Is the eight-element energy formula accurate enough to build the rest of the work on?

EXPERIMENTS.md · lines 682–718

E16b — The eight-element cluster expansion the rest of this log is built on

Date 2026-09-12 · Question E16 showed a four-element expansion works. Build the production one, and keep what it was fitted to. · Provenance scripts/build_ce.py, data/ce_8element.{icet,npz}

Method. All eight elements on a fixed bcc lattice at a = 3.2935 A, the mean of the elemental lattice constants; cutoffs 6.0 A for pairs and 4.5 A for triplets, giving 344 parameters. Fitted to MACE-MPA-0 mixing energies on random occupancies of a 16-site cell, with elemental references computed on the same lattice - the convention a fixed-lattice expansion requires, and the reason the earlier fit to raw energies was an order of magnitude worse (E16). Draws with a species at zero occupancy are discarded, so 2,600 attempts give 1,953 training structures, about 95 seconds of potential on CPU.

Result.

5.67 meV/atom cross-validated, against MACE-MPA-0's own 6.61 from DFT (E18): the expansion is a smaller error than the potential it is fitted to, so it is not the limiting approximation anywhere downstream.

What is kept, and why. The script stores the fit data - cluster vectors and target energies - and a 50-member bootstrap ensemble of parameter vectors alongside the expansion itself. Resampling the training structures and refitting is where the uncertainty on a prediction comes from, and it is the part that varies with composition (E24). A single parameter vector cannot say how far it should be trusted. The whole artifact rebuilds in about three minutes, so nothing here depends on a file nobody can regenerate.

Note on provenance. E21, E23 and E26 cite "the cluster expansion of E16b" for work done before this entry existed. The expansion is the same one and the numbers are unchanged; only the record of how it was built was missing.