A distance correlation-based Kriging modeling method for high-dimensional problems

Fu, Chongbo; Wang, Peng; Zhao, Liang; Wang, Xinjing

doi:10.1016/j.knosys.2020.106356

Cited by 33 publications

(8 citation statements)

References 39 publications

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“…In this section, the performance of KGEK is further tested and compared with GEK, PGEK and WGEK via a set of analytic test functions and an engineering example. Expressions of those analytic test functions (Fu et al , 2020) are presented in Table 1 with the variable range.…”

Section: Experimental Studymentioning

confidence: 99%

An efficient gradient-enhanced kriging modeling method assisted by fast kriging for high-dimension problems

He,

Tan,

et al. 2023

HFF

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Purpose The modeling cost of the gradient-enhanced kriging (GEK) method is prohibitive for high-dimensional problems. This study aims to develop an efficient modeling strategy for the GEK method. Design/methodology/approach A two-step tuning strategy is proposed for the construction of the GEK model. First, an auxiliary kriging is built efficiently. Then, the hyperparameter of the kriging model is served as a good initial guess to that of the GEK model, and a local optimal search is further used to explore the search space of hyperparameter to guarantee the accuracy of the GEK model. In the construction of the auxiliary kriging, the maximal information coefficient is adopted to estimate the relative magnitude of the hyperparameter, which is used to transform the high-dimension maximum likelihood estimation problem into a one-dimensional optimization. The tuning problem of the auxiliary kriging becomes independent of the dimension. Therefore, the modeling efficiency can be improved significantly. Findings The performance of the proposed method is studied with analytic problems ranging from 10D to 50D and an 18D aerodynamic airfoil example. It is further compared with two efficient GEK modeling methods. The empirical experiments show that the proposed model can significantly improve the modeling efficiency without sacrificing accuracy compared with other efficient modeling methods. Originality/value This paper developed an efficient modeling strategy for GEK and demonstrated the effectiveness of the proposed method in modeling high-dimension problems.

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Section: Experimental Studymentioning

confidence: 99%

An efficient gradient-enhanced kriging modeling method assisted by fast kriging for high-dimension problems

He,

Tan,

et al. 2023

HFF

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“…Needless to say, replacing EM analysis by fast surrogates is invaluable as an acceleration tool. Approximation models (kriging 50 , RBF 51 , PCE 52 , SVR 53 , ANNs and numerable variants thereof, e.g. convolutional neural networks (CNN) 54 or deep neural networks (DNN) 55 ) are particularly popular due to their accessibility 56 , 57 .…”

Section: Introductionmentioning

confidence: 99%

Two-stage variable-fidelity modeling of antennas with domain confinement

Pietrenko‐Dabrowska

Kozieł

Golunski

2022

Sci Rep

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Surrogate modeling has become the method of choice in solving an increasing number of antenna design tasks, especially those involving expensive full-wave electromagnetic (EM) simulations. Notwithstanding, the curse of dimensionality considerably affects conventional metamodeling methods, and their capability to efficiently handle nonlinear antenna characteristics over broad ranges of the system parameters is limited. Performance-driven (or constrained) modeling frameworks may be employed to mitigate these issues by considering a construction of surrogates from the standpoint of the antenna performance figures rather than directly geometry parameters. This permits a significant reduction of the model setup cost without restricting its design utility. This paper proposes a novel modeling framework, which capitalizes on the domain confinement concepts and also incorporates variable-fidelity EM simulations, both at the surrogate domain definition stage, and when rendering the final surrogate. The latter employs co-kriging as a method of blending simulation data of different fidelities. The presented approach has been validated using three microstrip antennas, and demonstrated to yield reliable models at remarkably low CPU costs, as compared to both conventional and performance-driven modeling procedures.

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“…The models of the former group are more popular, cheap to evaluate, generic, and easily accessible (e.g., [41], [42]). Some of widely used methods include kriging [43], radial basis functions [44], neural networks [45], support vector regression [46], and polynomial chaos expansion [47]. Unfortunately, a construction of accurate surrogates of microwave components is severely hindered by the curse of dimensionality.…”

Section: Introductionmentioning

confidence: 99%

Reduced-Cost Microwave Design Closure by Multi-Resolution EM Simulations and Knowledge-Based Model Management

2021

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Parameter adjustment through numerical optimization has become a commonplace of contemporary microwave engineering. Although circuit theory methods are ubiquitous in the development of microwave components, the initial designs obtained with such tools have to be further tuned to improve the system performance. This is particularly pertinent to miniaturized structures, where the cross-coupling effects cannot be adequately accounted for using equivalent networks. For the sake of reliability, design closure is normally performed using full-wave electromagnetic (EM) simulation models, which entails considerable computational expenses, often impractically excessive. Available mitigation techniques include acceleration of the conventional (e.g., gradient-based) routines using adjoint sensitivities or sparse sensitivity updates, surrogate-assisted and machine learning algorithms, the latter often combined with nature-inspired procedures. Another alternative is the employment of variable-fidelity simulations (e.g., space mapping, co-kriging), which is most often limited to two levels of accuracy (coarse/fine). This work discusses an EM model management approach coupled with trust-region gradient-based routine, which exploits problem-specific knowledge for continuous (multi-level) modification of the discretization density of the microwave structure at hand in the course of the optimization run. The optimization process is launched at the lowest discretization level, thereby allowing for low-cost exploitation of the knowledge about the device under study. Subsequently, based on the convergence indicators, the model fidelity is gradually increased to ensure reliability. The simulation fidelity selection is governed by the algorithm convergence indicators. Computational speedup (i.e., reduction in the number of EM simulations required by the optimization process to converge) is achieved by maintaining low resolution in the initial stages of the optimization run, whereas design quality is secured by eventually switching to the high-fidelity model when close to concluding the process. Numerical verification is carried out using two microstrip circuits, a dual-band power divider and a dual-band branch-line coupler, with the average savings of almost sixty percent when compared to single-fidelity optimization.

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A distance correlation-based Kriging modeling method for high-dimensional problems

Cited by 33 publications

References 39 publications

An efficient gradient-enhanced kriging modeling method assisted by fast kriging for high-dimension problems

An efficient gradient-enhanced kriging modeling method assisted by fast kriging for high-dimension problems

Two-stage variable-fidelity modeling of antennas with domain confinement

Reduced-Cost Microwave Design Closure by Multi-Resolution EM Simulations and Knowledge-Based Model Management

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