Official repository for the paper "Higher Rank Irreducible Cartesian Tensors for Equivariant Message Passing". It is built upon the ALEBREW repository and implements irreducible Cartesian tensors and their products.
Note: The codebase now also includes implementations of short- and long-range pair potentials, such as ZBL, two-body D4, and Coulomb potentials, including both Ewald summation and smooth particle mesh Ewald (SPME) methods. For further details, we refer to our paper "Performance of universal machine-learned potentials with explicit long-range interactions in biomolecular simulations".
Note: We additionally now have a workshop submission "Transferable long-range interactions in machine-learned interatomic potentials" which discusses our implementations of short- and long-range pair potentials in greater detail and evaluates them on the synthetic point-charge datasets available at https://doi.org/10.5281/zenodo.17652033.
Please consider citing us if you find the code and paper useful:
@misc{zaverkin2024higherrankirreduciblecartesiantensors,
title={Higher-Rank Irreducible Cartesian Tensors for Equivariant Message Passing},
author={Viktor Zaverkin and Francesco Alesiani and Takashi Maruyama and Federico Errica and Henrik Christiansen and Makoto Takamoto and Nicolas Weber and Mathias Niepert},
year={2024},
eprint={2405.14253},
archivePrefix={arXiv},
primaryClass={cs.LG},
url={https://arxiv.org/abs/2405.14253},
}
If you are using the ICTP models with analytic pair potentials:
@misc{zaverkin2025performanceuniversalmachinelearnedpotentials,
title={Performance of universal machine-learned potentials with explicit long-range interactions in biomolecular simulations},
author={Viktor Zaverkin and Matheus Ferraz and Francesco Alesiani and Mathias Niepert},
year={2025},
eprint={2508.10841},
archivePrefix={arXiv},
primaryClass={physics.chem-ph},
url={https://arxiv.org/abs/2508.10841},
}
If you find the synthetic point-charge datasets useful:
@inproceedings{
zaverkin2025transferable,
title={Transferable long-range interactions in machine-learned interatomic potentials},
author={Viktor Zaverkin and Matheus Ferraz and Francesco Alesiani and Henrik Christiansen and Makoto Takamoto and Federico Errica and Mathias Niepert},
booktitle={EurIPS 2025 Workshop on SIMBIOCHEM},
year={2025},
url={https://openreview.net/forum?id=ssfrYXdQ4x}
}
This repository implements:
- Irreducible Cartesian tensors up to a rank of three;
- Irreducible Cartesian tensor products (currently, only even tensor products);
- MACE-like architecture based on irreducible Cartesian tensors and their products;
- Short- and long-range pair potentials, such as ZBL, two-body D4, and Coulomb potentials, including both Ewald summation and smooth PME methods.
This source code is released under a non-commercial license; see LICENSE.txt for details.
Note: ictp/utils/dimos/bspline.py is released under a different license: see LICENSE_DIMOS.txt.
An environment with PyTorch (>=2.3.1) and ASE (>=3.22.1) installed. Also, some other dependencies may be necessary; see the ictp-cuda.yml file.
First, clone this repository into a directory of your choice git clone https://github.com/nec-research/ictp.git <dest_dir>. Then, move to <dest_dir> and install the required packages into a conda environment using, e.g., conda env create -f ictp-cuda.yml. Finally, set your PYTHONPATH environment variable to export PYTHONPATH=<dest_dir>:$PYTHONPATH.
We provide example scripts for training ICTP models for molecular (examples/run_training_DHA.py) and material (examples/run_training_HEA.py) systems. For the DHA molecule, first, download the corresponding data set by running wget http://www.quantum-machine.org/gdml/repo/static/md22_DHA.zip and unzip it with, e.g., unzip md22_DHA.zip. Then, store the md22_DHA.xyz file in the datasets/md22 subfolder and run python run_training_DHA.py to train your first ICTP model. The HEA data set can be downloaded from DaRUS. Please refer to examples/using_ictp.ipynb for more details on training ICTP models and using them in, e.g., molecular dynamics simulations.
How to reproduce the results from the paper "Higher Rank Irreducible Cartesian Tensors for Equivariant Message Passing"
In the experiments subfolder, we provide scripts to reproduce all results from the paper, along with data preparation scripts in the datasets subfolder. For the experiments with the original MACE source code, we used the commit 88d49f9ed6925dec07d1777043a36e1fe4872ff3.
How to reproduce the results from the paper "Performance of universal machine-learned potentials with explicit long-range interactions in biomolecular simulations"
In the examples/dimos subfolder, we provide example scripts and input files for all simulated systems. To run these, please install:
In the examples subfolder, we also provide a script run_training_SPICE.py for training ICTP models with short- and long-range pair potentials
How to reproduce the results from the workshop submission "Transferable long-range interactions in machine-learned interatomic potentials"
In the examples/point_charges subfolder, we provide example scripts for training and evaluating ICTP models with short- and long-range pair potentials on the point-charge datasets. The datasets/point_charges subfolder contains the scripts used to generate these datasets.