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

Review of multi-fidelity models

There is a wide number of problems in electromagnetic (EM) engineering that require a real-time response or in which the input–output relationship is not a-priori known or cannot be defined due to ...

Learning-by-examples techniques as applied to electromagnetics

Multifidelity surrogates are essential in cases where it is not affordable to have more than a few high-fidelity samples, but it is affordable to have as many low-fidelity samples as needed. In the...

Issues in Deciding Whether to Use Multifidelity Surrogates

A compact wideband dual-frequency microstrip antenna is proposed in this paper. By employing an ofiset microstrip-fed line and a strip close to the radiating edges in the circular slot patch, an antenna operating at dual frequency with the impedance bandwidth of 26.2% and 22.2% respectively is presented. By attaching a strip to the radiating edges opposite to the microstrip-fed line, this alters the current distribution and radiation on the antenna at the second resonant frequency. The second frequency is also tunable by varying the lengths of the microstrip-fed line. It is demonstrated that the proposed antenna covers the widebands of UHF and microwave for RFID application. A good agreement is obtained between the simulated and experimental results.

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Circular microstrip slot antenna for dual- frequency rfid application

A low profile coplanar waveguide (CPW) fed printed slot antenna is presented with uni-directional radiation properties. The slot antenna radiates above a closely spaced artificial magnetic conducting (AMC) reflector consisting of an array of rectangular patches, a substrate and an electric ground plane. The electromagnetic bandgap (EBG) performance of the cavity structure between the upper conducting surface in which the slot is etched, and the ground plane at the bottom of the reflector, is investigated using an equivalent waveguide feed in the place of a half-wavelength section of the slot antenna. From the reflection coefficient of the equivalent waveguide feed one can determine the frequency band where minimum energy will be lost due to unwanted radiation from the cavity sides. The dimensions of the cavity were found to be very important for minimum energy loss. Experimental results for the final antenna design (with a size of 1.02λ0×0.82λ0×0.063λ0), mounted on a 1.5λ0×1.5λ0 back plate, exhibit a 5% impedance bandwidth, maximum gain in excess of 10 dBi, low cross-polarization, and a front-to-back ratio of approximately 25 dB. This low-profile antenna with relatively high gain could be a good candidate for a 2.4 GHz WLAN application.

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CPW-Fed Cavity-Backed Slot Radiator Loaded With an AMC Reflector

A two-stage approach based on Gaussian process regression that achieves significantly reduced requirements for computationally expensive high-fidelity training data is presented for the modeling of planar antenna input characteristics Our method involves variable-fidelity electromagnetic simulations In the first stage, a mapping between electromagnetic models (simulations) of low and high fidelity is learned, which allows us to substantially reduce (by 80% or more) the computational effort necessary to set up the high-fidelity training data sets for the actual surrogate models (second stage), with negligible loss in predictive power We illustrate our method by modeling the input characteristics of three antenna structures with up to seven design variables The accuracy of the two-stage method is confirmed by the successful use of the surrogates within a space-mapping-based optimization/design framework

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Two-Stage Framework for Efficient Gaussian Process Modeling of Antenna Input Characteristics

The modeling of microwave antennas and devices typically requires that non-linear input-output mappings be determined between a set of variable parameters (such as geometry dimensions and frequency), and the corresponding scattering parameter(s). Support vector regression (SVR) employing an isotropic Gaussian kernel has been widely used for such tasks; this kernel has one tunable hyperparameter that can be optimized (along with the penalty constant C) using a standard procedure that involves a parameter grid search combined with cross-validation. The isotropic kernel however suffers from limited expressiveness, and might provide inadequate predictive accuracy for nonlinear mappings that involve multiple tunable input variables. The present study shows that Bayesian support vector regression using the inherently more flexible Gaussian kernel with automatic relevance determination (ARD) is eminently suitable for highly non-linear modeling tasks, such as the input reflection coefficient magnitude |S11| of broadband and ultrawideband antennas. The Bayesian framework enables efficient training of the multiple kernel ARD hyperparameters-a task that would be computationally infeasible for the grid search/cross-validation approach of standard SVR.

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Bayesian Support Vector Regression With Automatic Relevance Determination Kernel for Modeling of Antenna Input Characteristics

A methodology based on Gaussian process regression (GPR) for accurately modeling the resonant frequencies of dual-band microstrip antennas is presented. Two kinds of dual-band antennas were considered, namely a U-slot patch and a patch with a center square slot. Predictive results of high accuracy were achieved (normalized root-mean-square errors of below 0.6% in all cases), even for the square-slot patch modeling problem where all antenna dimensions and parameters were allowed to vary, resulting in a seven-dimensional input space. Training data requirements for achieving these accuracies were relatively modest. Furthermore, the automatic relevance determination property of GPR provided (at no additional cost) a mechanism for enhancing qualitative understanding of the antennas’ resonance characteristics—a facility not offered by neural network-based strategies used in related studies.

Efficient Resonant Frequency Modeling for Dual-Band Microstrip Antennas by Gaussian Process Regression

Gaussian process (GP) regression is proposed as a structured supervised learning alternative to neural networks for the modeling of CPW-fed slot antenna input characteristics. A Gaussian process is a stochastic process and entails the generalization of the Gaussian probability distribution to functions. Standard GP regression is applied to modeling S11 against frequency of a CPW-fed second- resonant slot dipole, while an approximate method for large datasets is applied to an ultrawideband (UWB) slot with U-shaped tuning stub | A challenging problem given the highly non-linear underlying function that maps tunable geometry variables and frequency to S11=input impedance. Predictions using large test data sets yielded results of an accuracy comparable to the target moment-method-based full-wave simulations, with normalized root mean squared errors of 0.50% for the slot dipole, and below 1.8% for the UWB antenna. The GP methodology has various inherent beneflts, including the need to learn only a handful of (hyper) parameters, and training errors that are efiectively zero for noise-free observations. GP regression would be eminently suitable for integration in antenna design algorithms as a fast substitute for computationally intensive full-wave analysis.

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Gaussian Process Modeling of CPW-Fed Slot Antennas

The applicability of Gaussian process (GP) regression as modeling tool within a genetic algorithm (GA) antenna optimization scheme is demonstrated. GP regression has recently been shown to be an efficient alternative to artificial neural networks (ANNs) when many accurate and fast estimates of antenna performance parameters, usually only obtainable from computationally intensive full-wave analyses, are required. GP regression has the important advantage that far fewer free parameters need to be determined; it furthermore is not subject to the implementation issues associated with neural nets. By using genetic algorithm optimization, two kinds of CPW-fed slot antennas were designed to operate within pre-specified frequency bands: an ultrawide-band (UWB) slot antenna with U-shaped tuning stub, and a dual-band slot loop antenna with separate T-shaped and insert tuning stubs. In both cases, the associated modeling problems were challenging, involving highly nonlinear mappings of several tunable geometry varia...

J. P. Jacobs

Papers

Two-Stage Framework for Efficient Gaussian Process Modeling of Antenna Input Characteristics

Bayesian Support Vector Regression With Automatic Relevance Determination Kernel for Modeling of Antenna Input Characteristics

Efficient Resonant Frequency Modeling for Dual-Band Microstrip Antennas by Gaussian Process Regression

Gaussian Process Modeling of CPW-Fed Slot Antennas

Gaussian-Process-Regression-Based Design of Ultrawide-Band and Dual-Band CPW-FED Slot Antennas