MLFF Geometry Optimization
This task measures how closely machine-learning force-field relaxations reproduce DFT-relaxed crystal structures across the 257k-material WBM test set. It compares normalized structure-matching RMSD, retained symmetry, and the relaxation settings used by each model.
Not all models relaxed every structure, but each reported model was evaluated on at least 249k relaxations. Symmetry detection uses moyopy, a Rust successor to spglib.
Leaderboard
The table ranks current model-YAML results and exposes training-data, openness, output, and column filters.
Symmetry-tolerance caveat: RMSD is
symprec-invariant. The leaderboard shows symmetry metrics at bothsymprec=1e-2andsymprec=1e-5, while Aggregate Diagnostics usesymprec=1e-5. Compare symmetry values within a single view.
| Symmetry | Hyperparams | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Model | RMSD ↓ | Σ= 10-2 | Σ↓ 10-2 | Σ↑ 10-2 | Σ= 10-5 | Σ↓ 10-5 | Σ↑ 10-5 | Optimizer | Steps | fmax (eV/Å) | Cell filter |
| TECE-OAM-RRA-1.0 | 0.058 | 81.83% | 4.98% | 12.45% | 59.07% | 18.46% | 21.02% | FIRE | 500 | 0.02 | Frechet |
| GRACE-3L-OAM-L | 0.058 | 82.4% | 3.84% | 13% | 69.29% | 4.27% | 25.94% | FIRE | 500 | 0.01 | Frechet |
| EquFlashV2 | 0.058 | 82.02% | 4.74% | 12.51% | 70.05% | 5.07% | 24.34% | FIRE | 500 | 0.02 | Frechet |
| EquiformerV3+DeNS-OAM | 0.059 | 74.24% | 12.9% | 11.37% | 37.11% | 45.54% | 12.99% | FIRE | 500 | 0.02 | Frechet |
| PET-OAM-XL | 0.060 | 80.7% | 6.67% | 11.85% | 13.08% | 86.68% | 0.09% | FIRE | 500 | 0.02 | Frechet |
| MatRIS-10M-OAM | 0.060 | 81.53% | 5.47% | 12.27% | 59.55% | 19.5% | 19.96% | FIRE | 500 | 0.02 | Frechet |
| EquFlash | 0.060 | 81.98% | 4.68% | 12.64% | 70.19% | 4.89% | 24.4% | FIRE | 500 | 0.02 | Frechet |
| TACE-OAM-L | 0.061 | 81.88% | 4.79% | 12.6% | 69.22% | 6.03% | 24.15% | FIRE | 500 | 0.02 | Frechet |
| eSEN-30M-OAM | 0.061 | 71.03% | 16.16% | 10.85% | 36.36% | 47.39% | 11.88% | FIRE | 500 | 0.02 | Frechet |
| SevenNet-Omni-i12* | 0.062 | 81.87% | 4.69% | 12.72% | 70.56% | 4.39% | 24.54% | FIRE | 800 | 0.02 | Frechet |
| Nequip-OAM-XL | 0.063 | 82.23% | 2.53% | 14.37% | 68.34% | 9.75% | 21.17% | GOQN | 500 | 0.005 | Frechet |
| GRACE-2L-OAM-L | 0.064 | 81.66% | 5.37% | 12.26% | 73.43% | 5.39% | 20.67% | FIRE | 500 | 0.03 | Frechet |
| Nequip-OAM-L | 0.065 | 81.6% | 5.43% | 12.26% | 71.25% | 7.92% | 20.18% | GOQN | 500 | 0.05 | Frechet |
| Allegro-OAM-L | 0.065 | 81.6% | 5.42% | 12.26% | 71.63% | 7.53% | 20.23% | GOQN | 500 | 0.05 | Frechet |
| GRACE-2L-OAM | 0.067 | 81.59% | 5.63% | 12.09% | 73.3% | 3.25% | 23.01% | FIRE | 500 | 0.03 | Frechet |
| DPA-4.0.1-Pro-MPtrj | 0.069 | 66.31% | 20.8% | 10.37% | 38.99% | 41% | 14.22% | FIRE | 500 | 0.02 | Frechet |
| eqV2 M | 0.069 | 77.25% | 11.18% | 10.52% | 14.22% | 85.2% | 0.45% | FIRE | 500 | 0.02 | Frechet |
| DPA-3.1-3M-FT | 0.069 | 81.09% | 5.02% | 13.17% | 72.74% | 5.39% | 21.38% | FIRE | 500 | 0.05 | Exp |
| EquiformerV3+DeNS-MP | 0.070 | 64.13% | 23.01% | 10.22% | 39.19% | 42.23% | 13.08% | FIRE | 500 | 0.02 | Frechet |
| MatRIS-10M-MP | 0.072 | 79.92% | 7.89% | 11.45% | 57.66% | 23.95% | 17.2% | FIRE | 500 | 0.05 | Frechet |
| GRACE-1L-OAM | 0.072 | 81.4% | 5.76% | 12.16% | 73.36% | 3.29% | 22.92% | FIRE | 500 | 0.03 | Frechet |
| MACE-MPA-0 | 0.073 | 81.44% | 5.56% | 12.31% | 73.24% | 3.28% | 23.05% | FIRE | 500 | 0.05 | Frechet |
| MatterSim v1 5M | 0.073 | 81.48% | 5.24% | 12.54% | 68.74% | 7.55% | 23.05% | FIRE | 500 | 0.02 | Exp |
| ORB v3 | 0.075 | 72.8% | 15.9% | 10.1% | 13% | 86.9% | 0.01% | FIRE | 500 | 0.02 | Frechet |
| eSEN-30M-MP | 0.075 | 61.06% | 26.04% | 9.8% | 38.59% | 42.81% | 12.82% | FIRE | 500 | 0.02 | Frechet |
| eqV2 S DeNS | 0.076 | 53.96% | 37.24% | 6.53% | 13.22% | 86.71% | 0.06% | FIRE | 500 | 0.02 | Frechet |
| AlphaNet-v1-OAM* | 0.079 | 74.31% | 14.46% | 10.37% | 14.16% | 85.05% | 0.67% | FIRE | 500 | 0.03 | Frechet |
| HIENet | 0.080 | 80.02% | 7.55% | 11.63% | 45.21% | 34.93% | 15.32% | FIRE | 500 | 0.05 | Frechet |
| Allegro-MP-L | 0.082 | 81.25% | 5.72% | 12.3% | 72.11% | 7.12% | 20.15% | GOQN | 500 | 0.05 | Frechet |
| Eqnorm MPtrj | 0.084 | 81.13% | 5.89% | 12.24% | 69.83% | 6.39% | 23.16% | FIRE | 500 | 0.02 | Frechet |
| SevenNet-l3i5* | 0.085 | 78.8% | 8.95% | 11.34% | 44.12% | 36.67% | 14.51% | FIRE | 500 | 0.05 | Frechet |
| Nequix MP | 0.085 | 81.11% | 5.54% | 12.61% | 69.99% | 6.07% | 23.35% | FIRE | 500 | 0.02 | Frechet |
| Nequip-MP-L | 0.086 | 81.09% | 5.92% | 12.27% | 71.63% | 7.88% | 19.82% | GOQN | 500 | 0.05 | Frechet |
| Nequix MP PFT | 0.087 | 81.09% | 5.4% | 12.76% | 69.76% | 6.02% | 23.62% | FIRE | 500 | 0.02 | Frechet |
| GRACE-2L-MPtrj | 0.090 | 81.07% | 5.96% | 12.28% | 73.15% | 3.49% | 22.92% | FIRE | 300 | 0.03 | Frechet |
| MACE-MP-0 | 0.091 | 81.12% | 5.99% | 12.2% | 73.85% | 3.35% | 22.39% | FIRE | 500 | 0.05 | Frechet |
| CHGNet | 0.095 | 79.21% | 9.22% | 10.76% | 60.62% | 22.41% | 16.01% | FIRE | 500 | 0.05 | Frechet |
| ORB v2 MPA | 0.097 | 49.26% | 45.47% | 4.53% | 14.33% | 85.31% | 0.34% | FIRE | 500 | 0.02 | Frechet |
| ORB v2 MPtrj | 0.101 | 43.32% | 52.13% | 3.87% | 13.35% | 86.55% | 0.09% | FIRE | 500 | 0.02 | Frechet |
| M3GNet | 0.112 | 80.31% | 6.81% | 12.17% | 74.08% | 6.71% | 18.69% | FIRE | 500 | 0.05 | Exp |
RMSD measures the normalized, unitless structure-matching RMSD between ML- and DFT-relaxed ground state structures, as returned by
pymatgen’sStructureMatcherafter matching. Optimizer, Steps, fmax, and Filter show the ASE optimizer, maximum relaxation steps, force convergence criterion (eV/Å), and cell filter used during structure relaxation. Σ= / Σ↓ / Σ↑ denote the fraction of structures that retain, increase, or decrease the symmetry of the DFT-relaxed structure during MLFF relaxation. The match criterion is for the ML ground state to have identical spacegroup as DFT. For Σ↓ / Σ↑, the number of symmetry operations for a structure decreased / increased during MLFF relaxation. Note that the symmetry metrics are sensitive to thesymprecvalue passed tospglibso we show results for multiple values. See thespglibdocs and paper for details.
Model Comparison
Use the axis, color, and size controls to compare the models with geometry-optimization metrics directly from the current model YAML data.
Σ= 10-2 vs RMSD
The default view compares structure-matching RMSD (lower is better) with the
fraction of matching spacegroups at symprec=1e-2 (higher is better). Marker
size defaults to model parameters and color to training-set size.
Aggregate Diagnostics
These views use the per-structure symprec=1e-5 analyses. The model picker applies to every view below.
- TECE-OAM-RRA-1.0
- GRACE-3L-OAM-L
- EquFlashV2
- DPA-4.0.1-Pro-MPtrj
- TACE-OAM-L
Cumulative Distribution of RMSD
Cumulative distribution of RMSD between ML and DFT-relaxed structures.
Difference in Number of Symmetry Operations vs DFT
Difference in number of symmetry operations of ML vs DFT-relaxed structures. Models are sorted by the standard deviation σ of ΔNsym ops = Nsym ops,ML - Nsym ops,DFT.
Sankey Diagrams for ML vs DFT Spacegroups
The Sankey diagrams show corresponding spacegroups of DFT-relaxed and MLFF-relaxed structures at symprec=1e-5. For visual clarity, only the 10 most common pairs of (DFT, MLFF) spacegroups are shown.
EquFlashV2
TECE-OAM-RRA-1.0
GRACE-3L-OAM-L
TACE-OAM-L
DPA-4.0.1-Pro-MPtrj
Relaxation-protocol caveat
The WBM DFT references were generated with MPRelaxSet: ISYM=2, ISIF=3, and IBRION=2 (conjugate gradient). Most MLFF relaxations instead use FIRE. Different symmetry constraints and optimizers can reach different minima, so a lower symmetry-match rate can occasionally indicate a valid symmetry-broken structure rather than a model error. See MPRelaxSet.yaml. Thanks to Alex Ganose for highlighting this distinction.