Efficient high-dimensional metamodeling strategy using recursive decomposition coupled with sequential sampling method
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RESEARCH PAPER
Efficient high-dimensional metamodeling strategy using recursive decomposition coupled with sequential sampling method Kyeonghwan Kang 1 & Ikjin Lee 1 Received: 10 May 2020 / Revised: 10 May 2020 / Accepted: 28 July 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Metamodel has been widely used to solve computationally expensive engineering problems, and there have been many studies on how to efficiently and accurately generate metamodels with limited number of samples. However, applications of these methods could be limited in high-dimensional problems since it is still challenging due to curse of dimensionality to generate accurate metamodels in high-dimensional design space. In this paper, recursive decomposition coupled with a sequential sampling method is proposed to identify latent decomposability and efficiently generate high-dimensional metamodels. Whenever a new sample is inserted, variable decomposition is repeatedly performed using interaction estimation from a full-dimension Kriging metamodel. The sampling strategy of the proposed method consists of two units: decomposition unit and accuracy improvement unit. Using the proposed method, latent decomposability of a function can be identified using reasonable number of samples, and a highdimensional metamodel can be generated very efficiently and accurately using the identified decomposability. Numerical examples using both decomposable and indecomposable problems show that the proposed method shows reasonable decomposition results, and thus improves metamodel accuracy using similar number of samples compared with conventional methods. Keywords Surrogate modeling . Metamodeling . High dimension . Decomposition . Sequential sampling
1 Introduction Computer simulation is frequently used to solve complex engineering problems instead of actual experiments to save design development cost. However, cost for computer simulation could be very high in cases when the simulation model is very complex. Metamodeling methods, which approximate an expensive performance function using limited number of samples, are widely used to resolve this computation cost problem, and have been successfully applied to design optimization due to its efficiency (Liang et al. 2014; Zhao et al. 2011; Shan and Wang 2010a; Chen et al. 2010; Jin et al. 2002).
Responsible Editor: Shapour Azarm * Ikjin Lee [email protected] Kyeonghwan Kang [email protected] 1
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea
A great deal of researches have been implemented to efficiently and accurately generate metamodels with limited number of samples: polynomial regression, response surface method, Gaussian process regression (GPR), radial basis function (RBF), etc. (Jin et al. 2001). High-dimensional model representation (HDMR) has been frequently used for highdimensional metamodeling (Sobol 2003), and extended to various approaches such as random sampling based HDMR (Li et al. 2006; Li et al.
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