Abstract
For the optimal design of electromagnetic devices, it is the most time consuming to obtain the training samples from full wave electromagnetic simulation software, including HFSS, CST, and IE3D. Traditional machine learning methods usually use only labeled samples or unlabeled samples, but in practical problems, labeled samples and unlabeled samples coexist, and the acquisition cost of labeled samples is relatively high. This paper proposes a semisupervised learning Gaussian Process (GP), which combines unlabeled samples to improve the accuracy of the GP model and reduce the number of labeled training samples required. The proposed GP model consists two parts: initial training and self-training. In the process of initial training, a small number of labeled samples obtained by full wave electromagnetic simulation are used for training the initial GP model. Afterwards, the trained GP model is copied to another GP model in the process of self-training, and then the two GP models will update after crosstraining with different unlabeled samples. Using the same test samples for testing and updating, a model with a smaller error will replace another. Repeat the self-training process until a predefined stopping criterion is met. Four different benchmark functions and resonant frequency modeling problems of three different microstrip antennas are used to evaluate the effectiveness of the GP model. The results show that the proposed GP model has a good fitting effectiveness on benchmark functions. For microstrip antennas resonant frequency modeling problems, in the case of using the same labeled samples, its predictive ability is better than that of the traditional supervised GP model.
Highlights
In recent years, for the optimization design of electromagnetic devices, some excellent research results have been achieved by numerical simulation calculation or combining full wave electromagnetic simulation software such as HFSS with global optimization algorithm, such as particle swarm optimization (PSO) [1]
Based on the traditional self-training method, this paper proposes the SSL-based Gaussian process (GP) model, which is used to predict the resonant frequency of microstrip antennas (MSAs) that belongs to the regression problems. e SSL-based GP model proposed in this study includes two parts: initial training and self-training
In order to improve the optimal design efficiency of electromagnetic devices and save the time for collecting the training samples simulated by full wave electromagnetic software, this study proposes a semisupervised GP model, which covers initial training process and self-training process
Summary
For the optimization design of electromagnetic devices, some excellent research results have been achieved by numerical simulation calculation or combining full wave electromagnetic simulation software such as HFSS with global optimization algorithm, such as particle swarm optimization (PSO) [1]. GP is a machine learning method that has developed rapidly in recent years It has a strict statistical theoretical basis and is suitable for dealing with complex problems such as high dimensions, small samples, and nonlinearity [10, 11]. SSL is a learning method between supervised and unsupervised learning [15], mainly considering the combination of labeled samples and unlabeled samples to improve the learning efficiency, which is suitable for regression and classification problems. Based on the traditional self-training method, this paper proposes the SSL-based GP model, which is used to predict the resonant frequency of microstrip antennas (MSAs) that belongs to the regression problems. Rough the experiments of test functions and resonant frequency of three different MSAs, we can get the conclusion that the predictive ability of the proposed GP model in this study is better than that of the traditional supervised GP model
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