Calculation, utilization, and inference of spatial statistics in practical spatio-temporal data

Abstract

The direct influence of spatial and structural arrangement in various length scales to the performance characteristics of materials is a core premise of materials science. Spatial correlations in the form of n-point statistics have been shown to be very effective in robustly describing the structural features of a plethora of materials systems, with a high number of cases where the obtained futures were successfully used to establish highly accurate and precise relationships to performance measures and manufacturing parameters. This work addresses issues in calculation, representation, inference and utilization of spatial statistics under practical considerations to the materials researcher. Modifications are presented to the theory and algorithms of the existing convolution based computation framework in order to accommodate deformed, irregular, rotated, missing or degenerate data, with complex or non-probabilistic state definitions. Memory efficient personal computer oriented implementations are discussed for the extended framework. A universal microstructure generation framework with the ability to efficiently address a vast variety of geometric or statistical constraints including those imposed by spatial statistics is assembled while maintaining scalability, and compatibility with structure generators in literature.