Implicit space mapping optimization exploiting preassigned parameters
TL;DR: The idea of implicit space mapping (ISM) is introduced and how it relates to the well-established (explicit) space mapping between coarse and fine device models is shown.
Abstract: We introduce the idea of implicit space mapping (ISM) and show how it relates to the well-established (explicit) space mapping between coarse and fine device models. Through comparison, a general space mapping concept is proposed. A simple algorithm based on the novel ISM concept is implemented. It is illustrated on a contrived "cheese-cutting problem" and is applied to electromagnetics-based microwave modeling and design. An auxiliary set of parameters (selected preassigned parameters) is extracted to match the coarse model with the fine model. The calibrated coarse model (the surrogate) is then (re)optimized to predict a better fine model solution. This is an easy space mapping technique to implement since the mapping itself is embedded in the calibrated coarse model and updated automatically in the procedure of parameter extraction. We illustrate our approach through optimization of a high-temperature superconducting filter using Agilent ADS with Momentum and Agilent ADS with Sonnet's em.
Citations
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TL;DR: For the first time, a mathematical motivation is presented and SM is placed into the context of classical optimization to achieve a satisfactory solution with a minimal number of computationally expensive "fine" model evaluations.
Abstract: 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.
1,044 citations
Additional excerpts
...Neural inverse space mapping (NISM) simplifies (re)optimization by inversely connecting the ANN [17]....
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Journal Article•
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TL;DR: A generic space-mapping optimization algorithm is formulated, explained step-by-step using a simple microstrip filter example, and its robustness is demonstrated through the fast design of an interdigital filter.
Abstract: 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.
327 citations
Cites background from "Implicit space mapping optimization..."
...Implicit Space Mapping Among the developments in the art of space mapping, implicit space mapping [31], [39], [42] is probably the simplest technique to implement....
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TL;DR: A comprehensive approach to engineering design optimization exploiting space mapping (SM) using a new generalization of implicit SM to minimize the misalignment between the coarse and fine models of the optimized object over a region of interest.
Abstract: This paper presents a comprehensive approach to engineering design optimization exploiting space mapping (SM). The algorithms employ input SM and a new generalization of implicit SM to minimize the misalignment between the coarse and fine models of the optimized object over a region of interest. Output SM ensures the matching of responses and first-order derivatives between the mapped coarse model and the fine model at the current iteration point in the optimization process. We provide theoretical results that show the importance of the explicit use of sensitivity information to the convergence properties of our family of algorithms. Our algorithm is demonstrated on the optimization of a microstrip bandpass filter, a bandpass filter with double-coupled resonators, and a seven-section impedance transformer. We describe the novel user-oriented software package SMF that implements the new family of SM optimization algorithms
296 citations
Cites background or methods from "Implicit space mapping optimization..."
...It provides sockets to popular simulators (e.g., Sonnet’s em, Agilent’s ADS, and FEKO) that allow automatic fine/coarse model data acquisition and, consequently, fully automatic SM optimization....
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...5, 8, and 10–13 are available online at http://ieeexplore.ieee.org....
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TL;DR: It is found that time savings are highly problem dependent and that MFM methods provided time savings up to 90% and guidelines for authors to present their MFM savings in a way that is useful to future MFM users are included.
Abstract: Simulations are often computationally expensive and the need for multiple realizations, as in uncertainty quantification or optimization, makes surrogate models an attractive option. For expensive high-fidelity models (HFMs), however, even performing the number of simulations needed for fitting a surrogate may be too expensive. Inexpensive but less accurate low-fidelity models (LFMs) are often also available. Multi-fidelity models (MFMs) combine HFMs and LFMs in order to achieve accuracy at a reasonable cost. With the increasing popularity of MFMs in mind, the aim of this paper is to summarize the state-of-the-art of MFM trends. For this purpose, publications in this field are classified based on application, surrogate selection if any, the difference between fidelities, the method used to combine these fidelities, the field of application and the year published.
Available methods of combining fidelities are also reviewed, focusing our attention especially on multi-fidelity surrogate models in which fidelities are combined inside a surrogate model. Computation time savings are usually the reason for using MFMs, hence it is important to properly report the achieved savings. Unfortunately, we find that many papers do not present sufficient information to determine these savings. Therefore, the paper also includes guidelines for authors to present their MFM savings in a way that is useful to future MFM users. Based on papers that provided enough information, we find that time savings are highly problem dependent and that MFM methods we surveyed provided time savings up to 90%.
Keywords: Multi-fidelity, Variable-complexity, Variable-fidelity, Surrogate models, Optimization, Uncertainty quantification, Review, Survey
217 citations
Cites background from "Implicit space mapping optimization..."
...The space mapping concept has been extended to include aggressive space mapping [16], trust regions [10], artificial neural networks [11], implicit space mapping [18], neural-based space mapping [197] [198], inverse problems [151], corrected space mapping [156] and tuning space mapping [100]....
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TL;DR: 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 and can obtain better accuracy in challenging applications involving high dimension of geometric parameter space and large geometrical variations, compared with conventional modeling methods.
Abstract: 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.
148 citations
Cites background from "Implicit space mapping optimization..."
...Implicit space mapping [86], [87] explores the flexibility of the preassigned parameter such as dielectric constant, substrate height in the design optimization process....
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...Efforts on space mapping have focused on several areas, such as implicit space mapping [86], [87], output space mapping [88]−[90], neural space mapping [91]−[95], generalized space mapping [96], tuning space mapping [97], [98], portable space mapping [99], parallel space mapping [25], coarse and fine mesh space mapping [100], [101]....
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References
More filters
Journal Article•
TL;DR: A brief history of microwave engineering is given in this paper, where the impact of computer-aided design and monolithic microwave integrated circuits on microwave design is examined, along with suggestions for related studies that would be useful to the microwave engineer.
Abstract: A brief history of microwave engineering is given. The impact of computer-aided design and monolithic microwave integrated circuits on microwave design is examined. The career potential of microwave engineering is discussed, along with suggestions for related studies that would be useful to the microwave engineer. >
3,169 citations
"Implicit space mapping optimization..." refers methods in this paper
...The design specifications are for GHz and for GHz for GHz GHz This corresponds to 1.25% bandwidth....
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...This mapping is iteratively updated....
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...This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant OGP0007239 and Grant STR234854-00 through the Micronet Network of Centres of Excellence and Bandler Corporation....
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...We can show that, after the modeling procedure, the prediction is (11) This agrees with the steps of aggressive SM [3] using a unit mapping....
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...This contrasts with [13], where the mapping is explicit [see Fig....
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TL;DR: For the first time, a mathematical motivation is presented and SM is placed into the context of classical optimization to achieve a satisfactory solution with a minimal number of computationally expensive "fine" model evaluations.
Abstract: 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.
1,044 citations
"Implicit space mapping optimization..." refers background in this paper
...0018-9480/04$20.00 © 2004 IEEE iteration, then the solution (best current prediction of the fine model) can be evaluated directly....
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TL;DR: In this article, the authors propose space mapping (SM) for circuit optimization utilizing a parameter space transformation, which is demonstrated by the optimization of a microstrip structure for which a convenient analytical/empirical model is assumed to be unavailable.
Abstract: 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. >
584 citations
TL;DR: In this paper, the authors proposed a significantly improved space mapping (SM) strategy for electromagnetic (EM) optimization, which leverages every available EM analysis, producing dramatic results right from the first step, instead of waiting for upfront EM analyses at several base points.
Abstract: 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.
387 citations
"Implicit space mapping optimization..." refers background or methods in this paper
...Both use an iterative approach to update the mapping and predict the new design....
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...The width (preassigned parameter) of the (coarse) model is shrunk to 2.4 units to match the fine model weight (parameter extraction)....
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TL;DR: In this paper, the authors presented modeling of microwave circuits using artificial neural networks (ANN's) based on space-mapping (SM) technology, which decrease the cost of training, improve generalization ability, and reduce the complexity of the ANN topology with respect to the classical neuromodeling approach.
Abstract: For the first time, we present modeling of microwave circuits using artificial neural networks (ANN's) based on space-mapping (SM) technology, SM-based neuromodels decrease the cost of training, improve generalization ability, and reduce the complexity of the ANN topology with respect to the classical neuromodeling approach. Five creative techniques are proposed to generate SM-based neuromodels. A frequency-sensitive neuromapping is applied to overcome the limitations of empirical models developed under quasi-static conditions, Huber optimization is used to train the ANN's. We contrast SM-based neuromodeling with the classical neuromodeling approach as well as with other state-of-the-art neuromodeling techniques. The SM-based neuromodeling techniques are illustrated by a microstrip bend and a high-temperature superconducting filter.
216 citations
"Implicit space mapping optimization..." refers methods in this paper
...The procedure continues in this manner until the irregular block is sufficiently close to the desired weight of 30 units....
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...Both use an iterative approach to update the mapping and predict the new design....
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