Experiments · E107
Yes. It probably should replace ours: it stays compact as elements are added and reached 4 meV/atom on six elements.
In the log: pyeCE: what it is, and why our expansion should probably be replaced by it
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Asked twice and answered properly only now.
We are not using it. Our expansion is icet 4.0, conventional linear cluster expansion, 344 parameters at eight elements and 1068 at twelve.
pyeCE is the embedded cluster expansion - Müller & Natarajan, npj Computational
Materials 11, 60 (2025), with the software released as epfl-mades/pyece and described in
arXiv:2609.10190 (September 2026). Instead of one basis function per species, which is what
makes a conventional expansion intractable past three or four elements, it learns a
low-dimensional embedding of the species and computes the cluster coefficients with a
neural network. The parameter count stops exploding with element count.
Its demonstration case is very close to ours. The method paper builds a single model across the full composition space of the six-component V-Nb-Ta-Cr-Mo-W alloy - six of our twelve, including chromium - and reaches 4 meV/atom with a three-dimensional embedding. The software paper demonstrates a nine-component refractory alloy as one model, resolving short-range order and order-disorder behaviour, which is our rung 1.
The property that matters most to us is the one we are failing on. eCE "leverages similarities between chemical elements to efficiently extrapolate into compositional spaces that are not explicitly included in the training dataset" - they withhold element pairs entirely and the model still captures the withheld alloy's energetics. Every serious defect in our expansion this week is a failure of exactly that: 58 meV/atom error at pure molybdenum against a quoted 5.67 CV (E72), 59 meV/atom over-reporting on MoNbTaW, and a 168 meV/atom error at Cr0.64Ni0.36 because the four late transition metals are sparse in a training set built by sampling (E104).
| ours | eCE | |
|---|---|---|
| formalism | linear CE, one basis per species | learned species embedding + neural ECIs |
| parameters, 12 elements | 1068 | set by embedding dimension, not element count |
| accuracy | 8.07 meV/atom CV at 12 elements | 4 meV/atom at 6 elements |
| extrapolation to unsampled chemistry | the failure mode of E72, E104 | demonstrated by withholding element pairs |
| trained on | our own MACE labels, ideal lattice, unrelaxed | DFT |
And there is a direct external check on rung 1 we have never run. Kim & Widom, Phys. Rev. Materials 7, 063803 (2023), model MoTa and MoNbTaW on the bcc lattice and put the A2→B2 transition for MoNbTaW at T_c ≈ 1110 K, with the ordering driven by Mo-Ta pairs and a second transition below 300 K into B2-MoTa plus B32-NbW. Our rung 1 gives 556 K for the same alloy - a factor of two low, and in the direction that makes an alloy look safer than it is. That is a validation target sitting in the literature that costs nothing to compare against.
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