Physics-Informed Machine Learning for the Efficient Modeling of High-Frequency Devices

In this paper, we present a machine learning technique based on analytic extension of eigenvalues and neural networks for the efficient modeling of high-frequency devices. In the proposed method, neural networks are used to learn the mapping between device's geometry and its modal equivalent circuit parameters. These circuit parameters are extracted from the eigen-decomposition of the deviceâs <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z$</tex-math></inline-formula>-parameters at a few sample frequencies. The eigenvalues and eigenvectors of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z$</tex-math></inline-formula>-matrix are analytically extended to other frequencies based on functional equations constructed from the lumped equivalent circuit model, from which the full electromagnetic response can be recovered. In addition to fully-connected neural network layers, our proposed model introduces an analytical projection branch based on AEE principles to maximize the information gain from samples in the training dataset. To improve the robustness and efficiency of the learning process, we introduce an adaptive gradient update algorithm. The overall model is end-to-end differentiable and can be integrated into gradient-based optimization methods. Numerical examples are provided to demonstrate the capability of the proposed method. Compared with traditional neural network-based models, the proposed approach achieves higher accuracy using fewer data samples and generalizes better to out-of-domain inputs.