Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models

TL;DR

This paper introduces an efficient regression-based method combining Elastic Net regularization and feature ranking to improve Polynomial Chaos Expansion for uncertainty quantification in complex subsurface flow models, demonstrating faster convergence.

Contribution

The paper presents a novel approach that enhances PCE coefficient estimation using Elastic Net and data-driven feature ranking, especially effective in high-dimensional problems.

Findings

High convergence rates achieved in high-dimensional problems

Significant improvement over standard PCE methods

Effective application to subsurface flow and CO2 sequestration models

Abstract

Surrogate-modelling techniques including Polynomial Chaos Expansion (PCE) is commonly used for statistical estimation (aka. Uncertainty Quantification) of quantities of interests obtained from expensive computational models. PCE is a data-driven regression-based technique that relies on spectral polynomials as basis-functions. In this technique, the outputs of few numerical simulations are used to estimate the PCE coefficients within a regression framework combined with regularization techniques where the regularization parameters are estimated using standard cross-validation as applied in supervised machine learning methods. In the present work, we introduce an efficient method for estimating the PCE coefficients combining Elastic Net regularization with a data-driven feature ranking approach. Our goal is to increase the probability of identifying the most significant PCE components by assigning each of the PCE coefficients a numerical value reflecting the magnitude of the coefficient and its stability with respect to perturbations in the input data. In our evaluations, the proposed approach has shown high convergence rate for high-dimensional problems, where standard feature ranking might be challenging due to the curse of dimensionality. The presented method is implemented within a standard machine learning library (Scikit-learn) allowing for easy experimentation with various solvers and regularization techniques (e.g. Tikhonov, LASSO, LARS, Elastic Net) and enabling automatic cross-validation techniques using a widely used and well tested implementation. We present a set of numerical tests on standard analytical functions, a two-phase subsurface flow model and a simulation dataset for CO2 sequestration in a saline aquifer. For all test cases, the proposed approach resulted in a significant increase in PCE convergence rates.