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