Abstract
The general idea here is to produce a high quality representation of the indicator function of different phases of the material while adequately scaling with the storage requirements for high resolution Digital Material Representation (DMR). To this end, we propose a three-stage reduction algorithm combining Proper Orthogonal Decomposition (POD) and Proper Generalized Decomposition (PGD)- first, each snapshot pixel/voxel matrix is decomposed into a linear combination of tensor products of 1D basis vectors. Next a common basis is determined for the entire set of microstructure snapshots. Finally, the analysis of the dimensionality of the resulting nonlinear space yields the minimal set of parameters needed in order to represent the microstructure with sufficient precision. We showcase this approach by constructing a low-dimensional model of a two-phase composite microstructure.