The major bottleneck of electromagnetic (EM)‐driven antenna design is the high CPU cost of massive simulations required by parametric optimization, uncertainty quantification, or robust design procedures. Fast surrogate models may be employed to mitigate this issue to a certain extent. Unfortunately, the curse of dimensionality is a serious limiting factor, hindering the construction of conventional data‐driven models valid over wide ranges of the antenna parameters and operating conditions. This paper proposes a novel surrogate modeling approach that capitalizes on two recently proposed frameworks: the nested kriging approach and two‐stage Gaussian process regression (GPR). In our methodology, the first‐level surrogate, of nested kriging, is applied to define the confined domain of the model in which the final surrogate is constructed using two‐stage GPR. The latter permits blending information from a sparsely sampled high‐fidelity EM simulation model and a densely sampled low‐fidelity (or coarse‐mesh) model. This combination enables significant computational savings in terms of training data acquisition while retaining excellent predictive power of the surrogate. At the same time, the proposed framework inherits all the benefits of nested kriging, including ease of uniform sampling of the confined domain, as well as straightforward generation of a good initial design for surrogate model optimization. Comprehensive benchmarking carried out using two antenna examples demonstrates superiority of our technique over conventional surrogates (unconfined domain), and standard GPR applied to the confined domain. Application examples for antenna optimization are also provided.

中文翻译：

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使用域限制和两阶段高斯过程回归代理的天线输入特性可变保真度建模

电磁（EM）驱动天线设计的主要瓶颈是参数优化，不确定性量化或稳健的设计程序所要求的大规模仿真的高CPU成本。可以采用快速代理模型在一定程度上缓解此问题。不幸的是，维数的诅咒是一个严重的限制因素，阻碍了传统的数据驱动模型的构建，该模型可在宽范围的天线参数和工作条件下有效。本文提出了一种新颖的替代建模方法，该方法利用了最近提出的两个框架：嵌套克里金法和两阶段高斯过程回归（GPR）。在我们的方法中，嵌套kriging的第一级替代方法是 用于定义模型的受限域，在该域​​中使用两阶段GPR构建最终替代。后者允许混合来自稀疏采样的高保真度EM仿真模型和密集采样的低保真度（或粗网格）模型的信息。这种组合可以在节省训练数据的同时显着节省计算量，同时保留出色的替代预测能力。同时，所提出的框架继承了嵌套克里金法的所有优点，包括易于对受限域进行统一采样，以及为替代模型优化而直接生成良好的初始设计。使用两个天线示例进行的全面基准测试证明了我们的技术优于传统替代产品（无限制域），并将标准GPR应用于受限域。还提供了天线优化的应用示例。