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The dark side of the forces: assessing non-conservative force models for atomistic machine learning
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Compares conservative and non-conservative (direct-force) machine-learned interatomic potentials, showing direct forces cause energy drift, optimization failures and thermostat artifacts, and proposes pre-training on direct forces then conservative fine-tuning plus multiple time-stepping.
Problem
Non-conservative ML interatomic potentials that predict forces directly (not as energy derivatives) are increasingly used for efficiency, but their effect on atomistic simulations such as geometry optimization and molecular dynamics has not been systematically studied.
Approach
Shows that non-conservative forces break energy conservation and cause drift in NVE, thermostat artifacts in NVT, and optimization failures; proposes a hybrid usage where direct forces are pre-trained and then conservative fine-tuned, and used in multiple time-stepping with conservative corrections every M steps.
Key results
- Non-conservative PET-NC forces give about 30% higher force MAE (24.3 vs 18.6 meV/Å) than conservative PET-C; the hybrid PET-M NC head is within ~10% of the best models.
- In NVE MD, the PET-NC model shows a large kinetic temperature drift, about 7000 billion degrees per second of heating, with ORB showing roughly 10 times larger drift.
- Geometry optimization success on gas-phase water: SOAP-BPNN-NC 79% vs SOAP-BPNN-C 91%; ORB 69% vs MACE 94%; multiple time-stepping with conservative forces every 8 steps reproduces conservative trajectories at roughly 20% extra cost over pure direct-force MD.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train conservative PET on energy and forces rather than energy only | PET · Bulk water test set | Energy MAE: 4.7 -> 0.55 | Helped |
| Replace conservative force prediction with direct non-conservative force prediction | PET force-only model · Bulk water test set | Force MAE: 18.6 -> 24.3 | Hurt |
| Add an energy head and energy targets to the direct-force PET model (ablation) | PET-NC · Bulk water test set | Force MAE: 24.3 -> 24.8 | No clear effect |
| Add a direct-force head alongside conservative forces | PET-M · Bulk water test set | Conservative force MAE: 19.4 -> 20.2 | Hurt |
| Fine-tune the energy head of PET-NC to produce conservative forces | PET-NC · Bulk water test set | Energy MAE: 1.42 -> 0.50 | Helped |
| Increase the message-passing depth from 2 to 3 layers (ablation) | PET-NC · Bulk water test set | Force MAE: 32.8 -> 24.3 | Helped |
| Increase the message-passing depth from 2 to 3 layers (ablation) | PET-C · Bulk water test set | Force MAE: 20.8 -> 18.6 | Helped |
| Use direct non-conservative forces instead of conservative forces | PET · NVE water trajectory | Kinetic temperature stability: null | Hurt |
| Tighten white-noise Langevin coupling from τ=1000 fs to τ=100 fs (ablation) | PET-NC · NVT bulk water | Mean kinetic temperature excess: 12.8(5) -> 1.4(2) | Helped |
| Tighten white-noise Langevin coupling from τ=100 fs to τ=10 fs (ablation) | PET-NC · NVT bulk water | Diffusion coefficient: about 1.5 (τ=100 fs); 5 (τ=10 fs) | Mixed |
| Use stochastic velocity rescaling instead of white-noise Langevin (ablation) | PET-NC · NVT bulk water | Mean kinetic temperature: null | Helped |
| Correct direct forces with conservative forces every 8 steps | PET-M · NVT bulk water | Mean kinetic temperature excess: 0.3(1) -> 0.0(1) | Helped |
Surprising findings
- Global thermostat (SVR) controls mean temperature but O and H temperatures deviate by up to 10%, so it cannot fix non-conservative artifacts.
- The accuracy of direct-force models benefits much more from larger receptive radius than conservative models (PET-NC force MAE 32.8 to 24.3 vs PET-C 20.8 to 18.6 meV/Å).
Limitations
- Main experiments are on a single bulk water dataset with custom-trained models, so generality to other systems is limited.
- Non-conservative behavior is assessed mostly with small models and a single dataset; larger-scale training may reduce artifacts, as the authors note.
Experimental setup
Datasets: bulk water dataset MPtrj Alexandria QM9 OC20
Benchmarks: bulk water test set QM9 MPtrj
Metrics: MAE energy (meV/atom) MAE forces (meV/Å) kinetic temperature drift velocity-velocity correlation spectrum geometry optimization success rate Jacobian asymmetry lambda
Baselines: ORB-v2 MACE-MP-0 SevenNet EquiformerV2 SOAP-BPNN-C PET-C
Builds on: PET ORB MACE SOAP-BPNN stochastic velocity rescaling
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