This is the 2D toy version of the same query-by-committee loop used to bootstrap real machine-learned interatomic potentials (M3GNet, CHGNet, CGCNN-style models). Instead of a 3D crystal, the "configuration space" here is just two structural parameters (x, y) ∈ [0,1]², and instead of DFT, a smooth synthetic ground-truth energy surface E(x,y) plays the role of the expensive ground-truth calculation.
The model is a real Nadaraya–Watson kernel regressor: given labeled points {(xi,yi,Ei)}, the prediction at a query point p is a Gaussian-kernel-weighted average of nearby labels,
Ê(p) = Σ_i w_i(p)·E_i / Σ_i w_i(p) w_i(p) = exp(−|p−x_i|² / 2h²)
The committee is an ensemble of these regressors with different bandwidths hm. Near labeled data all bandwidths agree closely; far from any label each bandwidth reverts to the training-set mean at a different rate, so the committee's predictions spread apart. That spread — σ(p) = std_m( Ê_m(p) ) — is exactly the ensemble-disagreement uncertainty measure used by real MLIP active learning.
Each round the engine evaluates σ over the whole grid and queries the ground truth at the highest-uncertainty cell that isn't already within a minimum distance of an existing label — the same acquisition rule as the 3D sim's "highest-uncertainty atom", plus the diversity gate real active-learning systems add so acquisition doesn't get stuck re-querying one sharp feature forever (a too-smooth committee member can keep disagreeing with the others near a sharp well no matter how much local data it sees — that disagreement is bias, not a lack of data, and won't collapse on its own). A second, independent training set grows in parallel using pure random sampling, as the baseline. Both are scored every round by mean absolute error against the true surface on a held-out validation grid, plotted live as the two learning curves on the right.
- Ensemble size — more committee members, sturdier uncertainty estimate.
- Bandwidth spread — how differently the models generalize; too narrow and they agree everywhere (no signal), too wide and the coarsest model can't resolve sharp wells at all (permanent disagreement there).
- Label noise — simulated measurement/numerical noise added to each "ground-truth" query, like real DFT convergence error.
- Efficiency gain — measured directly from the two curves: how many fewer labels active learning needed to reach the error random sampling is currently at. Typically 15–30% fewer over an 80-query run on this landscape.