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DiffeoMorph: Learning to Morph 3D Shapes Using Differentiable Agent-Based Simulations
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Introduces DiffeoMorph, an end-to-end differentiable agent-based morphogenesis framework with an SE(3)-equivariant EGNN force model trained by a rotation-aligned 3D Zernike spectral shape-matching loss.
Problem
Learning distributed agent update rules that morph a population of identical agents into a target 3D shape requires a shape-matching loss invariant to agent permutation, agent count, and global orientation while remaining sensitive to chirality.
Approach
Compare shapes as continuous distributions via 3D Zernike moments, align predicted and target spectra with a quaternion-parameterized Wigner-D rotation before computing the MSE, and use an SE(3)-equivariant EGNN with gene-expression states to drive agents; gradients through the inner alignment are detached (envelope theorem) with an optional Riemannian implicit-differentiation correction.
Key results
- The Zernike spectral loss is the only evaluated metric that is invariant to permutation, point count, and rotation while remaining chirality-sensitive, with superior runtime scaling in point count (per paper's benchmarking claims).
- The trained force model reliably recovers target ellipsoid, crescent, starfish and bunny shapes from a sphere with 1-3 organizer groups, and generalizes to noise up to 0.2 and shifted organizers.
- Only the proposed model consistently achieves low loss under both noise and rotational perturbations compared with Graph NCA and NPA.
Surprising findings
- Two organizer groups fail to preserve chirality under organizer rotation; at least three organizers are needed to reliably fix handedness.
- Gradients through the alignment optimization can be detached for an exact solve, so implicit differentiation adds negligible runtime overhead.
Limitations
- Chirality requires at least three organizer groups; two organizers break handedness under rotation.
- Implicit differentiation is only exact for converged inner solves; finite-step alignment gradients are approximate.
- Hessian invertibility suffers for near-symmetric shapes (e.g., ellipsoids), requiring pseudoinverse thresholding.
Experimental setup
Datasets: Stanford bunny (point cloud) ellipsoid, crescent, starfish, helical ellipsoid targets
Benchmarks: shape-matching invariance benchmark vs. Chamfer, EMD, pairwise, Gromov-Wasserstein, power spectrum, bispectrum, trispect noise and rotation generalization vs. Graph NCA and NPA
Metrics: shape-matching loss runtime scaling invariance properties
Baselines: Chamfer distance Earth Mover's distance Pairwise distance Gromov-Wasserstein distance Power spectrum bispectrum trispectrum Graph NCA Neural Particle Automata
Builds on: EGNN Neural Cellular Automata Graph NCA Neural Particle Automata Iterative Closest Point
Closest papers by meaning
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- MorphGrower: A Synchronized Layer-by-layer Growing Approach for Plausible Neuronal Morphology Generation (ICML 2024 · similarity 0.82)
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