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The space mapping methodology for modeling and design optimization of engineering systems was first discovered by John Bandler in 1993. It uses relevant existing knowledge to speed up model generation and design optimization of a system. The knowledge is updated with new validation information from the system when available.
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 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).
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 (coarse space). 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 surrogate model), 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 ("feedback"), 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. [1] 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.
Following John Bandler's concept in 1993, [1] [2] algorithms have utilized Broyden updates (aggressive space mapping), [3] trust regions, [4] and artificial neural networks. [5] Developments include implicit space mapping, [6] 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. [7] Tuning space mapping [8] 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 large-signal statistical modeling of nonlinear microwave devices. [9] [10] Space mapping is supported by sound convergence theory and is related to the defect-correction approach. [11]
A 2016 state-of-the-art review is devoted to aggressive space mapping. [12] It spans two decades of development and engineering applications. A comprehensive 2021 review paper [13] discusses space mapping in the context of radio frequency and microwave design optimization; in the context of engineering surrogate model, feature-based and cognition-driven design; and in the context of machine learning, intuition, and human intelligence.
The space mapping methodology can also be used to solve inverse problems. Proven techniques include the Linear Inverse Space Mapping (LISM) algorithm, [14] as well as the Space Mapping with Inverse Difference (SM-ID) method. [15]
Space mapping optimization belongs to the class of surrogate-based optimization methods, [16] that is to say, optimization methods that rely on a surrogate model.
The space mapping technique has been applied in a variety of disciplines including microwave and electromagnetic design, civil and mechanical applications, aerospace engineering, and biomedical research. Some examples:
Various simulators can be involved in a space mapping optimization and modeling processes.
Three international workshops have focused significantly on the art, the science and the technology of space mapping.
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, surrogate model, 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, simulation 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, predistortion (of design specifications), manifold mapping, defect correction, model management, multi-fidelity models, variable fidelity/variable complexity, multigrid method, coarse grid, fine grid, surrogate-driven, simulation-driven, model-driven, feature-based modeling.
Mathematical optimization or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
A metamodel is a model of a model, and metamodeling is the process of generating such metamodels. Thus metamodeling or meta-modeling is the analysis, construction, and development of the frames, rules, constraints, models, and theories applicable and useful for modeling a predefined class of problems. As its name implies, this concept applies the notions of meta- and modeling in software engineering and systems engineering. Metamodels are of many types and have diverse applications.
Finite-difference time-domain (FDTD) or Yee's method is a numerical analysis technique used for modeling computational electrodynamics. Since it is a time-domain method, FDTD solutions can cover a wide frequency range with a single simulation run, and treat nonlinear material properties in a natural way.
Scientific modelling is an activity that produces models representing empirical objects, phenomena, and physical processes, to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features. Different types of models may be used for different purposes, such as conceptual models to better understand, operational models to operationalize, mathematical models to quantify, computational models to simulate, and graphical models to visualize the subject.
A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so an approximate mathematical model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as a function of design variables. For example, in order to find the optimal airfoil shape for an aircraft wing, an engineer simulates the airflow around the wing for different shape variables. For many real-world problems, however, a single simulation can take many minutes, hours, or even days to complete. As a result, routine tasks such as design optimization, design space exploration, sensitivity analysis and "what-if" analysis become impossible since they require thousands or even millions of simulation evaluations.
A radio-frequency microelectromechanical system is a microelectromechanical system with electronic components comprising moving sub-millimeter-sized parts that provide radio-frequency (RF) functionality. RF functionality can be implemented using a variety of RF technologies. Besides RF MEMS technology, III-V compound semiconductor, ferrite, ferroelectric, silicon-based semiconductor, and vacuum tube technology are available to the RF designer. Each of the RF technologies offers a distinct trade-off between cost, frequency, gain, large-scale integration, lifetime, linearity, noise figure, packaging, power handling, power consumption, reliability, ruggedness, size, supply voltage, switching time and weight.
Michael B. Steer is a Lampe professor of electrical and computer engineering at North Carolina State University and one of the leading electrical engineers in today's analog/RF and microwave world. He has published numerous articles in the "IEEE Microwave and Antennas" journal, along with leading the NCSU Dinosauria project. He is credited with being the first IEEE Fellow to fine-tune all of his constitutive relations and as a result, creating a paperless office.
Robert Jackson Marks II is an American electrical engineer, computer scientist and Distinguished Professor at Baylor University. His contributions include the Zhao-Atlas-Marks (ZAM) time-frequency distribution in the field of signal processing, the Cheung–Marks theorem in Shannon sampling theory and the Papoulis-Marks-Cheung (PMC) approach in multidimensional sampling. He was instrumental in the defining of the field of computational intelligence and co-edited the first book using computational intelligence in the title. A Christian and an old earth creationist, he is a subject of the 2008 pro-intelligent design motion picture, Expelled: No Intelligence Allowed.
Compact Software was the first commercially successful microwave computer-aided design (CAD) company. The company was founded in 1973 by Les Besser to commercialize his eponymous program COMPACT, released when he was at Farinon Electric Company.
Sir Christopher Maxwell Snowden, is a British electronic engineer and academic. He was the former Vice-Chancellor of Surrey University (2005–2015), and of the University of Southampton (2015–2019). He was president of Universities UK for a two-year term until 31 July 2015. He is currently the chairman of the ERA Foundation.
RF microwave CAE CAD is computer-aided design (CAD) using computer technology to aid in the design, modeling, and simulation of an RF or microwave product. It is a visual and symbol-based method of communication whose conventions are particular to RF/microwave engineering.
In numerical analysis, coarse problem is an auxiliary system of equations used in an iterative method for the solution of a given larger system of equations. A coarse problem is basically a version of the same problem at a lower resolution, retaining its essential characteristics, but with fewer variables. The purpose of the coarse problem is to propagate information throughout the whole problem globally.
Engineering optimization is the subject which uses optimization techniques to achieve design goals in engineering. It is sometimes referred to as design optimization.
Microwave engineering pertains to the study and design of microwave circuits, components, and systems. Fundamental principles are applied to analysis, design and measurement techniques in this field. The short wavelengths involved distinguish this discipline from electronic engineering. This is because there are different interactions with circuits, transmissions and propagation characteristics at microwave frequencies.
John William Bandler was a Canadian professor, engineer, entrepreneur, artist, speaker, playwright, and author of fiction and nonfiction. Bandler is known for his invention of space mapping technology and his contributions to device modeling, computer-aided design, microwave engineering, mathematical optimization, and yield-driven design.
Multidimensional Digital Pre-distortion (MDDPD), often referred to as multiband digital pre-distortion (MBDPD), is a subset of digital predistortion (DPD) that enables DPD to be applied to signals (channels) that cannot or do not pass through the same digital pre-distorter but do concurrently pass through the same nonlinear system. Its ability to do so comes from the portion of multidimensional signal theory that deals with one dimensional discrete time vector input - 1-D discrete time vector output systems as defined in Multidimensional Digital Signal Processing. The first paper in which it found application was in 1991 as seen here. None of the applications of MDDPD are able to make use of the linear shift invariant (LSI) system properties as by definition they are nonlinear and not shift-invariant although they are often approximated as shift-invariant (memoryless).
Palghat P. Vaidyanathan is the Kiyo and Eiko Tomiyasu Professor of Electrical Engineering at the California Institute of Technology, Pasadena, California, USA, where he teaches and leads research in the area of signal processing, especially digital signal processing (DSP), and its applications. He has authored four books, and authored or coauthored close to six hundred papers in various IEEE journals and conferences. Prof. Vaidyanathan received his B.Tech. and M.Tech. degrees from the Institute of Radiophysics and Electronics, Science College campus of University of Kolkata, and a Ph.D. degree in Electrical Engineering from University of California Santa Barbara in 1982.
Optimization Systems Associates (OSA) was founded by John Bandler in 1983. OSA produced the first commercial implementation of space mapping optimization to enhance the speed and accuracy of engineering design. OSA’s primary thrust was in computer-aided design (CAD) and simulation and optimization of radio-frequency and microwave circuits and systems. Its products included developments of Bandler's space mapping concept and methodology, which facilitates effective modeling and design optimization of computationally intensive engineering systems.
Nuno Miguel Gonçalves Borges de Carvalho from the Universidade de Aveiro, Aveiro, Portugal was named Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 2015 for contributions on characterization and design of nonlinear RF circuits.
Mahta Moghaddam is an Iranian-American electrical and computer engineer and William M. Hogue Professor of Electrical Engineering in the Ming Hsieh Department of Electrical and Computer Engineering at the University of Southern California Viterbi School of Engineering. Moghaddam is also the president of the IEEE Antennas and Propagation Society and is known for developing sensor systems and algorithms for high-resolution characterization of the environment to quantify the effects of climate change. She also has developed innovative tools using microwave technology to visualize biological structures and target them in real-time with high-power focused microwave ablation.
