311:. Developments include implicit space mapping, in which we allow preassigned parameters not used in the optimization process to change in the coarse model, and output space mapping, where a transformation is applied to the response of the model. A 2004 paper reviews the state of the art after the first ten years of development and implementation. Tuning space mapping utilizes a so-called tuning model—constructed invasively from the fine model—as well as a calibration process that translates the adjustment of the optimized tuning model parameters into relevant updates of the design variables. The space mapping concept has been extended to neural-based space mapping for
295:"), where the mapping-augmented coarse model or surrogate is updated (enhanced, realigned with the fine model) through an iterative optimization process termed "parameter extraction". The mapping formulation itself incorporates "intuition", part of the engineer's so-called "feel" for a problem. In particular, the Aggressive Space Mapping (ASM) process displays key characteristics of cognition (an expert's approach to a problem), and is often illustrated in simple cognitive terms.
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291:), for example, the low-fidelity physics or "knowledge" model. In a space-mapping design optimization phase, there is a prediction or "execution" step, where the results of an optimized "mapped coarse model" (updated surrogate) are assigned to the fine model for validation. After the validation process, if the design specifications are not satisfied, relevant data is transferred to the optimization space ("
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model, computational model, tuning model, calibration model, surrogate model, surrogate update, mapped coarse model, surrogate optimization, parameter extraction, target response, optimization space, validation space, neuro-space mapping, implicit space mapping, output space mapping, port tuning,
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The space mapping methodology employs a "quasi-global" formulation that intelligently links companion "coarse" (ideal or low-fidelity) and "fine" (practical or high-fidelity) models of different complexities. In engineering design, space mapping aligns a very fast coarse model with the
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At the core of the process is a pair of models: one very accurate but too expensive to use directly with a conventional optimization routine, and one significantly less expensive and, accordingly, less accurate. The latter (fast model) is usually referred to as the "coarse" model
287:). The former (slow model) is usually referred to as the "fine" model. A validation space ("reality") represents the fine model, for example, a high-fidelity physics model. The optimization space, where conventional optimization is carried out, incorporates the coarse model (or
872:
561:, low fidelity (resolution) model, high fidelity (resolution) model, empirical model, simplified physics model, physics-based model, quasi-global model, physically expressive model, device under test, electromagnetics-based model,
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expensive-to-compute fine model so as to avoid direct expensive optimization of the fine model. The alignment can be done either off-line (model enhancement) or on-the-fly with surrogate updates (e.g., aggressive space mapping).
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A 2016 state-of-the-art review is devoted to aggressive space mapping. It spans two decades of development and engineering applications. A comprehensive 2021 review paper discusses space mapping in the context of
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There is a wide spectrum of terminology associated with space mapping: ideal model, coarse model, coarse space, fine model, companion model, cheap model, expensive model,
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predistortion (of design specifications), manifold mapping, defect correction, model management, multi-fidelity models, variable fidelity/variable complexity,
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356:. Proven techniques include the Linear Inverse Space Mapping (LISM) algorithm, as well as the Space Mapping with Inverse Difference (SM-ID) method.
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Proceedings of the 7th
Symposium on Building Physics in the Nordic Countries, vol. 1, pp. 896-903. The Icelandic Building Research Institute, 2005.
1307:"Machine learning techniques and space mapping approaches to enhance signal and power integrity in high-speed links and power delivery networks,"
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of the topic and provide significant coverage of it beyond a mere trivial mention. If notability cannot be shown, the article is likely to be
999:"Using surrogate models and response surfaces in structural optimization—with application to crashworthiness design and sheet metal forming,"
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Space mapping optimization belongs to the class of surrogate-based optimization methods, that is to say, optimization methods that rely on a
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873:"Power in simplicity with ASM: tracing the aggressive space mapping algorithm over two decades of development and engineering applications"
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Third
International Workshop on Surrogate Modelling and Space Mapping for Engineering Optimization (Reykjavik, Iceland, Aug. 2012)
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Second
International Workshop on Surrogate Modelling and Space Mapping for Engineering Optimization (Lyngby, Denmark, Nov. 2006)
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First
International Workshop on Surrogate Modelling and Space Mapping for Engineering Optimization (Lyngby, Denmark, Nov. 2000)
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Juan C. Cervantes-González, J. E. Rayas-Sánchez, C. A. López, J. R. Camacho-Pérez, Z. Brito-Brito, and J. L. Chavez-Hurtado,
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827:"Efficient analytical formulation and sensitivity analysis of neuro-space mapping for nonlinear microwave device modeling,"
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1105:"The Ellipsoidal Technique for Design Centering of Microwave Circuits Exploiting Space-Mapping Interpolating Surrogates,"
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1267:"Space mapping for codesigned magnetics: optimization techniques for high-fidelity multidomain design specifications,"
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Three international workshops have focused significantly on the art, the science and the technology of space mapping.
1223:"On the alignment of low-fidelity and high-fidelity simulation spaces for the design of microwave waveguide filters,"
1163:"Reconstruction of local magnetic properties of steel sheets by needle probe methods using space mapping techniques,"
959:"Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping,"
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1247:"Design of dispersive delay structures (DDSs) formed by coupled C-sections using predistortion with space mapping,"
1092:"Space mapping optimization of handset antennas considering EM effects of mobile phone components and human body,"
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devices. Space mapping is supported by sound convergence theory and is related to the defect-correction approach.
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307:'s concept in 1993, algorithms have utilized Broyden updates (aggressive space mapping), trust regions, and
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906:"A linear inverse space-mapping (LISM) algorithm to design linear and nonlinear RF and microwave circuits"
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of a system. The knowledge is updated with new validation information from the system when available.
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J.E. Rayas-Sánchez, F.E. Rangel-Patiño, B. Mercado-Casillas, F. Leal-Romo, and J.L. Chávez-Hurtado,
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IEEE J. Emerging and
Selected Topics in Power Electronics, vol. 9, no. 4, pp. 5097-5112, Aug. 2021.
1202:
1183:"Space mapping techniques for a structural optimization problem governed by the p-Laplace equation"
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The space mapping technique has been applied in a variety of disciplines including microwave and
1203:"EM-based design of large-scale dielectric-resonator filters and multiplexers by space mapping,"
1118:"Application of Output Space Mapping method for Fast Optimization using Multi-physical Modeling"
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Medical & Biological
Engineering & Computing, vol. 46, no. 8, pp. 767-777, August 2008.
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J.W. Bandler, Q. Cheng, S.A. Dakroury, A.S. Mohamed, M.H. Bakr, K. Madsen and J. Søndergaard,
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840:"Statistical neuro-space mapping technique for large-signal modeling of nonlinear devices,"
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Various simulators can be involved in a space mapping optimization and modeling processes.
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Hany L. Abdel-Malek, Abdel-karim S.O. Hassan, Ezzeldin A. Soliman, and Sameh A. Dakroury,
979:"Optimization of the new Saab 9-3 exposed to impact load using a space mapping technique,"
8:
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Journal of
Computational and Applied Mathematics, vol. 215, no. 2, pp. 339-347, May 2008.
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886:“Advanced RF and microwave design optimization: a journey and a vision of future trends,”
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1039:"A hybrid algorithm for solving the EEG inverse problem from spatio-temporal EEG data,"
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A.J. Booker, J.E. Dennis, Jr., P.D. Frank, D.B. Serafini, V. Torczon, and M.W. Trosset,
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2020 IEEE 11th Latin
American Symposium on Circuits & Systems (LASCAS), Feb. 2020.
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Structural and
Multidisciplinary Optimization, vol. 27, no. 5, pp. 411-420, July 2004.
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in 1993. It uses relevant existing knowledge to speed up model generation and design
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Computational Methods in Applied Mathematics, vol. 5, no, 2, pp. 107-136, Jan. 2005.
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G. Crevecoeur, H. Hallez, P. Van Hese, Y. D'Asseler, L. Dupré, and R. Van de Walle,
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It may require cleanup to comply with Knowledge's content policies, particularly
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IEEE Trans. Microwave Theory Tech., vol. 61, no. 12, pp. 4040-4051, Dec. 2013.
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IEEE Trans. Microwave Theory Tech., vol. 66, no. 12, pp. 5183-5196, Dec. 2018.
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IEEE Trans. Microwave Theory Tech., vol. 46, no. 12, pp. 2412-2425, Dec. 1998.
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IEEE Trans. Microwave Theory Tech., vol. 42, no. 12, pp. 2536-2544, Dec. 1994.
705:"Have you ever wondered about the engineer's mysterious 'feel' for a problem?"
1339:
1059:"Space mapping optimization of handset antennas exploiting thin-wire models,"
939:"A rigorous framework for optimization of expensive functions by surrogates,"
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IEEE Trans. Microwave Theory Tech., vol. 53, no. 9, pp. 2752-2767, Sep. 2005.
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IEEE Trans. Microwave Theory Tech., vol. 52, no. 1, pp. 386-392, Jan. 2004.
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919:"Solving Inverse Problems by Space Mapping with Inverse Difference Method,"
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IEEE Trans. Microwave Theory Tech., vol. 57, no. 2, pp. 383-394, Feb. 2009.
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IEEE Trans. Microwave Theory Tech., vol. 52, no. 1, pp. 337-361, Jan. 2004.
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IEEE Trans. Microwave Theory Tech., vol. 52, no. 1, pp. 378-385, Jan. 2004.
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J.W. Bandler, R.M. Biernacki, S.H. Chen, P.A. Grobelny, and R.H. Hemmers,
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M.H. Bakr, J.W. Bandler, M.A. Ismail, J.E. Rayas-Sánchez and Q.J. Zhang,
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J. Ossorio, J.C. Melgarejo, V.E. Boria, M. Guglielmi, and J.W. Bandler,
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IEEE Trans. Antennas Propag., vol. 61, no. 7, pp. 3797-3807, July 2013.]
788:"Implicit space mapping optimization exploiting preassigned parameters,"
762:"A trust region aggressive space mapping algorithm for EM optimization,"
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IEEE MTT-S Int. Microwave Symp. Digest (Boston, MA, 2000), pp. 879-882.
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1131:"Space Mapping for Optimal Control of Partial Differential Equations".
814:"Accelerated microwave design optimization with tuning space mapping,"
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IEEE Power Electronics Magazine, vol. 7, no. 2, pp. 47-52, Jun. 2020.
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Int. J. RF and Microwave CAE, vol. 26, no. 2, pp. 121-128, Feb. 2016.
895:(invited), IEEE J. Microwaves, vol. 1, no. 1, pp. 481-493, Jan. 2021.
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J.W. Bandler, R.M. Biernacki, S.H. Chen, R.H. Hemmers, and K. Madsen,
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1327:"Modeling thermally active building components using space mapping,"
1072:"Space mapping outpaces EM optimization in handset-antenna design,"
749:"Electromagnetic optimization exploiting aggressive space mapping,"
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341:, feature-based and cognition-driven design; and in the context of
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IEEE Trans. Microwave Theory Tech., vol. 54, no. 10, October 2006.
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M.H. Bakr, J.W. Bandler, R.M. Biernacki, S.H. Chen and K. Madsen,
1150:"Space mapping optimization of a cylindrical voice coil actuator"
875:, IEEE Microwave Magazine, vol. 17, no. 4, pp. 64-76, April 2016.
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Please help to demonstrate the notability of the topic by citing
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G. Crevecoeur, L. Dupre, L. Vandenbossche, and R. Van de Walle,
1152:, IEEE Trans. Ind. Appl., vol. 42, no. 6, pp.1437-1444, 2006.
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775:"Neural space mapping EM optimization of microwave structures,"
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L. Encica, J. Makarovic, E.A. Lomonova, and A.J.A. Vandenput,
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S. Tu, Q.S. Cheng, Y. Zhang, J.W. Bandler, and N.K. Nikolova,
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S. Koziel, J. Meng, J.W. Bandler, M.H. Bakr, and Q.S. Cheng,
736:"Space mapping technique for electromagnetic optimization,"
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M.A. Ismail, D. Smith, A. Panariello, Y. Wang, and M. Yu,
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J.E. Rayas-Sanchez, F. Lara-Rojo and E. Martanez-Guerrero,
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T.D. Robinson, M.S. Eldred, K.E. Willcox, and R. Haimes,
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L. Zhang, J. Xu, M.C.E. Yagoub, R. Ding, and Q.J. Zhang,
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J.W. Bandler, Q.S. Cheng, N.K. Nikolova and M.A. Ismail,
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The space mapping methodology can also be used to solve
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Journal of Applied Physics, vol. 99, no. 08H905, 2006.
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IEEE Canadian Review, no. 70, pp. 50-60, Summer 2013.
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A major contributor to this article appears to have a
1019:"EEG source analysis using space mapping techniques,"
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methodology for modeling and design optimization of
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Mathematics in Industry, vol. 14, 2010, pp 453-460.
337:design optimization; in the context of engineering
1285:K. Booth, H. Subramanyan, J. Liu, and S.M. Lukic,
884:J.E. Rayas-Sánchez, S. Koziel, and J.W. Bandler,
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1181:O. Lass, C. Posch, G. Scharrer and S. Volkwein,
968:AIAA Journal, vol. 46, no. 11, November 2008.
725:, vol. 19, no. 2, pp.112-122, Mar./Apr. 2018.
1325:F. Pedersen, P. Weitzmann, and S. Svendsen,
430:Reconstruction of local magnetic properties
380:design, civil and mechanical applications,
53:Learn how and when to remove these messages
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997:T. Jansson, L. Nilsson, and M. Redhe,
801:"Space mapping: the state of the art,"
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853:"Space mapping and defect correction"
716:Reprinted in IEEE Microwave Magazine
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1351:Optimization algorithms and methods
838:L. Zhang, Q.J. Zhang, and J. Wood,
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440:microwave filters and multiplexers
388:Optimizing aircraft wing curvature
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444:Optimization of delay structures
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1346:Electromagnetic radiation
1265:K. Booth and J. Bandler,
977:M. Redhe and L. Nilsson,
75:may not meet Knowledge's
601:Engineering optimization
257:was first discovered by
641:Model-dependent realism
434:Structural optimization
676:Support vector machine
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606:Finite element method
596:Computer-aided design
508:CST Microwave Studio
382:aerospace engineering
197:neutral point of view
1356:Microwave technology
616:Linear approximation
407:Design centering of
316:statistical modeling
871:J.E. Rayas-Sanchez,
255:engineering systems
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