Differentiable Voronoi Diagrams for Simulation of Cell-Based Mechanical Systems

TL;DR

This paper introduces a differentiable Voronoi diagram-based method for simulating cell-based mechanical systems, enabling efficient, topology-changing simulations with continuous geometry updates and broad boundary coupling.

Contribution

The paper presents a novel cell-centered approach using differentiable Voronoi diagrams that simplifies topology handling and improves computational efficiency in cell-based simulations.

Findings

Enables simulation of cell splitting and merging with continuous geometry.

Achieves faster computation times compared to explicit cell models.

Successfully matches soap foam images in inverse problem applications.

Abstract

Navigating topological transitions in cellular mechanical systems is a significant challenge for existing simulation methods. While abstract models lack predictive capabilities at the cellular level, explicit network representations struggle with topology changes, and per-cell representations are computationally too demanding for large-scale simulations. To address these challenges, we propose a novel cell-centered approach based on differentiable Voronoi diagrams. Representing each cell with a Voronoi site, our method defines shape and topology of the interface network implicitly. In this way, we substantially reduce the number of problem variables, eliminate the need for explicit contact handling, and ensure continuous geometry changes during topological transitions. Closed-form derivatives of network positions facilitate simulation with Newton-type methods for a wide range of per-cell energies. Finally, we extend our differentiable Voronoi diagrams to enable coupling with arbitrary rigid and deformable boundaries. We apply our approach to a diverse set of examples, highlighting splitting and merging of cells as well as neighborhood changes. We illustrate applications to inverse problems by matching soap foam simulations to real-world images. Comparative analysis with explicit cell models reveals that our method achieves qualitatively comparable results at significantly faster computation times.