An Improved Approach for Estimating the Hyperparameters of the Kriging Model for High-Dimensional Problems through the Partial Least Squares Method

Abstract

During the last years, kriging has become one of the most popular methods in computer simulation and machine learning. Kriging models have been successfully used in many engineering applications, to approximate expensive simulation models. When many input variables are used, kriging is inefficient mainly due to an exorbitant computational time required during its construction. To handle high-dimensional problems (100+), one method is recently proposed that combines kriging with the Partial Least Squares technique, the so-called KPLS model. This method has shown interesting results in terms of saving CPU time required to build model while maintaining sufficient accuracy, on both academic and industrial problems. However, KPLS has provided a poor accuracy compared to conventional kriging on multimodal functions. To handle this issue, this paper proposes adding a new step during the construction of KPLS to improve its accuracy for multimodal functions. When the exponential covariance functions are used, this step is based on simple identification between the covariance function of KPLS and kriging. The developed method is validated especially by using a multimodal academic function, known as Griewank function in the literature, and we show the gain in terms of accuracy and computer time by comparing with KPLS and kriging.

Efficient global optimization for high-dimensional constrained problems by using the Kriging models combined with the partial least squares method

“…In this paper, two new methods for solving high-dimensional constrained optimization problems are developed, both based on SEGO approach: (i) SEGOKPLS uses SEGO with the KPLS model (Bouhlel et al 2016b); and (ii) SEGOKPLS+K uses SEGO with the KPLS+K model (Bouhlel et al 2016a). The SEGOKPLS(+K) algorithms build KPLS(+K) for each output function at each iteration of optimization.…”

An Overview of Gradient-Enhanced Metamodels with Applications

“…Beyond 10000 points, computer memory would be an additional limitation. Recent works on Gaussian Processes have introduced strategies to deal with large number of points [137,138] and high-dimensional problems [139,140]. However these approaches remain currently limited to response-only data.…”

A clustered and surrogate-based MDA use case for MDO scenarios in AGILE project

“…• ONERA's tool, MOE, a Mixture of Experts technique which combines local surrogate models [31]. The local expert could be a polynomial model (linear, quadratic, cubic), a radial basis function or some specific kriging models adapted to high-dimensional problems [32,33]…”