Active Learning for Machine-Learned Interatomic Potentials

Ensemble & Sampling

Ensemble size 4 models

Exploration temperature 0.60

Acquisition threshold 45 meV/Å

Auto-query on threshold

Training Progress

DFT calls used0

Mean ensemble uncertainty— meV/Å

Estimated force MAE— meV/Å

How it works

A machine-learned interatomic potential (MLIP — the family M3GNet, CHGNet, CGCNN and "universal" NN potentials belong to) is a graph neural network trained to reproduce DFT energies and forces, F = −∇E(r), thousands of times faster than solving the electronic structure directly. The bottleneck is which atomic environments to label with real DFT, since each DFT single-point calculation is expensive.

Query-by-committee active learning solves this by training a small ensemble of N potentials on the same (small) labeled set. For an atom at position r_i, each ensemble member m predicts a force F_m,i. The predictive uncertainty is their spread:

σ_i = std_m( F_m,i )        (per-atom force disagreement)
query if  max_i σ_i  >  threshold τ

Atoms are colored blue → red by σ_i. As the lattice explores new configurations (thermal jitter, controlled by the temperature slider), the ensemble members — each with slightly different systematic errors — disagree most on environments unlike anything in the training set. When disagreement crosses τ, that local environment is "sent to DFT": a real ground-truth label is added, and the uncertainty of that atom and its neighbors collapses, because the committee now agrees on similar geometries too.

Ensemble size — more committee members give a more reliable uncertainty estimate but cost more to train.
Exploration temperature — how far the MD-like trajectory wanders from equilibrium, controlling how fast new environments are discovered.
Acquisition threshold τ — low values query aggressively (many DFT calls, fast convergence); high values save compute but leave more of configuration space unlabeled.
Estimated force MAE — a synthetic proxy that falls as the labeled training set covers more of the space the ensemble disagrees about, mirroring the real training curves reported for M3GNet/CHGNet-style universal potentials.

This loop — explore, disagree, label the worst case, retrain — is exactly how modern universal MLIPs bootstrap DFT-accuracy force fields from a few thousand calculations instead of the millions a brute-force dataset would need.

Low ensemble uncertainty High ensemble uncertainty Just queried (DFT label added)

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