Kriging Hyperparameter Tuning Strategies

Toal, David J. J.; Bressloff, Neil W.; Keane, Andy J.

doi:10.2514/1.34822

Cited by 150 publications

(68 citation statements)

References 18 publications

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“…It is the maximization of (30) that lies at the heart of the computational expense of the Kriging technique. Much research effort is directed at devising suitable training strategies and reducing the expense of the multiple matrix inversions required (see, e.g., Toal et al [77], Zhang and Leithead [87]). Still though, this parameter estimation stage limits the method to problems of low dimensionality, with k usually limited to around 20, depending on the expense of the analyses the Kriging model is to be used in lieu of.…”

Section: Krigingmentioning

confidence: 99%

Recent advances in surrogate-based optimization

Forrester

Keane

2009

Progress in Aerospace Sciences

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1,916

954

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The evaluation of aerospace designs is synonymous with the use of long running and computationally intensive simulations. This fuels the desire to harness the efficiency of surrogate-based methods in aerospace design optimization. Recent advances in surrogate-based design methodology bring the promise of efficient global optimization closer to reality. We review the present state of the art of constructing surrogate models and their use in optimization strategies. We make extensive use of pictorial examples and, since no method is truly universal, give guidance as to each method's strengths and weaknesses.

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Section: Krigingmentioning

confidence: 99%

Recent advances in surrogate-based optimization

Forrester

Keane

2009

Progress in Aerospace Sciences

Self Cite

1,916

954

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“…Because there is no analytical solution for the optimal θ, we have to use numerical optimization algorithm [71] to maximize the concentrated joint logarithm likelihood function:…”

Section: Correlation Functions and Hyperparameter Tuningmentioning

confidence: 99%

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

et al. 2017

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A novel formulation of gradient-enhanced surrogate model, called weighted gradient-enhanced kriging, is proposed and used in combination with the cheap gradients obtained by the adjoint method to ameliorate the "curse of dimensionality". The core idea is to build a series of submodels with much smaller correlation matrices and then sum them up with appropriate weight coefficients, aiming to avoid the prohibitive cost associated with decomposing the large correlation matrix of a gradient-enhanced kriging. A self-contained derivation of the proposed method is presented, and then it is verified by surrogate modeling test cases. The present method is integrated into a surrogatebased optimizer and tested for design optimizations. It is further demonstrated for inverse design of a transonic wing, parameterized with a number of design variables in the range from 36 to 108, using Reynolds-averaged Navier-Stokes flow and adjoint solvers. It is observed that, for the wing design with 36 and 54 variables, the weighted and conventional gradient-enhanced kriging are comparable, and both are much more efficient than kriging without using any gradient. For the wing design with 72 and 108 variables, the cost of training a gradient-enhanced kriging increases rapidly and becomes prohibitive. In contrast, the cost of training a weighted gradient-enhanced kriging is kept in an acceptable level, which makes it more practical for higher-dimensional problems.

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“…This strategy was found by Toal et al [36] to offer a significant reduction in tuning cost while having minimal impact on the performance of the optimization.…”

Section: Standard Kriging-based Optimizationmentioning

confidence: 99%

Geometric Filtration Using Proper Orthogonal Decomposition for Aerodynamic Design Optimization

et al. 2010

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When carrying out design searches, traditional variable screening techniques can find it extremely difficult to distinguish between important and unimportant variables. This is particularly true when only a small number of simulations are combined with a parameterization that results in a large number of variables of seemingly equal importance. Here, the authors present a variable reduction technique that employs proper orthogonal decomposition to filter out undesirable or badly performing geometries from an optimization process. Unlike traditional screening techniques, the presented method operates at the geometric level instead of the variable level. The filtering process uses the designs that result from a geometry parameterization instead of the variables that control the parameterization. The method is shown to perform well in the optimization of a two-dimensional airfoil for the minimization of drag-to-lift ratio, producing designs better than those resulting from traditional krigingbased surrogate model optimization and with a significant reduction in surrogate tuning cost.

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Kriging Hyperparameter Tuning Strategies

Cited by 150 publications

References 18 publications

Recent advances in surrogate-based optimization

Recent advances in surrogate-based optimization

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

Geometric Filtration Using Proper Orthogonal Decomposition for Aerodynamic Design Optimization

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