Objective-sensitive principal component analysis for high-dimensional inverse problems

We introduce a novel approach of data-driven dimensionality reduction for solving high-dimensional optimization problems, including history matching. Objective-Sensitive parameterization of the argument accounts for the corresponding change of objective function value. The result is achieved via an extension of the conventional loss function, which only quantifies approximation error over realizations. This paper contains three instances of such an approach based on Principal Component Analysis (PCA). Gradient-Sensitive PCA (GS-PCA) exploits a linear approximation of the objective function. Two other approaches solve the problem approximately within the framework of stationary perturbation theory (SPT). All the algorithms are verified and tested with a synthetic reservoir model. The results demonstrate improvements in parameterization quality regarding the reveal of the unconstrained objective function minimum. Also, we provide possible extensions and analyze the overall applicability of the Objective-Sensitive approach, which can be combined with modern parameterization techniques beyond PCA.