AI Insight
DiffeoMorph is a computational framework that uses artificial intelligence to teach groups of simple agents how to collectively organize themselves into complex three-dimensional shapes without centralized control, mimicking biological development. The system employs rotation-invariant graph neural networks and a novel shape-matching metric based on 3D Zernike polynomials that compares shapes as continuous distributions rather than discrete points. The researchers demonstrate that their approach can successfully guide agent populations to form various complex target shapes starting from simple initial configurations.
Why it matters
This work has potential applications in distributed robotics, programmable matter, and understanding how biological organisms develop complex structures through decentralized control. The framework could enable design of self-assembling swarms of robots or programmable materials that autonomously organize into desired shapes, and may provide insights into developmental biology by modeling how cells coordinate to form organs and tissues.
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⚠️ Preprint – Noch nicht peer-reviewed
Dieser Artikel wurde noch nicht von unabhängigen Experten begutachtet. Die Ergebnisse sind vorläufig und sollten mit Vorsicht interpretiert werden.
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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 orientation. To achieve rotation invariance while preserving reflection sensitivity, we include an alignment step that optimally rotates the predicted Zernike spectrum to match the target before computing the loss. We perform benchmarking to establish the advantages of our shape-matching loss over other standard distance metrics for shape comparison tasks. We then demonstrate that DiffeoMorph can form a range of complex shapes from minimally patterned initial conditions. DiffeoMorph provides a general framework for learning distributed control strategies for morphogenesis, swarm robotics, and programmable self-assembly.
Source: DiffeoMorph: Learning Distributed 3D Morphogenesis with Rotation-Invariant Spectral Shape Matching