The increasing significance of digital twin technology across engineering and industrial domains, such as aerospace, infrastructure, and automotive, is undeniable. However, the lack of detailed application-specific information poses challenges to its seamless implementation in practical systems. Data-driven models play a crucial role in digital twins, enabling real-time updates and predictions by leveraging data and computational models. Nonetheless, the fidelity of available data and the scarcity of accurate sensor data often hinder the efficient learning of surrogate models, which serve as the connection between physical systems and digital twin models. To address this challenge, we propose a novel framework that begins by developing a robust multi-fidelity surrogate model, subsequently applied for tracking digital twin systems. Our framework integrates polynomial correlated function expansion (PCFE) with the Gaussian process (GP) to create an effective surrogate model called H-PCFE. Going a step further, we introduce deep-HPCFE, a cascading arrangement of models with different fidelities, utilizing nonlinear auto-regression schemes. These auto-regressive schemes effectively address the issue of erroneous predictions from low-fidelity models by incorporating space-dependent cross-correlations among the models. To validate the efficacy of the multi-fidelity framework, we first assess its performance in uncertainty quantification using benchmark numerical examples. Subsequently, we demonstrate its applicability in the context of digital twin systems.

翻译：数字孪生技术在航空航天、基础设施和汽车等工程与工业领域的重要性日益凸显。然而，缺乏针对具体应用场景的详细信息，给其在实际系统中的无缝实施带来了挑战。数据驱动模型在数字孪生中扮演着关键角色，通过利用数据和计算模型实现实时更新与预测。尽管如此，可用数据的保真度不足以及精确传感器数据的稀缺性，往往阻碍了作为物理系统与数字孪生模型之间桥梁的代理模型的高效学习。为解决这一难题，我们提出了一种新颖框架：首先构建鲁棒的多保真代理模型，随后将其应用于数字孪生系统的跟踪。该框架将多项式相关函数展开（PCFE）与高斯过程（GP）相结合，创建了名为H-PCFE的高效代理模型。更进一步，我们引入了deep-HPCFE——一种通过非线性自回归方案实现的不同保真度模型的级联排列。这些自回归方案通过纳入模型间的空间依赖交叉相关性，有效解决了低保真模型错误预测的问题。为验证多保真框架的有效性，我们首先通过基准数值示例评估其在不确定性量化中的性能，随后展示了其在数字孪生系统背景下的适用性。