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Gradual Optimization Learning for Conformational Energy Minimization
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Proposes GOLF, a data-efficient training scheme for neural network potentials that adds DFT-labeled conformations collected from NNP-driven optimization trajectories, selected via a cheap MMFF surrogate oracle, to match DFT-level conformational energy minimization with ~50x less additional data.
Problem
Neural network potentials used as force fields for molecular conformation energy minimization suffer from distribution shift along optimization trajectories, and matching DFT-oracle optimization quality by adding full optimization trajectories needs very many expensive oracle calls.
Approach
Use the NNP's own gradient-based optimizer trajectories, check for energy increases with a cheap surrogate oracle (RDKit MMFF), and send only the first conformation where the NNP's forces are wrong to the expensive DFT oracle, adding it to training in an active-learning loop.
Key results
- GOLF-10k reaches 98.8% average energy minimized and 0.5 kcal/mol residual energy, matching traj-500k while using about 50x less additional data.
- GOLF-1k (1k DFT calls) outperforms traj-100k in pct_success (62.9% vs 52.7%) with 100x less data.
- On SPICE, GOLF-10k reaches 94.2% average minimized energy versus 90.4% for the baseline.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add optimization trajectories from oracle to training data (traj-500k vs baseline) | PaiNN NNP · nablaDFT test | pct_T / pct_success: pct_T 77.9 -> 98.8; success 8.2 -> 73.4 | Helped |
| Use GOLF data-collecting scheme with 10k oracle interactions instead of full trajectories | PaiNN NNP · nablaDFT test | pct_success: 77.3 vs 73.4 for traj-500k (50x less data) | Helped |
| Use GOLF with 1k oracle interactions instead of traj-100k | PaiNN NNP · nablaDFT test | pct_T: 97.3 (GOLF-1k) vs 96.2 (traj-100k) with 100x less data | Helped |
| Select training conformations with GOLF data-collecting scheme vs training on MMFF-optimized conformations (rdkit) (ablation) | PaiNN NNP · nablaDFT test | pct_T / pct_success: pct_T 98.8 vs 93.0; success 77.3 vs 35.4 (GOLF-10k vs rdkit) | Helped |
| Apply GOLF (10k) on SPICE instead of baseline | PaiNN NNP · SPICE test | pct_T: 94.2 vs 90.4 baseline | Helped |
| Apply GOLF (10k) on SPICE vs traj-220k | PaiNN NNP · SPICE test | pct_success: 40.9 vs 41.6 for traj-220k with ~22x more data | No clear effect |
| Train on GOLF-10k vs traj-500k on large molecules (unseen larger molecules) | PaiNN NNP · Large molecules (36-57 atoms) | pct_T / E_res: pct_T 97.7 vs 97.4; E_res 1.0 vs 1.1; pct_div 2.7 vs 1.9 | Mixed |
| Replace L-BFGS external optimizer with Adam or SGD-momentum for GOLF training/evaluation (ablation) | GOLF-10k · nablaDFT test | pct_T / pct_div: L-BFGS best pct_T; Adam has lower pct_div | Hurt |
Surprising findings
- Trained NNPs can converge to lower-energy local minima than the DFT oracle, giving percentage minimized above 100%.
- Adding DFT-optimized trajectories alone can make NNP optimization match DFT quality only after roughly 5e5 additional oracle interactions.
Limitations
- Performance on large molecules is lower in success rate than on the training distribution (61.4% vs 73.4%).
- Only gas-phase drug-like molecules are studied; solvent and protein environments are not modeled.
- Surrogate MMFF may miss errors that DFT would reveal.
Experimental setup
Datasets: nablaDFT SPICE
Benchmarks: nablaDFT test subset SPICE test subset large molecules subset
Metrics: average percentage of minimized energy residual energy success rate within chemical precision divergence percentage COV MAT
Baselines: RDKit MMFF ConfOpt Torsional diffusion Uni-Mol+ traj-500k NNP RDKit-optimal NNP
Builds on: PaiNN L-BFGS SchNetPack 2.0
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