Tensor Atomic/Edge Cluster Expansion (TACE/TECE)

TACE is designed with physical priors and strong inductive biases to enhance extrapolation capability. It performs Atomic Cluster Expansion and Edge Cluster Expansion based on spherical tensors or irreducible Cartesian tensors, with an optional attention architecture.

Docs

https://tace.readthedocs.io/en/latest/index.html

SOTA Foundation Model

https://github.com/xvzemin/tace-foundations

Default Ranking on Matbench as of July 8, 2026

Fine-tuning

• ✅ Full-parameter.
• ✅ Freeze-parameter.
• ✅ LoRA.

Tutorial and Train from scratch

The docs contain a complete tutorial.

We also provide complete input files and a series of example scripts, including ASE, TorchSim ..., at

https://github.com/xvzemin/tace/tree/main/example

# Minimal training example
git clone https://github.com/xvzemin/tace.git
cd tace
pip install .
cd example/train
tace-train -cn tace.yaml

Overview

Currently, the officially supported properties include:

• Energy
• Forces (conservative | direct)
• Hessian (conservative, predict only)
• Stress (conservative | direct)
• Virials (conservative | direct)
• Charges (lagrangian or uniform_distribution)
• Dipole moment (conservative | direct)
• Polarization (conservative, multi-value for PBC systems)
• Polarizability (conservative | direct)
• Born effective charges (conservative, under electric field or LES) (LES predict only)
• Atomic stresses (conservative, predict only)
• Atomic virials (conservative, predict only)
• absolute final collinear magmoms
• Noncollinear magnetic forces (full O(3))

For embedding property, we support:

• fidelity_idx (different computational levels)
• charges
• total charge
• electric field
• initial (non)collinear magmoms
• magnetic field (full O(3))

Plugins

TACE currently supports the following plugin:

• LES (Latent Ewald Summation)

Interfaces

• ✅ Supports integration with ASE Calculator.
• ✅ Supports integration with LAMMPS-ML-IAP.
• ✅ Supports integration with TorchSim.
• ✅ Supports integration with OpenMM-ML (OpenMM-ML -> ASE -> TACE).
• ✅ Supports integration with USPEX (USPEX -> LAMMPS-ML-IAP -> TACE) (Python=3.9).

Citing

If you use TACE, please cite our papers:

@misc{xu2026spectralspatialtensoratomiccluster,
   title={Spectral/Spatial Tensor Atomic Cluster Expansion with Universal Embeddings in Cartesian Space},
   author={Zemin Xu and Wenbo Xie and P. Hu},
   year={2026},
   eprint={2509.14961},
   archivePrefix={arXiv},
   primaryClass={stat.ML},
   url={https://arxiv.org/abs/2509.14961},
}

@misc{xu2026edgeclusterexpansionradial,
   title={Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentials},
   author={Zemin Xu and Wenbo Xie and P. Hu},
   year={2026},
   eprint={2607.10664},
   archivePrefix={arXiv},
   primaryClass={stat.ML},
   url={https://arxiv.org/abs/2607.10664},
}

If you use cartnn, Cartesian-3j, cMACE, cNequIP, cAllegro, please cite our papers:

@inproceedings{
   xu2026a,
   title={A Cartesian-3j Framework for Machine Learning Interatomic Potentials},
   author={Zemin Xu and Chenyu Wu and Wenbo Xie and Peijun Hu},
   booktitle={Forty-third International Conference on Machine Learning},
   year={2026},
   url={https://openreview.net/forum?id=9ZWK6gneWq}
}

Contact

For bugs or feature requests, please use https://github.com/xvzemin/tace/issues.

License

The TACE code is published and distributed under the MIT License.