# Anisotropic power diagrams for polycrystal modelling: efficient generation of curved grains via optimal transport

arXiv: https://arxiv.org/abs/2403.03571 · HTML: https://mlsanity.com/paper/2403.03571/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Mar 2024.

## Built on by (most cited first, 3 of 3)

- [Semi-Discrete Optimal Transport: Nearly Minimax Estimation With Stochastic Gradient Descent and Adaptive Entropic Regularization](https://mlsanity.com/paper/2405.14459/) (2024)
- [Fitting Generalized Power Diagrams to 3D Image Data: A Prerequisite for Virtual Materials Testing](https://mlsanity.com/paper/2507.14268/) (2025)
- [Decreasing Entropic Regularization Averaged Gradient for Semi-Discrete Optimal Transport](https://mlsanity.com/paper/2510.27340/) (2025)

## Abstract (arXiv)

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.