InfGCN for Electron Density Estimation

By Chaoran Cheng, Oct 1, 2023

OpenReview, ArXiv

Official implementation of the NeurIPS 23 spotlight paper Equivariant Neural Operator Learning with Graphon Convolution for modeling operators on continuous data.

UPDATE: The pretrained model is available here.

Requirements

All codes are run with Python 3.9.15 and CUDA 11.6. Similar environment should also work, as this project does not rely on some rapidly changing packages. Other required packages are listed in requirements.txt.

Datasets

QM9

The QM9 dataset contains 133885 small molecules consisting of C, H, O, N, and F. The QM9 electron density dataset was built by Jørgensen et al. (paper) and was publicly available via Figshare. Each tarball needs to be extracted, but the inner lz4 compression should be kept. We provided code to read the compressed lz4 file.

Cubic

The Cubic dataset contains electron charge density for 16421 (after filtering) cubic crystal system cells. The dataset was built by Wang et al. (paper) and was publicly available via Figshare. Each tarball needs to be extracted, but the inner xz compression should be kept. We provided code to read the compressed xz file.

WARNING: A considerable proportion of the samples uses the rhombohedral lattice system (i.e., primitive rhomhedral cell instead of unit cubic cell). Some visualization tools (including plotly) may not be able to handle this.

MD

The MD dataset contains 6 small molecules (ethanol, benzene, phenol, resorcinol, ethane, malonaldehyde) with different geometries sampled from molecular dynamics (MD). The dataset was curated from here by Bogojeski et al. and here by Brockherde et al. The dataset is publicly available at the Quantum Machine website.

We assume the data is stored in the <data_root>/<mol_name>/<mol_name>_<split>/ directory, where mol_name should be one of the molecules mentioned above and split should be either train or test. The directory should contain the following files:

• structures.npy contains the coordinates of the atoms.
• dft_densities.npy contains the voxelized electron charge density data.

This is the format for the latter four molecules (you can safely ignore other files). For the former two molecules, run python generate_dataset.py to generate the correctly formatted data. You can also specify the data directory with --root and the output directory with --out.

All MD datasets assume a cubic box with side length of 20 Bohr and 50 grids per side. The densities are store as Fourier coefficients, and we provided code to convert them.

Running the code

Most hyperparameters are specified in the config files. More parameters in the YAML file is self-explanatory. See this readme for more details on modifying the config files. Free feel to modify the config files to suit your needs or to add new models. The pretrained model together with a sample electron density file is available here.

Training

To train the model, run

python main.py configs/qm9.yml --savename test

Evaluation

To evaluate the model, run

python main.py configs/qm9.yml --savename test --mode inf --resume <model_path>

Inference

To see the visualization of the predicted density, run inference.ipynb with JupyterLab or Jupyter Notebook.

Extending to other models

To utilize the code for other (GNN-based) models, you need to register the model class in using the models.register_model decorator. Your model's forward function should take same arguments as our InfGCN, but the initialization arguments can be different (see the instructions on modifying the config file).

Result

The below figures demonstrate the normalized mean absolute error (NMAE) vs the model size of our model and all the baseline model on the QM9 dataset. Here, s0 to s6 refer to the maximum degree of spherical harmonics used in the model (InfGCN is s7). no-res refers to the model without residual connection and fc refers to the model without fully-connected tensor product. The pink points are interpolation GNNs and oranges points are neural operators.

Citation

If you find this code useful, please cite our paper

@InProceedings{Cheng2023infgcn,
  title={Equivariant Neural Operator Learning with Graphon Convolution},
  author={Chaoran Cheng and Jian Peng},
  booktitle={Advances in Neural Information Processing Systems 37: Annual Conference on Neural Information Processing Systems 2023, NeurIPS 2023, December 10-16, 2023},
  month={December},
  year={2023},
}