Kernel principal component analysis for efficient, differentiable parametrization of multipoint geostatistics (Q930824)

The authors adopt methods from machine learning theory and apply them for geological model parametrization. Especially they use the socalled kernel principal component analysis (KPCA) introduced by Scholkopf and coworkers [see \textit{B. Scholkopf, A. J. Smola, K. R. Muller}, Nonlinear component analysis as a kernel eigenvalue problem. Neur. Comput. 10, 1299--1319 (1998)]. Using the ``kernel trick'' drawbacks of the traditionally used standard Karhunen-Loeve expansion can be avoided (like high dimensionality of the underlying covariance matrix, restriction to linear relationships for parametrization). After detailed introduction into KPCA the authors apply this method to history match a water flooding problem.