Polynomial Chaos Expansion for an Efficient Uncertainty and Sensitivity Analysis of Complex Numerical Models

Abstract : In this work we address the problem of performing uncertainty and sensitivity analysis of complex physical systems where classical Monte-Carlo methods are too expensive to be applied due to the high computational complexity. We consider the Polynomial Chaos Expansion (PCE) as an efficient way of computing a response surface for a model of gas injection into an incompressible porous media aiming at assessing the sensitivity indices and the main distributional features of the maximal spread of the gas cloud. The necessity of an uncertainty study for such a model arises in case of CO2 storage risk assessment and is here performed by jointly using a numerical scheme to solve the system of partial differential equation (PDE) governing the model and the PCE method to efficiently simulate the physical system response by a meta-model. The performances of the PCE method and a standard MC approach are compared through an extended simulation study showing that the computational gain of the PCE approach is remarkable without significant loss in the precision of the estimates.