Multifidelity surrogate modelling combines data of varying accuracy and cost
from different sources. It strategically uses low-fidelity models for rapid
evaluations, saving computational resources, and high-fidelity models for
detailed refinement. It improves decision-making by addressing uncertainties
and surpassing the limits of single-fidelity models, which either oversimplify
or are computationally intensive. Blending high-fidelity data for detailed
responses with frequent low-fidelity data for quick approximations facilitates
design optimisation in various domains.
Despite progress in interpolation, regression, enhanced sampling, error
estimation, variable fidelity, and data fusion techniques, challenges persist
in selecting fidelity levels and developing efficient data fusion methods. This
study proposes a new fusion approach to construct multi-fidelity surrogate
models by constructing gradient-only surrogates that use only gradients to
construct regression surfaces. Results are demonstrated on foundational example
problems that isolate and illustrate the fusion approach's efficacy, avoiding
the need for complex examples that obfuscate the main concept.

多重保真度代理模型结合了不同来源的准确性和成本不同的数据。它战略性地使用低保真度模型进行快速评估，节省计算资源，并使用高保真度模型进行详细优化，它通过解决不确定性和超越单一保真度模型的限制来改善决策。融合高保真度数据用于详细响应，并且频繁融合低保真度数据用于快速近似，有助于在各个领域进行设计优化。

多保真代理模型：一种新的数据融合视角

Multifidelity Surrogate Models: A New Data Fusion Perspective

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。