Fitting the topology of synthetic particle systems with a novel graph representation

2026-07-20

AI Summary

This work addresses the challenge of efficiently modeling the topological structure of synthetic particle systems, which existing methods struggle to capture due to the high computational cost associated with large-scale 3D voxel data. The authors propose a generative-model-agnostic graph representation framework that shifts persistent homology computation from the image domain to the graph domain. By integrating graph representation learning, persistent homology, and topological data analysis, the method preserves key morphological features—such as geometric consistency and particle size distribution—while enabling, for the first time, efficient topological modeling of particle systems. This approach significantly enhances the alignment between synthetic and real systems in both topological and geometric characteristics.

Abstract

The shape and arrangement of particles in a material determine its macroscopic properties. The generation of synthetic data with varying particle structure, often represented as 3D voxel images, combined with simulation of macroscopic properties reveals structure-property relations. Most particle generation models focus on single-particle characteristics like shape and size. We aim at fitting the topology of the particle system using tools from persistent homology. However, the large size of the required 3D image data makes existing methods computationally infeasible. We bridge this gap by introducing a novel graph representation of particle systems and transferring the computation of persistent homology from the image domain to the graph domain. This yields a postprocessing method for synthetic images of particle systems, that is independent of the underlying generation method and improves topological and geometrical agreement with real particle systems while preserving morphological characteristics such as the particle size distribution.

Problem

• particle systems
• topology
• persistent homology
• 3D voxel images
• computational feasibility

Innovation

• graph representation
• persistent homology
• particle systems
• topological data analysis
• synthetic data generation