Modeling a domain wall network in BiFeO₃ with stochastic geometry and entropy-based similarity measure

A compact and tractable two-dimensional model to generate the topological network structure of domain walls in BiFeO₃ thin films is presented in this study. Our method combines the stochastic geometry parametric model of the centroidal Voronoi tessellation optimized using the von Neumann entropy, a novel information-theoretic tool for networks. The former permits the generation of image-based stochastic artificial samples of domain wall networks, from which the network structure is subsequently extracted and converted to the graph-based representation. The von Neumann entropy, which reflects information diffusion across multiple spatiotemporal scales in heterogeneous networks, plays a central role in defining a fitness function. It allows the use of the network as a whole rather than using a subset of network descriptors to search for optimal model parameters. The optimization of the parameters is carried out by a genetic algorithm through the maximization of the fitness function and results in the desired graph-based network connectivity structure. Ground truth empirical networks are defined, and a dataset of network connectivity structures of domain walls in BiFeO₃ thin films is undertaken through manual annotation. Both a versatile tool for manual network annotation of noisy images and a new automatic network extraction method for high-quality images are developed.