Does more training data pin down the ordering temperature?

EXPERIMENTS.md · lines 2074–2101

E41 — The transition temperature does not converge with data, and E39 over-read one run

Date 2026-09-12 · Question How much data does a local expansion need before the short-range order and the transition temperature settle? · Provenance …/{local_ce,odt_converge,wl_test}.py

The literature said what to expect, and half of it applied. Xie, Zhou, Luan and Jiang (J. Chem. Theory Comput. 18, 3795, 2022) found that a training set large enough for the cross-validation score to converge still leaves the transition temperature badly uncertain, needing a few thousand configurations - which is why they generated theirs with a machine-learning force field rather than DFT. Our first pass reproduced their symptom exactly: fit error fell from 16.8 to 3.5 meV/atom while the transition wandered 450-900 K.

Their fix did not work here, which is the finding. Carried to 3,000 structures, with four independent Monte Carlo runs per fit so the transition comes with an error bar:

The scatter is 96-150 K at every training size, while the fit converges by 400 structures. The uncertainty is Monte Carlo run-to-run, not the fit - so more training data cannot reduce it, and the bottleneck here is not the one the literature identified. Our transition is 500 +/- 130 K.