Samir Touzani

Smoothing spline analysis of variance approach for global sensitivity analysis of computer codes

The paper investigates a nonparametric regression method based on smoothing spline analysis of variance (ANOVA) approach to address the problem of global sensitivity analysis (GSA) of complex and computationally demanding computer codes. The two steps algorithm of this method involves an estimation procedure and a variable selection. The latter can become computationally demanding when dealing with high dimensional problems. Thus, we proposed a new algorithm based on Landweber iterations. Using the fact that the considered regression method is based on ANOVA decomposition, we introduced a new direct method for computing sensitivity indices. Numerical tests performed on several analytical examples and on an application from petroleum reservoir engineering showed that the method gives competitive results compared to a more standard Gaussian process approach.

A workflow for decision making under uncertainty

We propose a workflow for decision making under uncertainty aiming at comparing different field development plan scenarios. The approach applies to mature fields where the residual uncertainty is estimated using a probabilistic inversion approach. Moreover, a robust optimization method is presented to optimize controllable parameters in the presence of uncertainty. The key element of this approach is the use of response surface model to reduce the very high number of simulator model evaluations that are classically needed to perform such workflows. The major issue is to be able to build an efficient and reliable response surface. This is achieved using a Gaussian process (kriging) statistical model and using a particular training set (experimental design) developed to take into account the variable correlation induced by the probabilistic inversion process. For the problem of optimization under uncertainty, an iterative training set is proposed, aiming at refining the response surface iteratively such as to effectively reduce approximation errors and converging faster to the true solution. The workflow is illustrated on a realistic test case of a mature field where the approach is used to compare two new development plan scenarios both in terms of expectation and of risk mitigation and to optimize well position parameters in the presence of uncertainty.

A Workflow for Decision Making Under Uncertainty

We propose a workflow for decision making under uncertainty aiming at comparing different development plan scenarios under uncertainty. The approach applies to mature fields where the residual uncertainty is estimated using a probabilstic inversion approach. Moreover a robust optimization method is discussed to optimize controllable parameters in the presence of uncertainty. The key elements of this approach are the use of response surface models to reduce the very high number of simulator model evaluations needed. To build efficient and reliable response surfaces for this application we discuss an experimental design method for correlated input variables where the correlation is induced by the probabilistic inversion process. For the problem of optimization under uncertainty an iterative approach is proposed aiming at refining the response surface iteratively such as to reduce effectively approximation errors and converging faster to the true solution. The workflow is illustrated on a realistic test case of a mature field where the approach is used to compare two new development plan scenarios both in terms of expectation and of risk mitigation and to optimize well position parameters in the presence of uncertainty.