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Data-driven selection of tessellation models describing polycrystalline microstructures. (English) Zbl 1405.82034

Summary: Tessellation models have proven to be useful for the geometric description of grain microstructures in polycrystalline materials. With the use of a suitable tessellation model, the complex morphology of grains can be represented by a small number of parameters assigned to each grain, which not only entails a significant reduction in complexity, but also facilitates the investigation of certain geometric features of the microstructure. However, for a given set of microstructural data, the choice of a particular geometric model is traditionally based on researcher intuition. The model should provide a sufficiently good approximation to the data, while keeping the number of parameters small. In this paper, we discuss general aspects of the process of model selection and suggest several criteria for selecting an appropriate candidate from a certain set of tessellation models. The choice of candidate represents a trade-off between accuracy and complexity of the model. Here, the selected model is used solely to approximate given data samples, but it also provides guidance for developing stochastic tessellation models and generating virtual microstructures. Model fitting is carried out by simulated annealing, applied in a consistent manner to twelve different tessellation models.

MSC:

82D25 Statistical mechanics of crystals
62F07 Statistical ranking and selection procedures
05B45 Combinatorial aspects of tessellation and tiling problems
60D05 Geometric probability and stochastic geometry
62B10 Statistical aspects of information-theoretic topics

Software:

DREAM.3D
PDFBibTeX XMLCite
Full Text: DOI

References:

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