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

Area of Science:

• Computational Biology
• Robotics
• Artificial Intelligence

Background:

• Biological systems exhibit complex 3D structures formed by collective agent behavior without central control.
• Understanding distributed control in morphogenesis is crucial for developmental biology, robotics, and multi-agent learning.

Purpose of the Study:

• Introduce DiffeoMorph, a differentiable framework for learning morphogenesis protocols.
• Enable a population of agents to collectively form a target 3D shape.

Main Methods:

• Utilize an attention-based SE(3)-equivariant graph neural network for agent position and state updates.
• Employ a novel shape-matching loss based on 3D Zernike polynomials for continuous shape comparison.
• Implement an alignment step with implicit differentiation for SO(3) invariance.

Main Results:

• Demonstrate the superiority of the 3D Zernike polynomial loss over standard metrics.
• Showcase DiffeoMorph's ability to generate diverse 3D shapes from simple to complex morphologies.
• Validate the framework's effectiveness using minimal spatial cues.

Conclusions:

• DiffeoMorph provides an effective end-to-end differentiable framework for learning collective shape formation.
• The developed shape-matching loss and gradient computation methods are robust and efficient.
• This work offers a promising approach for designing self-organizing systems in biology and artificial intelligence.