Usually, traditional machine learning (ML) methods use only labeled samples for learning. However, in practical problems including electromagnetic optimization design, the acquisition cost of labeled samples is relatively high. Obtaining label training samples is the most time‐consuming part, so how to use relatively few label samples for training to obtain a high‐precision surrogate model is a hot topic. This study proposes a co‐training algorithm of semi‐supervised Gaussian Process (GP) with different kernel functions, based on the differences between these two different GP models. The algorithm is conducted by a small number of labeled samples in combination with unlabeled samples, so as to continuously improve the accuracy of the models. Stop criteria is set in advance to control the number of unlabeled samples introduced, preventing the accuracy of the model reduced by introducing too much unlabeled samples. Furthermore, the proposed algorithm is evaluated by benchmark functions and resonant frequency modeling problems of two different antennas. Results show that the proposed GP model has good fitting effects on the benchmark functions. For the problems of resonant frequency modeling, in the case of the same labeled samples, its predictive ability is better than that of the traditional supervised learning (SL) method.

中文翻译：

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基于不同核函数的半监督高斯过程协同训练的天线谐振频率建模

通常，传统的机器学习（ML）方法仅使用标记的样本进行学习。然而，在包括电磁优化设计在内的实际问题中，标记样品的采集成本相对较高。获取标签训练样本是最耗时的部分，因此如何使用相对较少的标签样本进行训练以获得高精度的替代模型是一个热门话题。基于这两种不同GP模型之间的差异，本研究提出了一种具有不同内核功能的半监督高斯过程（GP）的协同训练算法。该算法是通过少量标记的样本与未标记的样本相结合来进行的，从而不断提高模型的准确性。预先设置了停止标准，以控制引入的未标记样品的数量，防止由于引入过多未标记的样本而降低了模型的准确性。此外，通过基准函数和两个不同天线的谐振频率建模问题对所提出的算法进行了评估。结果表明，提出的GP模型对基准函数具有良好的拟合效果。对于共振频率建模的问题，在相同标记样本的情况下，其预测能力优于传统的监督学习（SL）方法。