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Learning Superconductivity from Ordered and Disordered Material Structures
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Builds SuperCon3D, a dataset pairing experimental superconducting Tc with ordered and disordered 3D crystal structures, and proposes SODNet (SE(3)-equivariant graph attention for disordered crystals) and DiffCSP-SC (transformer-based diffusion generator with Tc guidance).
Problem
Superconductivity's relationship to chemical and structural features is poorly understood, and no dataset pairs experimental Tc with 3D crystal structures including disordered (substitutionally or positionally disordered) sites; existing graph models mostly handle only ordered crystals.
Approach
Represents disordered sites as occupancy-weighted linear combinations of atomic embeddings in an equivariant graph attention network (SODNet), and extends DiffCSP with a transformer backbone and SODNet-based Tc guidance and evaluation for inverse design of superconductors.
Key results
- SODNet reaches MAE 0.505 logK and R2 0.748 on SuperCon3D with all disorder types, versus 0.748 MAE for Matformer on ordered data (about 17.6% MAE reduction on ordered data).
- DiffCSP-SC with pre-training achieves SR10/SR30/SR50 of 0.37/0.37/0.50, versus 0.30/0.30/0.45 for DiffCSP.
- Of seven recently reported superconductors, all but Ti (under 248 GPa) are predicted with relative error below about 21%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train SODNet on ordered and disordered structures rather than ordered structures only | SODNet · SuperCon3D ordered test | MAE (logK): 0.622±0.112 -> 0.584±0.119 | Helped |
| Train SODNet on ordered and disordered structures rather than ordered structures only | SODNet · SuperCon3D ordered test | R2: 0.595±0.101 -> 0.634±0.117 | Helped |
| Use SODNet instead of Matformer | SuperCon3D ordered test · SuperCon3D ordered test | MAE (logK): 0.748±0.043 -> 0.622±0.112 | Helped |
| Use occupancy-aware disorder node embedding (ablation) | SODNet · SuperCon3D | MAE (logK): 0.990±0.033 -> 0.505±0.055 | Helped |
| Use occupancy-aware disorder node embedding (ablation) | SODNet · SuperCon3D | R2: 0.365±0.044 -> 0.748±0.032 | Helped |
| Use disorder edge embedding (ablation) | SODNet · SuperCon3D | MAE (logK): 0.592±0.087 -> 0.505±0.055 | Helped |
| Use equivariant operations (ablation) | SODNet · SuperCon3D | MAE (logK): 0.611±0.046 -> 0.505±0.055 | Helped |
| Use DiffCSP-SC instead of DiffCSP | SuperCon3D inverse generation without pre-training · SuperCon3D inverse generation, O | SR50: 0.05 -> 0.10 | Helped |
| Use DiffCSP-SC instead of DiffCSP | SuperCon3D inverse generation with pre-training · SuperCon3D inverse generation, pre-training + O | SR10: 0.30 -> 0.37 | Helped |
| Use DiffCSP-SC instead of DiffCSP | SuperCon3D inverse generation with pre-training · SuperCon3D inverse generation, pre-training + O | NSR10: 0.25 -> 0.31 | Helped |
| Add transformer attention to DiffCSP-SC (ablation) | DiffCSP-SC · SuperCon3D inverse generation | SR10: 0.28 -> 0.37 | Helped |
| Add transformer attention to DiffCSP-SC (ablation) | DiffCSP-SC · SuperCon3D inverse generation | SR30: 0.28 -> 0.37 | Helped |
Surprising findings
- Adding disordered structures to training improved R2 and MAE on ordered-structure test sets, suggesting disordered data helps ordered-property prediction.
- Without pre-training, DiffCSP-SC success rates drop to 0.05/0.05/0.10, indicating pre-training is critical given the small dataset.
Limitations
- Accuracy is constrained by the small, uneven dataset (heavy skew toward Cu and O elements).
- Predictions are poor for materials under extreme pressure (Ti at 248 GPa, 67% error).
- Generated candidates are mostly unverified; only a few are supported by prior reports or DFT checks.
Experimental setup
Datasets: SuperCon ICSD Materials Project OQMD Matgen 3DSC
Benchmarks: SuperCon3D
Metrics: MAE R2 success rate (SR10/SR30/SR50) novelty success rate (NSR)
Baselines: RF SVM SchNet CGCNN DimeNet++ SphereNet ALIGNN Matformer MEGNet CDVAE SyMat DiffCSP
Builds on: DiffCSP CDVAE e3nn EGNN Matformer
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