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.

翻译：非线性系统（例如具有性能退化滞回行为的系统）在工程应用中经常遇到。此外，由于不确定性普遍存在，对此类系统的建模变得日益困难。另一方面，在不了解退化效应性质的情况下开发的初始模型所生成的数据集可以很容易获得。本文利用未考虑滞回系统退化效应的初始模型数据集，将其作为捕捉真实系统行为许多重要特征的低保真度表示，用于训练深度算子网络（DeepONet）。通过三个数值算例表明，本文提出的采用DeepONet对低保真度模型与真实系统响应之间的差异进行建模的方法，在模型参数存在不确定性的情况下，能够显著降低对性能退化滞回系统的预测误差。