Bayesian random persistence diagram generation: An application to material microstructure analysis

Abstract

Data analysis helps identify changes in the microstructure of materials, but is often hindered by the cost and time requirements of experimental data generation. Data augmentation provides an in silico alternative. A recent data augmentation algorithm, known as the random persistence diagram generator (RPDG), samples a sequence of synthetic topological summaries from a possibly limited amount of data. RPDG relies on a parametric model for persistence diagrams, namely a pairwise interacting point process (PIPP). Herein, we develop a Bayesian approach to infer the PIPP parameters and call the resulting pipeline the Bayesian RPDG (BRPDG). We showcase that BRPDG exhibits higher discriminative power than RPDG in the identification of materials structural changes.