This paper proposes an advanced technique to develop combined neural network and pole-residue-based transfer function models for parametric modeling of electromagnetic (EM) behavior of microwave components. In this technique, neural networks are trained to learn the relationship between pole/residues of the transfer functions and geometrical parameters. The order of the pole-residue transfer function may vary over different regions of geometrical parameters. We develop a pole-residue tracking technique to solve this order-changing problem. After the proposed modeling process, the trained model can be used to provide accurate and fast prediction of the EM behavior of microwave components with geometrical parameters as variables. The proposed method can obtain better accuracy in challenging applications involving high dimension of geometrical parameter space and large geometrical variations, compared with conventional modeling methods. The proposed technique is effective and robust especially in solving high-order problems. This technique is illustrated by three examples of EM parametric modeling.

This article introduces the deep neural network method into the field of high-dimensional microwave modeling. Deep learning is nowadays highly successful in solving complex and challenging pattern recognition and classification problems. This article investigates the use of deep neural networks to solve microwave modeling problems that are much more challenging than that solved by the previous shallow neural networks. The most commonly used activation function in the existing deep neural network is the rectified linear unit (ReLU), which is a piecewise hard switch function. However, such a ReLU is not suitable for microwave modeling where the input-output relationships are smooth and continuous. In this article, we propose a new deep neural network to perform high-dimensional microwave modeling. A smooth ReLU is proposed for the new deep neural network. The proposed deep neural network employs both the sigmoid function and the smooth ReLU as activation functions. The new deep neural network can represent the smooth input-output relationship that is required for microwave modeling. An advanced three-stage deep learning algorithm is proposed to train the new deep neural network model. This algorithm can determine the number of hidden layers with sigmoid functions and those with smooth ReLUs in the training process. It can also overcome the vanishing gradient problem for training the deep neural network. The proposed deep neural network technique can solve microwave modeling problems in a higher dimension than the previous neural network method, i.e., shallow neural network method. Two high-dimensional parameter-extraction modeling examples of microwave filters are presented to demonstrate the proposed deep neural network technique.

This article presents an overview of artificial neural network (ANN) techniques for a microwave computer-aided design (CAD). ANN-based techniques are becoming useful for performing forward/inverse modeling for active/passive components to enhance a circuit design. With measured or simulated data of microwave devices, ANNs can be trained to learn relevant microwave relationships, which are, otherwise, computationally expensive or for which efficient analytical formulas are not available. Fundamental concepts of the ANN structure and training, such as feedforward neural networks (FFNNs), recurrent neural networks (RNNs)/dynamic neural networks (DNNs)/time-delay neural networks (TDNNs), deep neural networks, and neural network training and extrapolation, are described. Knowledge-based neural networks (KBNNs) are described for improving the accuracy and reliability of modeling and design optimization. Various advanced ANN techniques, such as neuro-transfer function (neuro-TF) modeling, neural network inverse modeling, and deep neural network modeling, are discussed. The existing and emerging applications of ANN in microwave CAD are identified, such as electromagnetic (EM)/multiphysics modeling, modeling of nonlinear circuits and transistors, filter design, very large-scale integration (VLSI) interconnects, oscillator, transmitter and receiver modeling, and CAD applications in such as gallium nitride (GaN) high electron-mobility transistor (HEMT), wireless power transfer (WPT), microelectromechanical system (MEMS), and substrate-integrated waveguide (SIW).

Space mapping is a recognized method for speeding up electromagnetic (EM) optimization. Existing space-mapping approaches belong to the class of surrogate-based optimization methods. This paper proposes a cognition-driven formulation of space mapping that does not require explicit surrogates. The proposed method is applied to EM-based filter optimization. The new technique utilizes two sets of intermediate feature space parameters, including feature frequency parameters and ripple height parameters. The design variables are mapped to the feature frequency parameters, which are further mapped to the ripple height parameters. By formulating the cognition-driven optimization directly in the feature space, our method increases optimization efficiency and the ability to avoid being trapped in local minima. The technique is suitable for design of filters with equal-ripple responses. It is illustrated by two microwave filter examples.

This paper proposes a pole-residue-based adjoint neuro-transfer function (neuro-TF) technique with electromagnetic (EM) sensitivity analysis for parametric modeling of EM behavior of microwave components with respect to changes in geometrical parameters. The purpose is to increase model accuracy by utilizing EM sensitivity information and to speed up model development by reducing the number of training data required for developing the model. The proposed parametric model consists of original and adjoint pole-residue based neuro-TF models. New formulations are derived for calculating the second-order derivatives for training the adjoint pole-residue-based neuro-TF model. An advanced pole-residue tracking technique is proposed to exploit the sensitivity information to track the splitting of poles as geometrical parameters change. This pole-residue tracking technique allows the model to bridge the differences of the orders of transfer function over different regions of the geometrical parameters, and ultimately form smooth and continuous functions between the pole/residues and the geometrical variables. The proposed technique addresses the challenges of tracking pole splitting when training data are limited. By exploiting the sensitivity information, the proposed technique can speed up the model development process over the existing pole-residue parametric modeling method which does not use sensitivity analysis.