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Physics-Informed Weakly Supervised Learning For Interatomic Potentials
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Proposes physics-informed weakly supervised losses (PITC and PISC) that use Taylor-expansion and conservative-force path consistency to train MLIPs with sparse data, without needing force labels.
Problem
Machine-learned interatomic potentials often generalize poorly and are unstable in MD when training data is sparse, and high-accuracy references (e.g., CCSD(T)/CBS) lack force labels.
Approach
Generate approximate energies for locally perturbed structures via a Taylor expansion using the model's own energies and forces (PITC loss), and enforce path-independence of energy differences via conservative forces (PISC loss), combined with the supervised loss.
Key results
- On ANI-1x with 100 training samples, PIWSL reduced PaiNN energy RMSE from 168.01 to 109.89 kcal/mol and eSCN energy RMSE from 214.52 to 183.70 kcal/mol, with errors often lowered by 10-50%.
- Fine-tuning MACE-OFF on aspirin CCSD energies only (no forces), PIWSL reduced energy RMSE from 1.21 to 0.72 kcal/mol (950 samples) and force RMSE from 6.90 to 3.77 kcal/mol/Å, about 40% lower.
- On MD22 buckyball catcher with 50 samples, PIWSL reduced MACE-OFF energy MAE from 1.159 to 0.992 kcal/mol; improvements for MACE-MP were marginal.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add PIWSL loss to PaiNN | PaiNN · ANI-1x, 100 train | energy RMSE: 168.01 $\pm$ 1.22 -> 109.89 $\pm$ 11.46 | Helped |
| Add PIWSL loss to PaiNN | PaiNN · ANI-1x, 1000 train | energy RMSE: 56.62 $\pm$ 2.80 -> 24.53 $\pm$ 0.48 | Helped |
| Add PIWSL loss to eSCN | eSCN · TiO2, 2000 train | force RMSE: 0.42 $\pm$ 0.17 -> 0.16 $\pm$ 0.01 | Helped |
| Add PIWSL loss during fine-tuning without force labels | MACE-OFF · MD17(CCSD) aspirin, 950 samples | energy RMSE: 1.21 $\pm$ 0.00 -> 0.72 $\pm$ 0.01 | Helped |
| Add PIWSL loss | MACE-OFF · MD22 buckyball catcher, 50 samples | force MAE: 0.346 $\pm$ 0.003 -> 0.337 $\pm$ 0.001 | Helped |
| Add PIWSL loss rather than NoisyNode augmentation | MLIPs · ANI-1x | energy and force RMSE | Mixed |
| Use PIWSL rather than supervised training alone | MLIP models · Aspirin MD simulations | simulation stability | Helped |
Surprising findings
- NoisyNode data augmentation often deteriorated accuracy for most models except SchNet, e.g., PaiNN energy RMSE rose from 168 to 465 kcal/mol on ANI-1x with 100 samples.
- Improvement for MACE-MP on MD22 was negligible (energy MAE 2.111 vs 2.033), indicating sensitivity to choice of foundation model.
Limitations
- Method is tailored to models predicting energies and forces for atomic systems and does not apply to unrelated ML problems.
- Only up to second-order Taylor expansion is used; higher-order ODE-based alternatives are left for future work.
- Hyperparameters required Optuna tuning, and MACE-MP fine-tuning gains were small, indicating sensitivity to foundation model choice.
Experimental setup
Datasets: ANI-1x TiO2 rMD17 MD22 LMNTO SPICE
Benchmarks: ANI-1x TiO2 rMD17 aspirin (CCSD) MD22 buckyball catcher LMNTO
Metrics: energy RMSE force RMSE energy MAE force MAE MD stability time
Baselines: Baseline supervised training NoisyNode Weak label (Taylor-expansion) method Foundation models trained from scratch
Builds on: NoisyNode PINN Open Catalyst Project
Closest papers by meaning
- The dark side of the forces: assessing non-conservative force models for atomistic machine learning (ICML 2025 · similarity 0.90)
- Benchmarking Compositional Generalisation for Machine Learning Interatomic Potentials (NeurIPS 2026 · similarity 0.89)
- Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction (ICML 2025 · similarity 0.89)
- MLIP Arena: Advancing Fairness and Transparency in Machine Learning Interatomic Potentials via an Open, Accessible Benchmark Platform (NeurIPS 2025 · similarity 0.89)
- Stein Kernelized Molecular Dynamics for Active Learning of Interatomic Potentials (NeurIPS 2026 · similarity 0.88)
- EDBench: Large-Scale Electron Density Data for Molecular Modeling (NeurIPS 2025 · similarity 0.88)
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