Objective-Sensitive Principal Component Analysis for High-Dimensional Inverse Problems

TL;DR

This paper introduces an objective-sensitive PCA method that adaptively encodes large-scale random fields for high-dimensional inverse problems, improving optimization efficiency and accuracy.

Contribution

It develops a novel gradient-sensitive PCA technique that incorporates objective function behavior into the principal component basis, enhancing high-dimensional inverse problem solutions.

Findings

Improved encoding quality for history matching.

Enhanced objective function minimization.

Efficient algorithms with low computational costs.

Abstract

We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems, including history matching. The developed technique is based on principal component analysis (PCA) but modifies a purely data-driven basis of principal components considering objective function behavior. To define an efficient encoding, Gradient-Sensitive PCA uses an objective function gradient with respect to model parameters. We propose computationally efficient implementations of the technique, and two of them are based on stationary perturbation theory (SPT). Optimality, correctness, and low computational costs of the new encoding approach are tested, verified, and discussed. Three algorithms for optimal parameter decomposition are presented and applied to an objective of 2D synthetic history matching. The results demonstrate improvements in encoding quality regarding objective function minimization and distributional patterns of the desired field. Possible applications and extensions are proposed.