An efficient methodology for modeling complex computer codes with Gaussian processes

TL;DR

This paper introduces an efficient methodology for constructing Gaussian process-based metamodels to approximate complex computer codes, enabling faster uncertainty analysis, sensitivity studies, and optimization.

Contribution

The paper develops a specific estimation procedure for Gaussian process models tailored to complex, nonlinear, and high-dimensional cases, improving modeling accuracy and efficiency.

Findings

The proposed algorithm outperforms existing methods on analytical test cases.

Application to hydrogeological code demonstrates practical effectiveness.

Method handles nonlinearity, dispersion, discontinuities, and high dimensions.

Abstract

Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this inconvenience consists in replacing the complex computer code by a reduced model, called a metamodel, or a response surface that represents the computer code and requires acceptable calculation time. One particular class of metamodels is studied: the Gaussian process model that is characterized by its mean and covariance functions. A specific estimation procedure is developed to adjust a Gaussian process model in complex cases (non linear relations, highly dispersed or discontinuous output, high dimensional input, inadequate sampling designs, ...). The efficiency of this algorithm is compared to the efficiency of other existing algorithms on an analytical test case. The proposed methodology is also illustrated for the case of a complex hydrogeological computer code, simulating radionuclide transport in groundwater.