An improved approach to estimate the hyper-parameters of the kriging model for high-dimensional problems through the Partial Least Squares method

Abstract : During the last years, the kriging model has become one of the most popular methods in computer simulation and machine learning. Many engineering applications use the kriging model to approximate the physical phenomena which is modeled by expensive simulation models, especially aerodynamic and structural models. When many input variables are used, the conventional kriging model is inefficient mainly due to an exorbitant computational time required during its construction. To handle high-dimensional problems (up to 100), one method is recently proposed that combines the kriging model with the Partial Least Squares technique, the so-called KPLS model. For a large number of design variables (100+), 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, the KPLS model has provided a poor accuracy compared to the conventional kriging model on multimodal functions. To handle this issue, this paper proposes adding a new step during the construction of the KPLS model to improve its accuracy for multimodal functions. When the exponential covariance functions are used, this step is based on a simple identification between the covariance function of KPLS and kriging. The developed method
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Mathematical Problems in Engineering, Hindawi Publishing Corporation, 2016
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Dernière modification le : vendredi 12 août 2016 - 13:35:28
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Mohamed Amine Bouhlel, Nathalie Bartoli, Abdelkader Otsmane, Joseph Morlier. An improved approach to estimate the hyper-parameters of the kriging model for high-dimensional problems through the Partial Least Squares method. Mathematical Problems in Engineering, Hindawi Publishing Corporation, 2016. <hal-01342357>

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