Jacob Søndergaard

An Introduction to the Space Mapping Technique

The space mapping technique is intended for optimization of engineering models which involve very expensive function evaluations. It is assumed that two different models of the same physical system are available: Besides the expensive model of primary interest (denoted the fine model), access to a cheaper (coarse) model is assumed which may be less accurate.The main idea of the space mapping technique is to use the coarse model to gain information about the fine model, and to apply this in the search for an optimal solution of the latter. Thus the technique iteratively establishes a mapping between the parameters of the two models which relate similar model responses. Having this mapping, most of the model evaluations can be directed to the fast coarse model.In many cases this technique quickly provides an approximate optimal solution to the fine model that is sufficiently accurate for engineering purposes. Thus the space mapping technique may be considered a preprocessing technique that perhaps must be succeeded by use of classical optimization techniques. We present an automatic scheme which integrates the space mapping and classical techniques.

Space mapping optimization of microwave circuits exploiting surrogate models

A powerful new Aggressive Space Mapping (ASM) optimization algorithm is presented. It draws upon recent developments in both surrogate-based optimization and microwave device neuromodeling. Our surrogate formulation (new to microwave engineering) exploits, in a novel way, a linear frequency-space mapping. This is a powerful approach to severe response misalignments.

Review of the Space Mapping Approach to Engineering Optimization and Modeling

We review the Space Mapping (SM) concept and its applications in engineering optimization and modeling. The aim of SM is to avoid computationally expensive calculations encountered in simulating an engineering system. The existence of less accurate but fast physically-based models is exploited. SM drives the optimization iterates of the time-intensive model using the fast model. Several algorithms have been developed for SM optimization, including the original SM algorithm, Aggressive Space Mapping (ASM), Trust Region Aggressive Space Mapping (TRASM) and Hybrid Aggressive Space Mapping (HASM). An essential subproblem of any SM based optimization algorithm is parameter extraction. The uniqueness of this optimization subproblem has been crucial to the success of SM optimization. Different approaches to enhance the uniqueness are reviewed. We also discuss new developments in Space Mapping-based Modeling (SMM). These include Space Derivative Mapping (SDM), Generalized Space Mapping (GSM) and Space Mapping-based Neuromodeling (SMN). Finally, we address open points for research and future development.

Convergence of Hybrid Space Mapping Algorithms

The space mapping technique is intended for optimization of engineering models which involve very expensive function evaluations. It may be considered a preprocessing method which often provides a very efficient initial phase of an optimization procedure. However, the ultimate rate of convergence may be poor, or the method may even fail to converge to a stationary point.We consider a convex combination of the space mapping technique with a classical optimization technique. The function to be optimized has the form H ○ f where H : Rm → R is convex and f : Rn → Rm is smooth. Experience indicates that the combined method maintains the initial efficiency of the space mapping technique. We prove that the global convergence property of the classical technique is also maintained: The combined method provides convergence to the set of stationary points of H ○ f.

Space-mapping optimization of microwave circuits exploiting surrogate models

A powerful new space-mapping (SM) optimization algorithm is presented in this paper. It draws upon recent developments in both surrogate model-based optimization and modeling of microwave devices, SM optimization is formulated as a general optimization problem of a surrogate model. This model is a convex combination of a mapped coarse model and a linearized fine model. It exploits, in a novel way, a linear frequency-sensitive mapping. During the optimization iterates, the coarse and fine models are simulated at different sets of frequencies. This approach is shown to be especially powerful if a significant response shift exists. The algorithm is illustrated through the design of a capacitively loaded 10:1 impedance transformer and a double-folded stub filter. A high-temperature superconducting filter is also designed using decoupled frequency and SMs.

EM-based optimization exploiting partial space mapping and exact sensitivities

We present a family of robust techniques for exploiting sensitivities in EM-based circuit optimization through Space Mapping (SM). We utilize derivative information for parameter extractions and mapping updates. We exploit a Partial Space Mapping (PSM) concept where a reduced set of parameters is sufficient for parameter extraction optimization. Upfront gradients of both EM (fine) model and coarse surrogates can Initialize possible mapping approximations. Illustrations include a two-section 10:1 impedance transformer and a microstrip bandstop filter.

Automatic Mapping of Monitoring Data

This paper presents an approach, based on universal kriging, for automatic mapping of monitoring data. The performance of the mapping approach is tested on two datasets containing daily mean gamma dose rates in Germany reported by means of the national automatic monitoring network (IMIS). In the second dataset an accidental release of radioactivity in the environment was simulated in the South-Western corner of the monitored area. The approach has a tendency to smooth the actual data values, and therefore it underestimates extreme values, as seen in the second dataset. However, it is capable of identifying a release of radioactivity provided that the number of sampling locations is sufficiently high. Consequently, we believe that a combination of applying the presented mapping approach and the physical knowledge of the transport processes of radioactivity should be used to predict the extreme values.