We review the space-mapping (SM) technique and the SM-based surrogate (modeling) concept and their applications in engineering design optimization. For the first time, we present a mathematical motivation and place SM into the context of classical optimization. The aim of SM is to achieve a satisfactory solution with a minimal number of computationally expensive "fine" model evaluations. SM procedures iteratively update and optimize surrogates based on a fast physically based "coarse" model. Proposed approaches to SM-based optimization include the original algorithm, the Broyden-based aggressive SM algorithm, various trust-region approaches, neural SM, and implicit SM. Parameter extraction is an essential SM subproblem. It is used to align the surrogate (enhanced coarse model) with the fine model. Different approaches to enhance uniqueness are suggested, including the recent gradient parameter-extraction approach. Novel physical illustrations are presented, including the cheese-cutting and wedge-cutting problems. Significant practical applications are reviewed.

https://desi.iteso.mx/erayas/documents/CirOpt_course/Lectures/Space_Mapping/Bandler_04Jan_SM_State_of_the_Art.pdf

Space mapping: the state of the art

[1] Surrogate modeling, also called metamodeling, has evolved and been extensively used over the past decades. A wide variety of methods and tools have been introduced for surrogate modeling aiming to develop and utilize computationally more efficient surrogates of high-fidelity models mostly in optimization frameworks. This paper reviews, analyzes, and categorizes research efforts on surrogate modeling and applications with an emphasis on the research accomplished in the water resources field. The review analyzes 48 references on surrogate modeling arising from water resources and also screens out more than 100 references from the broader research community. Two broad families of surrogates namely response surface surrogates, which are statistical or empirical data-driven models emulating the high-fidelity model responses, and lower-fidelity physically based surrogates, which are simplified models of the original system, are detailed in this paper. Taxonomies on surrogate modeling frameworks, practical details, advances, challenges, and limitations are outlined. Important observations and some guidance for surrogate modeling decisions are provided along with a list of important future research directions that would benefit the common sampling and search (optimization) analyses found in water resources.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2011WR011527

Review of surrogate modeling in water resources

Neural-network computational modules have recently gained recognition as an unconventional and useful tool for RF and microwave modeling and design. Neural networks can be trained to learn the behavior of passive/active components/circuits. A trained neural network can be used for high-level design, providing fast and accurate answers to the task it has learned. Neural networks are attractive alternatives to conventional methods such as numerical modeling methods, which could be computationally expensive, or analytical methods which could be difficult to obtain for new devices, or empirical modeling solutions whose range and accuracy may be limited. This tutorial describes fundamental concepts in this emerging area aimed at teaching RF/microwave engineers what neural networks are, why they are useful, when they can be used, and how to use them. Neural-network structures and their training methods are described from the RF/microwave designer's perspective. Electromagnetics-based training for passive component models and physics-based training for active device models are illustrated. Circuit design and yield optimization using passive/active neural models are also presented. A multimedia slide presentation along with narrative audio clips is included in the electronic version of this paper. A hyperlink to the NeuroModeler demonstration software is provided to allow readers practice neural-network-based design concepts.

/pdf/artificial-neural-networks-for-rf-and-microwave-design-from-4388sc237c.pdf

Artificial neural networks for RF and microwave design - from theory to practice

We offer space mapping (SM), a fundamental new theory to circuit optimization utilizing a parameter space transformation. This technique is demonstrated by the optimization of a microstrip structure for which a convenient analytical/empirical model is assumed to be unavailable. For illustration, we focus upon a three-section microstrip impedance transformer and a double folded stub microstrip filter and explore various design characteristics utilizing an electromagnetic (EM) field simulator. We propose two distinct EM models: coarse for fast computations, and the corresponding fine for a few more accurate and well-targeted simulations. The coarse model, useful when circuit-theoretic models are not readily available, permits rapid exploration of different starting points, solution robustness, local minima, parameter sensitivities, yield-driven design and other design characteristics within a practical time frame. The computationally intensive fine model is used to verify the space-mapped designs obtained exploiting the coarse model, as well as in the SM process itself. >

Space mapping technique for electromagnetic optimization

The integration of optimization methodologies with computational analyses/simulations has a profound impact on the product design. Such integration, however, faces multiple challenges. The most eminent challenges arise from high-dimensionality of problems, computationally-expensive analysis/simulation, and unknown function properties (i.e., black-box functions). The merger of these three challenges severely aggravates the difficulty and becomes a major hurdle for design optimization. This paper provides a survey on related modeling and optimization strategies that may help to solve High-dimensional, Expensive (computationally), Black-box (HEB) problems. The survey screens out 207 references including multiple historical reviews on relevant subjects from more than 1,000 papers in a variety of disciplines. This survey has been performed in three areas: strategies tackling high-dimensionality of problems, model approximation techniques, and direct optimization strategies for computationally-expensive black-box functions and promising ideas behind non-gradient optimization algorithms. Major contributions in each area are discussed and presented in an organized manner. The survey exposes that direct modeling and optimization strategies to address HEB problems are scarce and sporadic, partially due to the difficulty of the problem itself. Moreover, it is revealed that current modeling research tends to focus on sampling and modeling techniques themselves and neglect studying and taking the advantages of characteristics of the underlying expensive functions. Based on the survey results, two promising approaches are identified to solve HEB problems. Directions for future research are also discussed.

/pdf/survey-of-modeling-and-optimization-strategies-to-solve-high-1tg25zsec9.pdf

Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions

We propose a significantly improved space mapping (SM) strategy for electromagnetic (EM) optimization. Instead of waiting for upfront EM analyses at several base points, our new approach aggressively exploits every available EM analysis, producing dramatic results right from the first step. We establish a relationship between the novel SM optimization and the quasi-Newton iteration for solving a system of nonlinear equations. Approximations to the matrix of first-order derivatives are updated by the classic Broyden formula. A high-temperature superconducting microstrip filter design solution emerges after only six EM simulations with sparse frequency sweeps. Furthermore, less CPU effort is required to optimize the filter than is required by one single detailed frequency sweep. We also extend the SM concept to the parameter extraction phase, overcoming severely misaligned responses induced by inadequate empirical models. This novel concept should have a significant impact on parameter extraction of devices.

Electromagnetic optimization exploiting aggressive space mapping

The authors review the current state of the art in circuit optimization, emphasizing techniques suitable for modern microwave CAD (computer-aided design). The main thrust in the field is currently the solution of realistic design and modeling problems, addressing such concepts as physical tolerances and model uncertainties. A unified hierarchical treatment of circuit models forms the basis of the presentation. It exposes tolerance phenomena at different parameter/response levels. The concepts of design centering, tolerance assignment, and postproduction tuning in relation to yield enhancement and cost reduction suitable for integrated circuits are discussed. Suitable techniques for optimization oriented worst-case and statistical design are reviewed. A generalized l/sub p/ centering algorithm is proposed and discussed. Multicircuit optimization directed at both CAD and robust device modeling is formalized. Tuning is addressed in some detail, both at the design stage and for production alignment. State-of-the-art gradient-based nonlinear optimization methods are reviewed with emphasis given to recent, but well tested, advances in minimax, l/sub 1/, and l/sub 2/ optimization. >

/pdf/circuit-optimization-the-state-of-the-art-2yre9izylm.pdf

Circuit optimization: the state of the art

A new robust algorithm for EM optimization of microwave circuits is presented. The algorithm integrates a trust region methodology with aggressive space mapping (ASM). A new automated multipoint parameter extraction process is implemented. EM optimization of a double-folded stub filter and of an HTS filter illustrate our new results.

/pdf/a-trust-region-aggressive-space-mapping-algorithm-for-em-48hy71qyvz.pdf

A trust region aggressive space mapping algorithm for EM optimization

A robust new algorithm for electromagnetic (EM) optimization of microwave circuits is presented. The algorithm (TRASM) integrates a trust region methodology with the aggressive space mapping (ASM). The trust region ensures that each iteration results in improved alignment between the coarse and fine models needed to execute ASM. The parameter extraction step is a crucial part of the ASM technique. The nonuniqueness of this step may result in the divergence of the technique. To improve the uniqueness of the extraction phase, we developed a recursive multipoint parameter extraction. This suggested step exploits all the available EM simulations for improving the uniqueness of parameter extraction. The new algorithm was successfully used to design a number of microwave circuits. Examples include the EM optimization of a double-folded stub filter and of a high-temperature superconducting (HTS) filter using Sonnet's em. The proposed algorithm was also used to design two-section, three-section, and seven-section waveguide transformers exploiting Maxwell Eminence. The design of a three-section waveguide transformer with rounded corners was carried out using HP HFSS. We show how the mapping can be used to carry out Monte Carlo analysis using only coarse model simulations.

S.H. Chen

Papers

Space mapping technique for electromagnetic optimization

Electromagnetic optimization exploiting aggressive space mapping

Circuit optimization: the state of the art

A trust region aggressive space mapping algorithm for EM optimization

A trust region aggressive space mapping algorithm for EM optimization