Abstract
This paper deals with the development of a Machine Learning (ML)-based regression for the construction of complex-valued surrogate models for the analysis of the frequency-domain responses of electromagnetic (EM) structures. The proposed approach relies on the combination of two-techniques: (i) the principal component analysis (PCA) and (ii) an unusual complex-valued formulation of the Least Squares Support Vector Machine (LS-SVM) regression. First, the training and test dataset is obtained from a set of parametric electromagnetic simulations. The spectra collected in the training set are compressed via the PCA by exploring the correlation among the available data. In the next step, the compressed dataset is used for the training of compact set of complex-valued surrogate models and their accuracy is evaluated on the test samples. The effectiveness and the performance of the complex-valued LS-SVM regression with three kernel functions are investigated on two application examples consisting of a serpentine delay structure with three parameters and a high-speed link with four parameters. Moreover, for the last example, the performance of the proposed approach is also compared with those provided by a real-valued multi-output feedforward Neural Network model.
Highlights
In recent decades, Machine Learning (ML) methods have been widely applied to construct accurate and fast-to-evaluate surrogate models able to reproduce the input– output behavior of electromagnetic (EM) structures as a function of deterministic and uncertain parameters [1,2,3,4,5,6,7,8,9,10,11,12,13,14]
In the above scenario, advanced data-driven and ML-based regressions, such as Polynomial Chaos Expansion [1,2,3,4], Support Vector Machine (SVM) regression [5,6], Least-Squares Support Vector Machine (LS-SVM) regression [7], Gaussian Process regression (GPR) [8], and feedforward [9,10,11,12], deep [12,13], convolutional [12] and Long Short-Term Memory (LSTM) [14] neural networks (NNs), have been successful applied to uncertainty quantification (UQ) and optimization in EM applications
This paper investigates the performances of a pure-complex implementation of a kernel-based ML technique such as the LS-SVM regression
Summary
Machine Learning (ML) methods have been widely applied to construct accurate and fast-to-evaluate surrogate models able to reproduce the input– output behavior of electromagnetic (EM) structures as a function of deterministic and uncertain parameters [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. This paper investigates the performances of a pure-complex implementation of a kernel-based ML technique such as the LS-SVM regression. The performance of compressed surrogate models constructed via the dual-channel and the pure complex-value LS-SVM regression with a complex and pseudo kernel are investigated by considering the frequency-domain responses of two test-cases consisting of a serpentine delay structure and a high-speed link, with three and four parameters, respectively.
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