This paper proposes a novel technique to develop a low-cost electromagnetic (EM) centric multiphysics parametric model for microwave components. In the proposed method, we use space mapping techniques to combine the computational efficiency of EM single physics (EM only) simulation with the accuracy of the multiphysics simulation. The EM responses with respect to different values of geometrical parameters in nondeformed structures without considering other physics domains are regarded as coarse model. The coarse model is developed using the parametric modeling methods such as artificial neural networks or neuro-transfer function techniques. The EM responses with geometrical and nongeometrical design parameters as variables in the practical deformed structures due to thermal and structural mechanical stress factors are regarded as fine model. The fine model represents the behavior of EM centric multiphysics responses. The proposed model includes the EM domain coarse model and two mapping neural networks to map the EM domain (single physics) to the multiphysics domain. Our proposed technique can achieve good accuracy for multiphysics parametric modeling with fewer multiphysics training data and less computational cost. After the modeling process, the proposed model can be used to provide accurate and fast prediction of EM centric multiphysics responses of microwave components with respect to the changes of design parameters within the training ranges. The proposed technique is illustrated by a tunable four-pole waveguide filter example at 10.5-11.5 GHz and an iris coupled microwave cavity filter example at 690-720 MHz.

This article proposes a novel parallel gradient-based electromagnetic (EM) optimization approach to microwave components using adjoint-sensitivity-based neuro-transfer function (neuro-TF) surrogate. In the proposed technique, the surrogate model is trained using not only the input-output behavior but also the adjoint sensitivity information generated from the EM simulation simultaneously. By exploiting adjoint EM sensitivity for surrogate modeling, the proposed technique can obtain accurate surrogate models with larger valid range using the same amount of fine model evaluations compared with the existing gradient-based surrogate optimization without adjoint sensitivity. Furthermore, because the surrogate model is developed using adjoint EM sensitivity, the gradients calculated using the developed surrogate model in the proposed technique are much more accurate. The accurate gradients lead to further speedup of the surrogate optimization and improved quality of surrogate optimal solution in each surrogate optimization iteration. Since the surrogate model is valid in a large neighborhood and the gradients are sufficiently accurate, the proposed technique can achieve the optimal EM solution faster than the existing gradient-based surrogate optimization without adjoint sensitivity. Three examples of EM optimizations of microwave components are used to demonstrate the proposed technique.

Space mapping is a recognized surrogate-based optimization method to accelerate the electromagnetic (EM) design. In this article, for the first time, space mapping is elevated from solving the problem of EM optimization to solving the problem of multiphysics optimization for high power microwave filters. Multiphysics analysis, which involves the EM domain with other physics domains, is increasingly important for high-performance microwave components to obtain an accurate system design. To speed up the multiphysics design, a space-mapping-based surrogate model including a coarse model and two mapping functions is proposed in this article. We propose to use EM single physics responses as the coarse model to provide good approximations to fine model multiphysics responses. To avoid repetitive EM simulations during the surrogate model training and optimization process, the coarse model is developed using an artificial neural network (ANN). Frequency mapping and explicit input mapping are further performed to develop the proposed surrogate model. Multiple EM and multiphysics training samples are evaluated in parallel to develop the surrogate model. A trust-region algorithm, tailored to the space-mapping-based multiphysics optimization technique, is proposed to improve the convergence. By exploiting the knowledge of the coarse model established by relatively inexpensive EM data, the proposed technique can provide a larger and more efficient optimization update in each optimization iteration, consequently obtaining optimal solutions faster than the existing multiphysics optimization without space mapping. Two examples of multiphysics optimization of high-power microwave filters are used to validate the proposed technique.

Artificial neural network technique has gained recognition as a powerful technique in microwave modeling and design. This paper proposes a novel deep neural network topology for parametric modeling of microwave components. In the proposed deep neural network, the outputs are S-parameters. The inputs of the proposed model include geometrical variables and the frequency. We divide the hidden layers in the proposed deep neural network topology into two parts. Hidden layers in Part I handle both the geometrical inputs and the frequency inputs while hidden layers in Part II only handle the geometrical inputs. In this way, more training parameters are utilized to specifically learn the relationship between the Sparameters and the geometrical variables, which are more complicated than that between the S-parameters and the frequency. The purpose is to reduce the total number of training parameters in the deep neural network model. New formulations are derived to calculate the derivatives of the error function with respect to training parameters in the deep neural network. Taking advantage of the calculated derivatives, we propose an advanced two-stage training algorithm for the deep neural network. The two-stage training algorithm can determine the number of hidden layers in both parts during the training process and guarantee that the proposed deep neural network model can achieve the required model accuracy. The proposed deep neural network can achieve similar model accuracy with less training parameters compared to the commonly used fully connected neural network. The proposed technique is demonstrated by two microwave parametric modeling examples.

For the high-performance microwave component and system design, besides electromagnetic (EM) physics domain, we also need to consider the operation of the real-world multiphysics (MP) environment that contains the effects of other physics domains. EM-centric MP analysis and design optimization become very important. In this article, for the first time, we develop a novel parallel EM-centric multiphysics optimization (MPO) technique. In our proposed technique, the pole/residue-based transfer function is exploited to build an effective and robust surrogate model. A group of modified quadratic mapping functions is formulated to map the relationships between pole/residues of the transfer function and the design variables. Multiple EM-centric MP evaluations are performed in parallel to generate the training samples for establishing the surrogate model. Using our proposed technique, the surrogate model can be valid in a relatively large neighborhood, which makes an effective and large optimization update in each optimization iteration. The trust region algorithm is performed to guarantee the convergence of the proposed MPO algorithm. Our proposed MPO technique takes a small number of iterations to obtain the optimal EM-centric MP response. Two microwave filter examples are used to demonstrate the validity of the proposed technique.