Jianguo Xue

The vector fitting (VF) technique is popularly used in neural network-transfer function (neuro-TF) modeling methods for electromagnetic (EM) behaviors of microwave filters. However, VF often produces nonsmooth and discontinuous transfer function (TF) coefficients under large geometrical variations, which degrade training stability and model accuracy. To address this issue, this article proposes a novel autoencoder-based neural network-TF (AENN-TF) parametric modeling method for EM behavior of microwave filters. In the proposed method, an advanced autoencoder (AE)-based feature parameter extraction technique is incorporated to develop a smooth relationship of TF parameters with respect to geometrical variables. This smooth relationship improves the neural network training accuracy, consequently improving the overall AENN-TF modeling accuracy for EM behavior. Novel derivative formulations are derived for the proposed model structure in order to perform fast gradient-based overall model training. Furthermore, we develop a novel four-step training framework with detailed modeling processes for the proposed AENN-TF modeling method. Compared to existing neuro-TF methods with the VF technique, the proposed AENN-TF method achieves better accuracy and robustness. The superior performance of the proposed method over existing neuro-TF methods is further demonstrated through two microwave application examples.

Space mapping (SM) accelerates full-wave electromagnetic (EM) optimization, but its efficiency depends strongly on the quality of the coarse model. In reduced-order modeling (ROM)-based SM, a reduced basis constructed at a nominal design may lose approximation capability under geometric deviations, thereby restricting the validity region of the reduced-order coarse model (ROCM). To address this issue, this article presents a common projection subspace (CPS)-based reduced-order coarse-modeling approach for ROM-based SM. By constructing a CPS from reduced bases extracted at multiple neighboring geometries, the proposed method improves the local modeling validity of the ROCM over the sampled neighborhood within each SM iteration while preserving high computational efficiency. Combined with mesh-deformation techniques, the method enables efficient coarse-model updating without repeated remeshing. Three representative microwave design examples, together with comparisons against direct EM optimization, mesh SM (MSM), aggressive SM (ASM), and nominal-basis ROM-SM, demonstrate that the proposed coarse-modeling strategy can reduce the number of SM iterations and total CPU cost in the tested cases while maintaining comparable final design accuracy.

Quantum computing in the electromagnetic (EM) field represents a transformative frontier with significant potential for advancement. Recent studies have demonstrated the potential of quantum computing for solving waveguide mode problems, solving finite element method (FEM) equations for EM problems, and scaling the FEM solution. Among these applications, the Harrow–Hassidim–Lloyd (HHL) algorithm is an algorithm with large quantum advantages and has attracted attention. However, existing quantum methods remain constrained by the problem that the quantum-based FEM solution only obtains electric field magnitude and lacks phase information. The lack of phase information results in the inability to solve an important characteristic of EM problems: scattering parameters (S-parameters). To address the above issue, this work proposes a novel quantum method of calculating multiport S-parameter magnitudes based on FEM and HHL algorithm for microwave components. The proposed method introduces novel mathematical formulations optimized for quantum architectures. To streamline the quantum computation process and avoid the need for multiple quantum circuit simulations for each S-parameter, we design an integrated quantum circuit capable of computing magnitudes of all multiport S-parameters within a single execution. Furthermore, a specific matrix-scaling method is also developed to simplify the proposed circuits. The specific matrix-scaling method is used to improve the condition of the FEM matrix and reduce the complexity of the designed quantum circuits. The proposed method is validated using two microwave structures, demonstrating how our proposed quantum method computes S-parameter magnitudes in practical EM applications.

Electromagnetic (EM) optimization of microwave components often relies on repeated full-wave simulations, which can be time-consuming even for routine design tasks. Existing acceleration techniques such as mesh space mapping (MSM) typically require manual coarse-mesh tuning and coarse–fine fitting, limiting automation and reproducibility. To address these issues, this article presents a multilevel model order reduction (MOR) framework that derives a reduced-order coarse model (ROCM) directly from the fine model, thereby avoiding mesh coarsening and empirical fitting. The first level enables rapid broadband evaluation via frequency-domain reduction; the second reuses a shared projection basis across nearby geometries with adaptive updates when surrogate error grows. Geometry changes are accommodated through mesh deformation, and sensitivities are computed efficiently by restricting adjoint-based updates to perturbed elements. The proposed method is validated on multiple waveguide filter designs and compared against direct fine-mesh optimization, single-level MOR, and MSM. Across the reported cases, the proposed method achieves the shortest total runtime while maintaining fine-model accuracy and stable convergence, eliminating the need for coarse-mesh construction and surrogate fitting. These results demonstrate a robust, automated workflow that combines high fidelity with substantial computational savings over practical design ranges.

The model order reduction (MOR)-based modeling method combining neural networks and the transfer function (neuro-TF) is widely used for efficient parametric modeling of electromagnetic (EM) behaviors in microwave components. However, the order of MOR is usually required to be much higher than the actual order of the microwave components to achieve accurate EM solutions. This extra order by MOR results in a high possibility of uncertainty and discontinuity of the extracted extra poles/zeros with respect to geometrical variations for neuro-TF model development. To address the above issue, this article proposes a novel dominant-order-based pole/zero matching technique for parametric modeling, incorporating dominant-order-based transfer functions and neural networks (short for neuro-DTF). The proposed dominant-order-based pole/zero matching technique is to identify dominant poles and zeros through a novel adaptive variable-order reduction process. Dominant poles and zeros are screened and retained by matching successive high- and low-order reduced systems, and nondominant poles and zeros are transferred into a complex exponential function. By combining the dominant poles and zeros with the complex exponential function, the dominant-order-based transfer function is obtained. The core objective is to retain poles and zeros with dominant influence on key frequency bands while simplifying nondominant dynamics. The proposed technique effectively eliminates pole/zero mismatch issues caused by the uncertainty and discontinuity of the extracted extra poles/zeros with respect to geometrical variations. Compared to conventional MOR-based neuro-TF parametric modeling, the proposed neuro-DTF method, incorporating the dominant-order-based pole/zero matching technique, achieves higher accuracy and robustness, especially under large geometrical parameter variations. Its effectiveness is verified through two microwave examples.

The neuro-transfer function (Neuro-TF) modeling approach has been widely used to accelerate the electromagnetic (EM) modeling and optimization process. In the standard Neuro-TF approach, the extracted transfer function (TF) parameters (e.g., poles/residues or zeros/poles) are complex values in the real frequency domain (i.e., the $j\omega $ -axis). Since the complex TF parameters are in the Laplace domain, the standard Neuro-TF approach inherently has a nonuniqueness parameter extraction issue with respect to geometrical parameters change. This article addresses this issue and proposes a robust parameter extraction technique based on complex-frequency-domain (CFD) EM behavior for Neuro-TF modeling of microwave filters. We approximately consider the real domain of CFD as a loss in this article. Therefore, we want to extract TF parameters not only from the frequency domain but also from the loss domain. In the proposed technique, we introduce the model-order reduction (MOR) technique to expedite the parameter extraction process, enabling fast frequency and loss sweeps simultaneously. The introduction of the MOR technique avoids the discrete solving of the EM response of each loss in the CFD, thus expediting the proposed parameter extraction process. The extracted parameters using the proposed technique have better correspondence with the information of CFD, improving the smoothness of extracted TF parameters. Therefore, the proposed technique enhances the robustness of TF parameter extraction and subsequently improves the accuracy of the Neuro-TF modeling over a relatively wide geometrical range. This article utilizes five microwave filter examples to demonstrate the advantages of the proposed method.

Model order reduction (MOR)-based neuro-transfer function (neuro-TF) method has become a trendy modeling technique for parametric modeling of microwave components. This article proposes a novel electromagnetic (EM) parametric modeling method for microwave filters incorporating multivalued neural networks (MNNs) and transfer functions (short for MNN-TFs). The original poles/zeros directly extracted through MOR are mismatched in different sequences for different geometrical samples, which is called the mismatch issue. In the proposed modeling approach, we develop an MNN-based pole-/zero-sorting algorithm to solve this issue. The proposed sorting algorithm introduces MNN to guide the sorting of poles and zeros with respect to geometrical variations. A classification method is proposed to divide the poles/zeros into subgroups for more effective sorting using MNNs. After the classification process, the poles/zeros in all the subgroups are automatically sorted using separate MNNs. Then the pole-/zero-matching is performed between the original poles/zeros and the predicted poles/zeros. The proposed sorting algorithm can obtain more continuous and smoother poles/zeros without EM sensitivity information. After the proposed sorting process, the sorted poles and zeros are used for preliminary training of neural networks, which can provide good initialization weights for the overall model. Finally, we perform overall neural network training to establish the MNN-TF model. The proposed method can obtain a more accurate overall model than the existing MOR-based neuro-TF methods, especially in cases of large geometrical variations. The trained MNN-TF model can be used for advanced circuit design, greatly accelerating the speed of high-level system design. The effectiveness of the proposed method is verified by two microwave examples of parametric modeling.