Tensor Atomic Cluster Expansion#

Documentation Structure#

Contents

Changelog

Overview#

TACE is a Cartesian-based machine learning model designed to predict both scalar and tensorial properties.

In principle, the framework supports any tensorial properties (either direct or conservative) determined by the underlying atomic structure. 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 (conservative)

For embedding property, we support:

  • fidelity_idx (different computational levels)

  • charges

  • total charge

  • electric field

  • initial (non)collinear magmoms

  • spin multiplicity (not tested by us)

  • electron_temperature (not tested by us)

  • magnetic field (not tested by us)

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).

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},
}

If you use Cartesian-3j, please cite our papers:

@misc{xu2025cartesiannjextendinge3nnirreducible,
      title={A Cartesian-3j Framework for Machine Learning Interatomic Potentials},
      author={Zemin Xu and Chenyu Wu and Wenbo Xie and P. Hu},
      year={2026},
      eprint={2512.16882},
      archivePrefix={arXiv},
      primaryClass={physics.chem-ph},
      url={https://arxiv.org/abs/2512.16882v2},
}

Contact#

For bugs or feature requests, please use xvzemin/tace#issues.

License#

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