Graph atomic cluster expansion for foundational machine learning interatomic potentials

Foundational machine learning interatomic potentials that can accurately and efficiently model a vast range of materials are critical for accelerating atomistic discovery. We introduce universal potentials based on the graph atomic cluster expansion (GRACE) framework, trained on several of the largest available materials datasets. Through comprehensive benchmarks, we demonstrate that the GRACE models establish a new Pareto front for accuracy versus efficiency among foundational interatomic potentials. We further showcase their exceptional versatility by adapting them to specialized tasks and simpler architectures via fine-tuning and knowledge distillation, achieving high accuracy while preventing catastrophic forgetting. This work establishes GRACE as a robust and adaptable foundation for the next generation of atomistic modeling, enabling high-fidelity simulations across the periodic table.

💡 Research Summary

The paper introduces GRACE (Graph Atomic Cluster Expansion), a universal machine‑learning interatomic potential (MLIP) framework that extends the traditional Atomic Cluster Expansion (ACE) to graph‑based representations. By treating atoms as nodes and their interactions as edges, GRACE provides a complete basis for describing interatomic forces as functions of both atomic positions and chemical species. The authors achieve sparsity and computational efficiency through low‑rank tensor decomposition of the expansion coefficients, enabling recursive evaluation that is mathematically equivalent to message‑passing but with linear scaling in both the number of recursion layers and the complexity of ACE messages.

Training data are drawn primarily from the OMat24 dataset, the largest publicly available collection of DFT calculations (≈110 M entries) covering 89 elements, diverse structural perturbations, AIMD snapshots, and post‑relaxation configurations. To broaden chemical coverage, the authors also incorporate subsets of the Alexandria and MP‑Traj datasets, carefully avoiding data leakage with the WBM test set. Multiple GRACE models are built: one‑layer (direct ACE star‑graph) and two‑layer (including semi‑local message passing) architectures, each in small, medium, and large variants. Chemical embeddings are compressed to 8–16 dimensions, yielding low‑rank representations that dramatically reduce memory and compute demands.

Comprehensive benchmarking demonstrates that GRACE models dominate the Pareto front of accuracy versus computational cost across several tasks:

1. MatBench Discovery – Geometry optimization of 257 k candidate crystals. The 2‑layer large model (GRACE‑2L‑OAM‑L) attains an F1 score of 0.89 and the lowest formation‑energy MAE among all tested universal potentials.
2. Thermal Conductivity (κ‑SRME) – Prediction of anharmonic thermal conductivity for 103 binary systems. GRACE‑2L‑OAM‑L achieves the smallest symmetric relative mean error (κ‑SRME = 0.168), indicating superior capture of third‑order force constants.
3. Elastic Constants – Evaluation of longitudinal, Poisson‑related, and shear moduli against Materials Project references. The same model yields the lowest SRME across all sub‑groups, outperforming MACE, DP‑A3, and other state‑of‑the‑art potentials.
4. Grain Boundary Energies – Formation energies of grain boundaries in pure metals. GRACE models maintain SRME between 0.27–0.40 and absolute errors below 5 meV/Ų, comparable to the best specialized potentials.
5. Surface Energies – Surface formation energies for elemental slabs. Errors range from SRME 0.17 to 0.28 and absolute deviations of 8–14 meV/Ų, again placing GRACE at the top of the performance spectrum.
6. Point Defects – Self‑interstitial and vacancy formation energies in BCC/FCC metals. SRME values lie between 0.1 and 0.3, with absolute errors of 0.2–0.4 eV (SIAs) and 0.1–0.2 eV (vacancies).

Computational efficiency is highlighted by timing tests on a 1024‑atom W‑BCC crystal using both ASE (Python) and LAMMPS (C++). GRACE models achieve per‑atom step times as low as 0.09 µs (LAMMPS) and 2.9 µs (ASE), substantially faster than competing universal potentials such as DP, MACE, and SevenNet.

The authors also explore model adaptability. Fine‑tuning the OMat24‑trained base models on the combined MP‑Traj/Alexandria data yields “‑OAM” variants that retain the original Pareto‑optimal performance while extending accuracy to datasets with different DFT settings. Knowledge distillation experiments compress the large GRACE model into a smaller network with roughly one‑quarter the parameters; the distilled model reproduces energies, forces, and stresses with negligible loss, demonstrating that high‑fidelity universal potentials can be made lightweight for large‑scale simulations.

Long‑time molecular dynamics stability is validated by a 1 ns NVE simulation of a ~3000‑atom FLiBe melt at 973 K. Energy drift is only 5 × 10⁻⁹ eV/atom/ns, confirming that GRACE potentials are numerically stable for extended trajectories—a critical requirement for realistic thermodynamic and kinetic studies.

In summary, GRACE unifies the expressive power of a complete ACE‑based basis with the scalability of graph neural networks. Trained on massive, chemically diverse DFT datasets, it delivers state‑of‑the‑art accuracy across a broad spectrum of materials properties while remaining computationally efficient. The demonstrated fine‑tuning and knowledge‑distillation pathways further position GRACE as a versatile foundation model for the next generation of atomistic simulations, enabling rapid, high‑fidelity exploration of the entire periodic table.