Is there a published search method that keeps every good family of alloys, not just one?

EXPERIMENTS.md · lines 5987–6031

E102 — The fix is a known algorithm, and it was published for this exact problem

E101 established the landscape is multi-basin with a 403 meV/atom ridge, so the repair is an archive rather than a reward. The literature has this, and closer to home than expected.

Quality-Diversity, and MAP-Elites in particular (Mouret & Clune 2015). The search keeps a grid over user-chosen feature dimensions and stores the best solution found in each cell, rather than a single global best. Every basin that occupies a distinct cell is retained by construction. The property that matters here is stated in the original paper: because it explores more of the space, it also tends to find a better single solution than a direct optimiser. The archive is not a tax on optimisation.

It has already been done on crystal structure prediction with an ML surrogate, which is our situation almost exactly - Wolinska, Walsh & Cully, Illuminating the property space in crystal structure prediction using Quality-Diversity algorithms, Digital Discovery 2024. They use a machine-learned interatomic potential precisely because MAP-Elites needs many cheap evaluations, and report finding the global minimum in 10 of 10 runs plus about ten other distinct structures per run. Code is open, adaptive-intelligent-robotics/QD4CSP.

And on composition space directly: DiSCoVeR (Baird, Diep & Sparks, Digital Discovery 2022) screens for compositions that are both high-performing and chemically distinct, using Element Mover's Distance with density-aware clustering to keep families separate. That is the same objective as reporting Cr-Ni alongside W-Ta.

What this means concretely for this project. The generator already produces thousands of cheap evaluations, which is the expensive prerequisite QD usually has to argue for. The missing piece is only the archive and a feature space to spread it over, and E101 measured what the features should be: the family split (refractory / group-4 / late transition) separates the basins, and the scan of E95 showed the promoted region is narrow in size misfit and element count while being wide in melting point. Those are two or three descriptors, which is the regime MAP-Elites was designed for; CVT-MAP-Elites (Vassiliades & Mouret 2017) covers the case where more are wanted.

The honest reading of the last several days. The convergence was diagnosed, then attributed to the reward, then to the uncertainty term, then to the acquisition function, then to the gate - four attempted repairs, each a reward modification, against a problem the field solved with an archive in 2015 and demonstrated on this exact kind of surrogate-driven materials search in 2024. Searching the literature first would have cost ten minutes.

Sources:

• https://ar5iv.labs.arxiv.org/html/1504.04909 (MAP-Elites, Mouret & Clune)
• https://pubs.rsc.org/en/content/articlehtml/2024/dd/d4dd00054d (QD for crystal structure prediction)
• https://github.com/adaptive-intelligent-robotics/QD4CSP/ (their code)
• https://doi.org/10.1039/d1dd00028d (DiSCoVeR, unique compositions)
• https://arxiv.org/pdf/2202.03057v2.pdf (Multi-Objective MAP-Elites)

EXPERIMENTS.md · lines 6063–6066

E102 stands but for a different reason. An archive is still the right answer - not because the fly cannot reach the other basins, but because a run that finds them and a report that shows one of them is a reporting failure, and the archive is what makes the report the whole run.