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

TL;DR

This paper introduces the FExD deep operator network as a novel spatio-temporal surrogate for dynamical systems, enabling accurate and efficient multi-location response predictions under uncertainty.

Contribution

The paper develops the FExD model, a new variant of DeepONet, enhancing expressiveness for full-field spatio-temporal response prediction in dynamical systems.

Findings

FExD outperforms vanilla DeepONet in accuracy.

FExD achieves higher computational efficiency.

FExD accurately captures responses at multiple locations.

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.