[2512.17129] DiffeoMorph: Learning to Morph 3D Shapes Using Differentiable Agent-Based Simulations

Computer Science > Machine Learning arXiv:2512.17129 (cs) [Submitted on 18 Dec 2025 (v1), last revised 7 May 2026 (this version, v2)] Title:DiffeoMorph: Learning to Morph 3D Shapes Using Differentiable Agent-Based Simulations Authors:Seong Ho Pahng, Guoye Guan, Benjamin Fefferman, Sahand Hormoz View a PDF of the paper titled DiffeoMorph: Learning to Morph 3D Shapes Using Differentiable Agent-Based Simulations, by Seong Ho Pahng and 3 other authors View PDF HTML (experimental) Abstract:Biological systems can form complex three-dimensional structures through the collective behavior of agents that share a common update rule and operate without central control. How such distributed control gives rise to precise global patterns remains a central question not only in developmental biology but also in distributed robotics, programmable matter, and multi-agent learning. Here, we introduce DiffeoMorph, an end-to-end differentiable framework for learning a morphogenesis protocol that guides a population of agents to morph into a target 3D shape. Each agent updates its position and internal state using an SE(3)-equivariant graph neural network, based on its own internal state and signals received from other agents. To train this system, we introduce a new shape-matching loss based on 3D Zernike polynomials, which compares the predicted and target shapes as continuous spatial distributions, not as discrete point clouds, and is invariant to agent ordering, number of agents, and global ...