2024/03/06 by Maciej Buze, Jean Feydy, Buze, Maciej +7 · 2 citations
Materials Science · #FOS: Mathematics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Microstructure and mechanical properties #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2403.03571
openalex publication_date 2024/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The microstructure of metals and foams can be effectively modelled with anisotropic power diagrams (APDs), which provide control over the shape of individual grains. One major obstacle to the wider adoption of APDs is the computational cost that is associated with their generation. We propose a novel approach to generate APDs with prescribed statistical properties, including fine control over the size of individual grains. To this end, we rely on fast optimal transport algorithms that stream well on Graphics Processing Units (GPU) and handle non-uniform, anisotropic distance functions. This allows us to find large APDs that best fit experimental data and generate synthetic high-resolution microstructures in (tens of) seconds. This unlocks their use for computational homogenisation, which is especially relevant to machine learning methods that require the generation of large collections of representative microstructures as training data. The paper is accompanied by a Python library, PyAPD, which is freely available at: www.github.com/mbuze/PyAPD.