Factorised Cartesian Atomic Cluster Expansion for Low-Cost Machine-Learning Interatomic Potentials
- 1Department of Materials Science and Engineering
- 2Indian Institute of Technology Kanpur
Abstract
Machine-learning interatomic potentials can reach the accuracy of density functional theory at a fraction of its cost, but the most accurate equivariant models remain expensive, mainly because of the tensor operations they perform for every pair of neighbouring atoms. We present FACE, a factorised Cartesian atomic cluster expansion that removes this bottleneck. Each neighbour contributes only a small set of radial functions and messages, and all mixing of feature channels is done once per atom, so the cost per neighbour no longer grows with the size of the model. Custom GPU kernels evaluate the remaining steps, and long-range electrostatics, dispersion and short-range repulsion attach through a single interface. We show that the training divergences we encountered originate in how the network weights are scaled, and we introduce a distillation scheme in which an ensemble generates additional, uncertainty-checked training data. On five rMD17 molecules, with identical training budgets and hardware, FACE is about as accurate as a 64-channel MACE model (over three seeds: better on one molecule, within the seed spread on two, 7–14% higher force errors on two), while it is 5.7 times faster at inference (4.9 times at the same cutoff) and needs 3.5–3.9 times less GPU memory. Training costs about the same per step. Distillation lowers the energy and force errors of a single aspirin model by 20% at fixed width, to 2.26 meV and 6.74 meV/Å, close to the published MACE values (2.2 and 6.6), and the distilled model runs stably in molecular dynamics.
Related
- Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentials
- Analysis of fine-tuned foundation interatomic potentials and their knowledge distillation into a cluster expansion for Ni–Pt ordering thermodynamics
- Correcting the Liquid Densities of Universal Machine-Learning Interatomic Potentials Using Local-Number-Density Repulsion
- pdb2reaction: End-to-End Reaction-Path Elucidation from PDB Structures Using Machine-Learning Interatomic Potentials
- Applicability Domain of Universal Machine Learning Interatomic Potentials at Solid-State Battery Interfaces
BibTeX
@misc{linda2026factorised,
title = {{Factorised Cartesian Atomic Cluster Expansion for Low-Cost Machine-Learning Interatomic Potentials}},
author = {Albert Linda},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010957/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010957/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Factorised Cartesian Atomic Cluster Expansion for Low-Cost Machine-Learning Interatomic Potentials
AU - Albert Linda
PY - 2026
DA - 2026/10/23
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010957/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010957/v1
AB - Machine-learning interatomic potentials can reach the accuracy of density functional theory at a fraction of its cost, but the most accurate equivariant models remain expensive, mainly because of the tensor operations they perform for every pair of neighbouring atoms. We present FACE, a factorised Cartesian atomic cluster expansion that removes this bottleneck. Each neighbour contributes only a small set of radial functions and messages, and all mixing of feature channels is done once per atom, so the cost per neighbour no longer grows with the size of the model. Custom GPU kernels evaluate the remaining steps, and long-range electrostatics, dispersion and short-range repulsion attach through a single interface. We show that the training divergences we encountered originate in how the network weights are scaled, and we introduce a distillation scheme in which an ensemble generates additional, uncertainty-checked training data. On five rMD17 molecules, with identical training budgets and hardware, FACE is about as accurate as a 64-channel MACE model (over three seeds: better on one molecule, within the seed spread on two, 7–14% higher force errors on two), while it is 5.7 times faster at inference (4.9 times at the same cutoff) and needs 3.5–3.9 times less GPU memory. Training costs about the same per step. Distillation lowers the energy and force errors of a single aspirin model by 20% at fixed width, to 2.26 meV and 6.74 meV/Å, close to the published MACE values (2.2 and 6.6), and the distilled model runs stably in molecular dynamics.
ER -