Title: Using Deep Operators to Create Spatio-temporal Surrogates for Dynamical Systems under Uncertainty Show Chinese title

Title: 利用深度算子构建不确定性动力系统下的时空代理模型

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. Show Chinese abstract

Abstract: 时空数据，即在不同时间和位置收集的响应或测量值，在土木基础设施的各种应用中无处不在。尽管科学与机器学习（SciML）方法在解决单个时间序列响应预测问题上取得了显著进展，但构建完整的时空代理模型仍是一项挑战。 本研究提出了一种深度算子网络（DeepONets）的新变体，即全场扩展DeepONet（FExD），作为时空代理模型，为动力系统提供多输出响应预测。所提出的FExD代理模型通过增强分支网络的表达能力并扩展主干网络的预测能力，有效学习了多个自由度上的完整解算符。 所提出的FExD代理模型被部署到一个测试模型中的多个传感位置，该测试模型模拟了一座悬索桥在随机地面运动下的动力学行为。FExD生成的响应预测结果与标准DeepONet和修改后的时空扩展DeepONet进行了全面比较。结果显示，所提出的FExD在准确性与计算效率方面均表现出色，代表了结构动力学应用中算子学习的重大进步。