For the optimal design of electromagnetic devices, it is the most time consuming to obtain the training samples from full wave\nelectromagnetic simulation software, including HFSS, CST, and IE3D. Traditional machine learning methods usually use only\nlabeled samples or unlabeled samples, but in practical problems, labeled samples and unlabeled samples coexist, and the acquisition\ncost of labeled samples is relatively high. This paper proposes a semisupervised learning Gaussian Process (GP), which\ncombines unlabeled samples to improve the accuracy of the GP model and reduce the number of labeled training samples\nrequired. The proposed GP model consists two parts: initial training and self-training. In the process of initial training, a small\nnumber of labeled samples obtained by full wave electromagnetic simulation are used for training the initial GP model. Afterwards,\nthe trained GP model is copied to another GP model in the process of self-training, and then the two GP models will\nupdate after crosstraining with different unlabeled samples. Using the same test samples for testing and updating, a model with a\nsmaller error will replace another. Repeat the self-training process until a predefined stopping criterion is met. Four different\nbenchmark functions and resonant frequency modeling problems of three different microstrip antennas are used to evaluate the\neffectiveness of the GP model. The results show that the proposed GP model has a good fitting effectiveness on benchmark\nfunctions. For microstrip antennas resonant frequency modeling problems, in the case of using the same labeled samples, its\npredictive ability is better than that of the traditional supervised GP model.
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