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

arXiv: https://arxiv.org/abs/2506.11761 · HTML: https://mlsanity.com/paper/2506.11761/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 44 references that are in the map.
- First posted on arXiv 13 Jun 2025.

## Builds on (most cited first, 10 of 10)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting](https://mlsanity.com/paper/2306.01984/) (2023)
- [Encoding physics to learn reaction-diffusion processes](https://mlsanity.com/paper/2106.04781/) (2021)
- [Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loads](https://mlsanity.com/paper/2306.08218/) (2023)
- [Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometries](https://mlsanity.com/paper/2403.14788/) (2024)
- [Discovering and forecasting extreme events via active learning in neural operators](https://mlsanity.com/paper/2204.02488/) (2022)
- [A multi-fidelity deep operator network (DeepONet) for fusing simulation and monitoring data: Application to real-time settlement prediction during tunnel construction](https://mlsanity.com/paper/2310.00057/) (2023)
- [Scalable Spatiotemporal Prediction with Bayesian Neural Fields](https://mlsanity.com/paper/2403.07657/) (2024)
- [Neural Operators for Stochastic Modeling of Nonlinear Structural System Response to Natural Hazards](https://mlsanity.com/paper/2502.11279/) (2025)
- [Neural operator for structural simulation and bridge health monitoring](https://mlsanity.com/paper/2305.07889/) (2023)

## Abstract (arXiv)

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.