Nested polynomial trends for the improvement of Gaussian process-based predictors

Journal Article · Sun Oct 01 04:00:00 EDT 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2017.05.051· OSTI ID:22701608

Soize, C. ^[1]; Marque-Pucheu, S. ^[2]; Garnier, J. ^[3]

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1. Université Paris-Est, MSME UMR 8208 CNRS, Marne-la-Vallée (France)
2. CEA/DAM/DIF, F-91297, Arpajon (France)
3. Laboratoire de Probabilités et Modèles Aléatoires, Laboratoire Jacques-Louis Lions, Université Paris Diderot, 75205 Paris Cedex 13 (France)

The role of simulation keeps increasing for the sensitivity analysis and the uncertainty quantification of complex systems. Such numerical procedures are generally based on the processing of a huge amount of code evaluations. When the computational cost associated with one particular evaluation of the code is high, such direct approaches based on the computer code only, are not affordable. Surrogate models have therefore to be introduced to interpolate the information given by a fixed set of code evaluations to the whole input space. When confronted to deterministic mappings, the Gaussian process regression (GPR), or kriging, presents a good compromise between complexity, efficiency and error control. Such a method considers the quantity of interest of the system as a particular realization of a Gaussian stochastic process, whose mean and covariance functions have to be identified from the available code evaluations. In this context, this work proposes an innovative parametrization of this mean function, which is based on the composition of two polynomials. This approach is particularly relevant for the approximation of strongly non linear quantities of interest from very little information. After presenting the theoretical basis of this method, this work compares its efficiency to alternative approaches on a series of examples.

• OSTI ID: 22701608
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 346; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPUTER CODES
GAUSSIAN PROCESSES
NESTS
NONLINEAR PROBLEMS
POLYNOMIALS
PROCESSING
SENSITIVITY ANALYSIS
STOCHASTIC PROCESSES