Code Repository "Finding symmetry breaking order parameters with Euclidean Neural Networks"

This is the code respository for the following paper. https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.L012002

Requirements

• torch
• pymatgen
• torch-geometric
• e3nn==0.1.1 (Install version 0.1.1 here for CUDA or via pip install e3nn==0.1.1 for CPU only)

Notebooks

square_to_rectangle.ipynb

• Demonstrates how E(3)NNs exhibit Curie's principle and that the gradients of the network can be used to find symmetry breaking input

perovskite_order_parameters_determine_irreps.ipynb

• Determines the irreps needed to describe octahedral distortions in perovskites in space group Pnma (62).

perovskite_order_parameters_spacegroup_74_from_62.ipynb

• Recovers an intermediate structure in space group 74 from input in space group 221 and output in space group 62.

perovskite_order_parameters_with_explicit_k.ipynb

• Recovers pseudovector order parameters for structure in space group 62 using explicit k-vectors.

Citing

If you find this repository helpful for your research. Please consider citing the following:

@article{Smidt2021,
  doi = {10.1103/physrevresearch.3.l012002},
  url = {https://doi.org/10.1103/physrevresearch.3.l012002},
  year = {2021},
  month = jan,
  publisher = {American Physical Society ({APS})},
  volume = {3},
  number = {1},
  author = {Tess E. Smidt and Mario Geiger and Benjamin Kurt Miller},
  title = {Finding symmetry breaking order parameters with Euclidean neural networks},
  journal = {Physical Review Research}
}

@misc{e3nn_symm_breaking,
  doi = {10.5281/ZENODO.4087189},
  url = {https://zenodo.org/record/4087189},
  author = {Smidt,  Tess},
  title = {Code repository for ``Finding symmetry breaking order parameters with Euclidean neural networks''},
  publisher = {Zenodo},
  year = {2020},
  copyright = {Open Access}
}