In this article we review state-of-the-art concepts of space mapping and place them con- textually into the history of design optimization and modeling of microwave circuits. We formulate a generic space-mapping optimization algorithm, explain it step-by-step using a simple microstrip filter example, and then demonstrate its robustness through the fast design of an interdigital filter. Selected topics of space mapping are discussed, including implicit space mapping, gradient-based space mapping, the optimal choice of surrogate model, and tuning space mapping. We consider the application of space mapping to the modeling of microwave structures. We also discuss a software package for automated space-mapping optimization that involves both electromagnetic (EM) and circuit simulators.

In this letter, we propose an efficient hybrid sampling method for microwave component modeling and optimization. The sampling method adaptively chooses samples from global and local samples to form a data set. The local samples are obtained using a greedy-like sampling method to exploit potential optimal solutions. The global samples are chosen using random sampling with minimum distance rejection to ensure the uniformity of the samples in the design space. The obtained data set is used to establish a surrogate model using the artificial neural networks (ANNs), and the optimal design parameters are obtained by optimizing the ANN model. A bandstop microstrip filter is taken as an example to verify the performance of the sampling method. The results show that the ANN model based on the proposed method achieves better modeling performance and yields better optimal design than the ANN model based on conventional sampling methods.

Reconfigurable intelligent surfaces (RISs) are of potential use in wireless communication systems due to their ability to perform beam steering, harmonic wave manipulation, and polarization conversion. However, the main challenge in designing RISs is to obtain their electromagnetic (EM) responses, which is time-consuming and computationally prohibitive. In this work, an efficient modeling method is proposed for fast evaluation of the reflection coefficient and far filed patterns of RISs. The proposed method utilizes the microwave network theory to compute the accurate reflection coefficient of RISs elements under the illumination of incident waves from arbitrary directions. Compared to the classical equivalent circuit model, it enables the separate design of meta-atoms and tunable devices at the network level. The proposed method is verified by the full-wave simulation results of two RIS elements and experimental results of a 3-bit RIS. This work forms a fast and feasible route to obtain the responses of RISs, which allows the RISs to find extensive applications in many scenarios.

This communication presents a novel surrogate-assisted Quasi-Newton enhanced global optimization algorithm. In this proposed method, the heuristic hypersphere sampling method is used to obtain representative samples. The surrogate model is built based on the low-fidelity model. The Quasi-Newton enhanced differential evolution method is designed to optimize the surrogate model. Finally, the optimal design of a high-fidelity model is obtained through a space mapping procedure. The proposed algorithm is verified through two antenna design examples including a dipole antenna with balun and a SIW cavity-backed slot antenna. The results show that the proposed algorithm finds a more accurate minimum value with less computational time than direct optimization using differential evolution.

Convergence is a well-known issue for standard space-mapping optimization algorithms. It is heavily dependent on the choice of coarse model, as well as the space-mapping transformations employed in the optimization process. One possible convergence safeguard is the trust region approach where a surrogate model is optimized in a restricted neighborhood of the current iteration point. In this paper, we demonstrate that although formal conditions for applying trust regions are not strictly satisfied for space-mapping surrogate models, the approach improves the overall performance of the space-mapping optimization process. Further improvement can be realized when approximate fine model Jacobian information is exploited in the construction of the space-mapping surrogate. A comprehensive numerical comparison between standard and trust-region-enhanced space mapping is provided using several examples of microwave design problems.

We present a robust space mapping (SM) algorithm exploiting electromagnetic (EM)-based adjoint sensitivities for microwave design optimization. Our approach utilizes low-cost EM-based adjoint sensitivities and trust region methods to improve an SM algorithm at three levels, which are: 1) to build a better overall surrogate while ensuring convergence; 2) to speed up and safeguard the parameter extraction steps; and 3) to speed up and safeguard the surrogate optimization process. We describe the implementation at each level in detail. We review relevant adjoint sensitivity analysis methods. We also review prior SM methods that exploit both sensitivity and adjoint sensitivity. We summarize these methods in four categories. We compare our proposed approach with them. Efficiency, robustness, and versatility of our method are demonstrated by three design examples: an antenna, a planar filter, and a 3-D resonator filter. We compare the results with those obtained by SM without using adjoint sensitivity information and by direct optimization of the high-fidelity EM models.