MACE-MH-1: Multi-Head Foundation Model for Atomistic Materials Chemistry

Highlights

MACE-MH-1 is a foundation machine-learning interatomic potential (MLIP) that bridges molecular, surface, and materials chemistry through cross-domain learning:

• Unified cross-domain capability spanning inorganic crystals, molecular systems, surface chemistry, and reactive organic chemistry with a single model
• State-of-the-art performance across materials, molecular crystals, surfaces, and molecular benchmarks with a global performance score of 0.862
• Enhanced MACE architecture with improved weight sharing across chemical elements and non-linear tensor decomposition in the product basis

Model Overview

MACE-MH-1 has the following features:

• Type: E(3)-equivariant graph neural network for interatomic potentials
• Architecture: MACE
• Interaction Blocks: Non-linear
• Training Stages: Pre-training on OMAT-24 (100M inorganic crystals) + Multi-head fine-tuning on diverse datasets
• Hyper-Parameters: 512 node channels, 128 edge channels, L=2, max_ell=3, 2 layers
• Chemical Coverage: 89 elements
• Cutoff Radius: 6 Å
• Multiple Heads: OMAT PBE (main), OMOL (ωB97M-VV10), OC20 (surfaces), SPICE, RGD1, MPTraj, Matpes (r2scan)

For more details, please refer to the paper, GitHub repository, and MACE foundations.

Performance

Materials Benchmarks (PBE+U Reference)

Benchmark	Metric	MACE-MH-1	ORB-v3	UMA-S-1.1
Phonon BZ	MAE (K)	5	15	9
Phonon ωavg	MAE (K)	3	5	4
Phonon ωmin	MAE (K)	11	29	21
Phonon ωmax	MAE (K)	12	12	11
Entropy (300K)	MAE (J/mol·K)	8	13	7
Helmholtz Free Energy (300K)	MAE (kJ/mol)	2	3	2
Heat Capacity	MAE (J/mol·K)	3	4	3
Bulk Modulus	MAE (GPa)	12.49	7.18	14.33
Shear Modulus	MAE (GPa)	7.95	8.03	8.18
Thermal Conductivity	RMSE (W/mK)	0.24	0.21	0.20

Molecular Crystal Benchmarks

Benchmark	Metric	MACE-MH-1-OMAT-D3	ORB-v3	UMA-S-1.1-OMAT-D3
X23 Formation Energy	MAE (kJ/mol)	15.82	28.76	27.99
Ice Polymorphs (DMC)	MAE (meV)	11.23	138.44	310.82

Surface Benchmarks

Benchmark	Metric	MACE-MH-1-OMAT-D3	ORB-v3-D3	UMA-S-1.1-OMAT-D3
S24 Adsorption	MAE (eV)	0.095	0.174	0.329
OC20 Adsorption	MAE (eV)	0.138	0.159	0.172
OC20 Correlation	Pearson's r	0.98	0.974	0.97

Molecular Benchmarks

Benchmark	Metric	MACE-MH-1-OMAT-D3	ORB-v3-D3	UMA-S-1.1-OMAT-D3
Wiggle150	MAE (kcal/mol)	4.80	7.65	6.60
GMTKN55 Overall	WTMAD (kcal/mol)	11.23	22.30	30.83
PLF547 (proteins)	MAE (kcal/mol)	0.626	1.829	2.935
S30L (host-guest)	MAE (kcal/mol)	10.13	13.64	15.14

Physicality Tests

Test	Metric	MACE-MH-1	ORB-v3	UMA-S-1.1
Slab Extensivity	Δ (meV)	0.0	-709.7	-453.8
H-Atom Additivity	max |ΔF| (meV/Å)	0.0	61.65	969.2
Diatomic Force Flips	Mean count	2.09	2.91	10.73
Diatomic Minima	Mean count	1.42	1.62	4.82

Training Data

Pre-training

• OMAT-24: 100M configurations of inorganic crystals (PBE/PBE+U) spanning 89 elements

Multi-Head Fine-tuning

• OMAT Replay: 10M configurations (10% subset) to prevent catastrophic forgetting
• MPTraj: 1.5M configurations from Materials Project with PBE+U
• SPICE-1: ~1M organic molecules (ωB97M-D3(BJ)/def2-TZVP)
• OC20: 2M metal surface slabs and adsorbate complexes (PBE)
• OMOL-1%: 1.2M diverse organic and organometallic configurations (ωB97M-VV10)
• RGD1: 300K organic reaction intermediates and transition states (B3LYP/6-31G*)
• MATPES R2SCAN: 400K inorganic crystals (r²SCAN)

Installation and Usage

Installation

pip install mace-torch

Basic Usage (Python)

from mace.calculators import mace_mp
from ase import Atoms

# Load the MACE-MH-1 model (using the OMAT/PBE head)
calc = mace_mp(model=path, default_dtype="float64", device="cuda", head="omat_pbe")

# Create an example structure
atoms = Atoms('H2O', positions=[[0, 0, 0], [0, 0, 1], [0, 1, 0]])
atoms.calc = calc

# Calculate energy and forces
energy = atoms.get_potential_energy()
forces = atoms.get_forces()

print(f"Energy: {energy} eV")
print(f"Forces:\n{forces}")

Available Model Heads

MACE-MH-1 contains multiple task-specific heads trained on different levels of theory:

Head Name	Level of Theory	Best For	Access
omat_pbe (default)	PBE/PBE+U	General materials, balanced performance across tasks	Specify in model
omol	ωB97M-VV10	1% of OMOL data: Molecular systems, organic chemistry, Organometallic	Specify in model
spice_wB97M	ωB97M-D3(BJ)	Molecular systems and organic chemistry	Specify in model
rgd1_b3lyp	B3LYP	Reaction chemistry	Specify in model
oc20_usemppbe	PBE	Surface catalysis, adsorbates	Specify in model
matpes_r2scan	r²SCAN meta-GGA	High-accuracy materials	Specify in model

By default, the OMAT head (PBE) is used, which provides the best cross-domain performance.

Best Practices

1. For fine-tuning: Use OMAT head first. Test other heads if needed.
2. For materials: Use OMAT head. Use D3 corrections for systems with dispersions. Test matpes_r2scan head if r2scan better reference.
3. For molecules: Consider using OMOL head (ωB97M-VV10) for improved intramolecular interactions. OMAT head good for condensed phase molecular systems, test it too.
4. For surfaces: OMAT head provides excellent performance; OC20 head available for specialized applications

Citation

If you use MACE-MH-1 in your research, please cite:

@article{batatia2025crosslearning,
  title={Cross Learning between Electronic Structure Theories for Unifying Molecular, Surface, and Inorganic Crystal Foundation Force Fields},
  author={Batatia, Ilyes and Lin, Chen and Hart, Joseph and Kasoar, Elliott and Elena, Alin M. and Norwood, Sam Walton and Wolf, Thomas and Cs{\'a}nyi, G{\'a}bor},
  journal={arXiv preprint arXiv:2510.25380},
  year={2025}
}

@article{batatia2022mace,
  title={MACE: Higher order equivariant message passing neural networks for fast and accurate force fields},
  author={Batatia, Ilyes and Kovacs, David Peter and Simm, Gregor and Ortner, Christoph and Cs{\'a}nyi, G{\'a}bor},
  journal={Advances in Neural Information Processing Systems},
  volume={35},
  pages={11423--11436},
  year={2022}
}

License

This model is released under the ASL License.

Acknowledgments

This work was supported by computational resources from:

• Jean Zay HPC (Grand Challenge GC010815458)
• Isambard-AI and Sovereign AI

Contact

• GitHub: ACEsuit/mace
• Foundations: mace-foundations
• Issues: Please report issues on the GitHub repository