Thermal Response Variability of Random Polycrystalline Microstructures (Communications in Computational Physics, 2011)
A data-driven model reduction strategy is presented for the representationof random polycrystal microstructures. Given a set of microstructure snapshots thatsatisfy certain statistical constraints such as given low-order moments of the grainsize distribution, using a non-linear manifold learning approach, we identify the intrinsiclow-dimensionality of the microstructure manifold. In addition to grain size,a linear dimensionality reduction technique (Karhunun-Loéve Expansion) is used toreduce the texture representation. The space of viable microstructures is mapped toa low-dimensional region thus facilitating the analysis and design of polycrystal microstructures.This methodology allows us to sample microstructure features in thereduced-order space thus making it a highly efficient, low-dimensional surrogate forrepresenting microstructures (grain size and texture). We demonstrate the model reductionapproach by computing the variability of homogenized thermal propertiesusing sparse grid collocation in the reduced-order space that describes the grain sizeand orientation variability.