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Equivariant Graph Mechanics Networks with Constraints
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Represent constraints with generalized coordinates and forward kinematics | GMN · Constrained N-Body systems | prediction error: 2.81 -> 1.84 | Helped |
| Represent molecular bonds with constrained kinematics | GMN · MD17, 7 of 8 molecules | prediction error | Helped |
| Use GMN for articulated body motion | GMN · CMU Motion Capture walking | prediction error: 59.1 -> 43.9 | Helped |
| Replace hand-crafted forward kinematics with learnable equivariant FK (ablation) | GMN · Constrained N-Body (3,2,1), train 500 | prediction error: 2.48 -> 3.19 | Hurt |
| Remove equivariance from φ₂ (ablation) | GMN · Constrained N-Body (3,2,1), train 500 | prediction error: 2.48 -> 3.74 | Hurt |
| Share full-input φ₂ parameters across sticks and hinges (ablation) | GMN · Constrained N-Body (3,2,1), train 500 | prediction error: 2.48 -> 3.86 | Hurt |
| Use the same full-input φ₂ form for sticks and hinges without sharing parameters (ablation) | GMN · Constrained N-Body (3,2,1), train 500 | prediction error: 2.48 -> 2.86 | Hurt |
| Use force-only φ₂ instead of the default object-specific acceleration inference (ablation) | GMN · Constrained N-Body (3,2,1), train 500 | prediction error: 2.48 -> 3.10 | Hurt |
| Remove normalization from the equivariant function (ablation) | GMN · Constrained N-Body | training stability: O.F. | Hurt |
| Model a hinge as two separate sticks (ablation) | GMN · Constrained N-Body (3,2,1), train 500 | prediction error: 2.48 -> 3.02 | Hurt |
| Move charges from edge features to node features (ablation) | GMN · Constrained N-Body (3,2,1), train 500 | prediction error: 2.48 -> 2.63 | No clear effect |
| Use bond constraints on a small, simple molecule | GMN · MD17 Ethanol | prediction error: 4.64 -> 4.83 | Hurt |
Closest papers by meaning
- Universally Invariant Learning in Equivariant GNNs (NeurIPS 2025 · similarity 0.90)
- SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases (ICLR 2024 · similarity 0.89)
- Equivariant Graph Neural Operator for Modeling 3D Dynamics (ICML 2024 · similarity 0.88)
- Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks? (NeurIPS 2024 · similarity 0.88)
- On the Generalization of Equivariant Graph Neural Networks (ICML 2024 · similarity 0.88)
- Large Language-Geometry Model: When LLM meets Equivariance (ICML 2025 · similarity 0.87)
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