A non-linear dimension reduction methodology for generating data-driven stochastic input models

Stochastic analysis of random heterogeneous media provides information of significance only if realistic input models of the topology and material property variations are used. This work introduces a framework to construct such input stochastic models for the topology, thermal diffusivity and permeability variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the topology and material properties. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology.