenges in long-horizon prediction of complex physical systems.<n>The PMNO framework replaces the single-step input with multi-step historical data in the forward pass and introduces an implicit time-stepping scheme during backpropagation.<n>We demonstrate the superior predictive performance of PMNO predictor across a diverse range of physical systems.
  arXiv  Detail & Related papers  (2025-06-02T12:33:50Z)
• Physics-informed Multiple-Input Operators for efficient dynamic response prediction of structures [0.07916635054977067]
  MIONet predicts structural responses continuously over both space and time.<n>Model is validated on both a simple beam and the KW-51 bridge, achieving FEM level accuracy within seconds.
  arXiv  Detail & Related papers  (2025-05-11T18:45:58Z)
• Latent Diffusion Planning for Imitation Learning [78.56207566743154]
  Latent Diffusion Planning (LDP) is a modular approach consisting of a planner and inverse dynamics model.<n>By separating planning from action prediction, LDP can benefit from the denser supervision signals of suboptimal and action-free data.<n>On simulated visual robotic manipulation tasks, LDP outperforms state-of-the-art imitation learning approaches.
  arXiv  Detail & Related papers  (2025-04-23T17:53:34Z)
• Dense ReLU Neural Networks for Temporal-spatial Model [13.8173644075917]
  We focus on fully connected deep neural networks utilizing the Rectified Linear Unit (ReLU) activation function for nonparametric estimation.<n>We derive non-asymptotic bounds that lead to convergence rates, addressing both temporal and spatial dependence in the observed measurements.<n>We also tackle the curse of dimensionality by modeling the data on a manifold, exploring the intrinsic dimensionality of high-dimensional data.
  arXiv  Detail & Related papers  (2024-11-15T05:30:36Z)
• Efficient Training of Deep Neural Operator Networks via Randomized Sampling [0.0]
  We introduce a random sampling technique to be adopted the training of DeepONet.<n>We demonstrate substantial reductions in training time while achieving comparable or lower overall test errors relative to the traditional training approach.<n>Our results indicate that incorporating randomization in the trunk network inputs during training enhances the efficiency and robustness of DeepONet.
  arXiv  Detail & Related papers  (2024-09-20T07:18:31Z)
• Adapting to Length Shift: FlexiLength Network for Trajectory Prediction [53.637837706712794]
  Trajectory prediction plays an important role in various applications, including autonomous driving, robotics, and scene understanding. Existing approaches mainly focus on developing compact neural networks to increase prediction precision on public datasets, typically employing a standardized input duration. We introduce a general and effective framework, the FlexiLength Network (FLN), to enhance the robustness of existing trajectory prediction against varying observation periods.
  arXiv  Detail & Related papers  (2024-03-31T17:18:57Z)
• Deep Cellular Recurrent Network for Efficient Analysis of Time-Series Data with Spatial Information [52.635997570873194]
  This work proposes a novel deep cellular recurrent neural network (DCRNN) architecture to process complex multi-dimensional time series data with spatial information. The proposed architecture achieves state-of-the-art performance while utilizing substantially less trainable parameters when compared to comparable methods in the literature.
  arXiv  Detail & Related papers  (2021-01-12T20:08:18Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)
• Spatio-Temporal Functional Neural Networks [11.73856529960872]
  We propose two novel extensions of the Neural Functional Network (FNN), a temporal regression model whose effectiveness has been proven by many researchers. The proposed models are then deployed to solve a practical and challenging precipitation prediction problem in the meteorology field.
  arXiv  Detail & Related papers  (2020-09-11T21:32:35Z)
• Supporting Optimal Phase Space Reconstructions Using Neural Network Architecture for Time Series Modeling [68.8204255655161]
  We propose an artificial neural network with a mechanism to implicitly learn the phase spaces properties. Our approach is either as competitive as or better than most state-of-the-art strategies.
  arXiv  Detail & Related papers  (2020-06-19T21:04:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.