Nonlinear systems, such as with degrading hysteretic behavior, are often encountered in engineering applications. In addition, due to the ubiquitous presence of uncertainty and the modeling of such systems becomes increasingly difficult. On the other hand, datasets from pristine models developed without knowing the nature of the degrading effects can be easily obtained. In this paper, we use datasets from pristine models without considering the degrading effects of hysteretic systems as low-fidelity representations that capture many of the important characteristics of the true system's behavior to train a deep operator network (DeepONet). Three numerical examples are used to show that the proposed use of the DeepONets to model the discrepancies between the low-fidelity model and the true system's response leads to significant improvements in the prediction error in the presence of uncertainty in the model parameters for degrading hysteretic systems.

本文利用深度操作网络（DeepONet）来建模退化滞后系统中的非线性系统，通过利用来源于无损蚀模型的数据进行训练，来捕捉真实系统行为重要特征的低保真度量，并通过三个数值实例证明其在存在退化滞后系统模型参数不确定性方面的显著预测误差改进。

一种双保真DeepONet方法用于建模不确定和退化的滞回系统