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A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction
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Proposes GMTNet, an O(3)-equivariant graph network with crystal space-group symmetry enforcement for predicting dielectric, piezoelectric, and elastic tensors, evaluated on a curated JARVIS-DFT tensor dataset.
Problem
Predicting general crystal tensor properties (dielectric, piezoelectric, elastic) that must be O(3)-equivariant and respect crystal space-group symmetry constraints, which prior ML models largely ignore.
Approach
Build an equivariant GNN (Comformer invariant layers plus tensor-field-network equivariant message passing) whose crystal-level features are averaged over space-group rotations, and generate tensors via tensor products with external field vectors (D = sum (G ⊗ E)), so that equivariance and symmetry constraints hold by construction.
Key results
- On dielectric tensors GMTNet reaches Fnorm 3.50 and EwT25% 84.5%, versus 3.92 / 81.3% for ETGNN and 4.16 / 74.9% for MEGNET.
- GMTNet achieves 100% success rate on zero-element and symmetry-equality tests across crystal systems, where MEGNET scores 0% and ETGNN scores as low as 0% on several systems.
- GMTNet reduces running time by 43% and parameters by 37% relative to ETGNN on the dielectric dataset (0.7M vs 1.1M parameters).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GMTNet instead of ETGNN | Dielectric tensor prediction · Dielectric test set | Fnorm: 3.92 -> 3.50 | Helped |
| Use GMTNet instead of ETGNN | Dielectric tensor prediction · Dielectric test set | EwT 25%: 81.3% -> 84.5% | Helped |
| Use GMTNet instead of ETGNN | Dielectric tensor prediction · Dielectric test set | EwT 10%: 41.6% -> 57.1% | Helped |
| Use GMTNet instead of ETGNN | Piezoelectric tensor prediction · Piezo test set | Fnorm | No clear effect |
| Remove equivariant tensor prediction (ablation) | GMTNet · Dielectric test set | Fnorm: 3.76 -> 4.15 | Hurt |
| Add structure correction (ablation) | GMTNet with equivariant tensor prediction · Dielectric test set | Fnorm: 3.76 -> 3.72 | Helped |
| Add symmetry-constrained crystal-level feature correction (ablation) | GMTNet with structure correction · Dielectric test set | Fnorm: 3.72 -> 3.56 | Helped |
| Add tolerance-guided prediction adjustment for equality (ablation) | GMTNet with symmetry constraints · Dielectric test set | Fnorm: 3.56 -> 3.50 | Helped |
| Apply group averaging to model outputs | MEGNET · Dielectric test set | Fnorm: 4.16 -> 4.51 | Hurt |
| Apply group averaging to model outputs | ETGNN · Dielectric test set | Fnorm: 3.92 -> 4.07 | Hurt |
| Use GMTNet instead of MEGNET | Symmetry-constrained zero dielectric elements · Cubic | Success rate: 0% -> 100% | Helped |
| Use GMTNet instead of ETGNN | Symmetry-constrained zero dielectric elements · Tetragonal | Success rate: 1.3% -> 100% | Helped |
Surprising findings
- Forcing space-group invariance by group averaging of outputs degrades accuracy (e.g., ETGNN Fnorm 3.92 rises to 4.07 with GA), so built-in design works better than post-hoc averaging.
- The MEGNET invariant baseline breaks O(3) equivariance under rotation, with Fnorm changing across rotated inputs.
Limitations
- The curated tensor dataset is small (under 15,000 samples per property) and could be expanded.
- Cannot generate tensor predictions for amorphous materials.
- Symmetry enforcement depends on distortion tolerance and tuned thresholds for equality detection.
Experimental setup
Datasets: JARVIS-DFT dielectric JARVIS-DFT piezoelectric JARVIS-DFT elastic
Benchmarks: curated JARVIS-DFT crystal tensor dataset (dielectric, piezoelectric, elastic)
Metrics: Frobenius norm distance error within threshold (EwT) 25%/10%/5% zero-element success rate mutually-dependent element success rate
Baselines: MEGNET ETGNN MEGNET-GA ETGNN-GA
Builds on: Comformer tensor field network CGCNN e3nn MEGNET
Closest papers by meaning
- Space Group Equivariant Crystal Diffusion (NeurIPS 2025 · similarity 0.89)
- WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry (ICML 2025 · similarity 0.88)
- Energy-conserving equivariant GNN for elasticity of lattice architected metamaterials (ICLR 2024 · similarity 0.87)
- Wyckoff Transformer: Generation of Symmetric Crystals (ICML 2025 · similarity 0.87)
- Local-Global Associative Frames for Symmetry-Preserving Crystal Structure Modeling (NeurIPS 2025 · similarity 0.87)
- Learning the Electronic Hamiltonian of Large Atomic Structures (ICML 2025 · similarity 0.87)
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