  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.
