Crystal Generation with Space Group Informed Transformer

CrystalFormer is a transformer-based autoregressive model specifically designed for space group-controlled generation of crystalline materials. The space group symmetry significantly simplifies the crystal space, which is crucial for data and compute efficient generative modeling of crystalline materials.

Generating Cs₂ZnFe(CN)₆ Crystal (mp-570545)

Contents

• Contents
• Model card
• Status
• Get Started
• Installation
  • CPU installation
  • CUDA (GPU) installation
  • install required packages
• Available Weights
• How to run
  • train
  • sample
  • evaluate
• Reinforcement Fine-tuning
  • $E_{hull}$ Reward
  • Dielectric FoM Reward
• How to cite

Model card

The model is an autoregressive transformer for the space group conditioned crystal probability distribution P(C|g) = P (W_1 | ... ) P ( A_1 | ... ) P(X_1| ...) P(W_2|...) ... P(L| ...), where

• g: space group number 1-230
• W: Wyckoff letter ('a', 'b',...,'A')
• A: atom type ('H', 'He', ..., 'Og')
• X: factional coordinates
• L: lattice vector [a,b,c, alpha, beta, gamma]
• P(W_i| ...) and P(A_i| ...) are categorical distributuions.
• P(X_i| ...) is the mixture of von Mises distribution.
• P(L| ...) is the mixture of Gaussian distribution.

We only consider symmetry inequivalent atoms. The remaining atoms are restored based on the space group and Wyckoff letter information. Note that there is a natural alphabetical ordering for the Wyckoff letters, starting with 'a' for a position with the site-symmetry group of maximal order and ending with the highest letter for the general position. The sampling procedure starts from higher symmetry sites (with smaller multiplicities) and then goes on to lower symmetry ones (with larger multiplicities). Only for the cases where discrete Wyckoff letters can not fully determine the structure, one needs to further consider factional coordinates in the loss or sampling.

Status

Major milestones are summarized below.

• v0.4.2 : Add implementation of direct preference optimization.
• v0.4.1 : Replace the absolute positional embedding with the Rotary Positional Embedding (RoPE).
• v0.4 : Add reinforcement learning (proximal policy optimization).
• v0.3 : Add conditional generation in the plug-and-play manner.
• v0.2 : Add Markov chain Monte Carlo (MCMC) sampling for template-based structure generation.
• v0.1 : Initial implementations of crystalline material generation conditioned on the space group.

Get Started

Notebooks: The quickest way to get started with CrystalFormer is our notebooks in the Google Colab and Bohrium (Chinese version) platforms:

• CrystalFormer Quickstart : GUI notebook demonstrating the conditional generation of crystalline materials with CrystalFormer;
• CrystalFormer Application : Generating stable crystals with a given structure prototype. This workflow can be applied to tasks that are dominated by element substitution.

Installation

Create a new environment and install the required packages, we recommend using python 3.10.* and conda to create the environment:

  conda create -n crystalgpt python=3.10
  conda activate crystalgpt

Before installing the required packages, you need to install jax and jaxlib first.

CPU installation

pip install -U "jax[cpu]"

CUDA (GPU) installation

Caution

CrystalFormer requires JAX versions between v0.4.25 and v0.4.35. Please avoid using versions newer than v0.4.35 to prevent compatibility issues. If you have already installed a newer version, please uninstall it first and then install one within the required range.

If you intend to use CUDA (GPU) to speed up the training, it is important to install the appropriate version of jax and jaxlib. It is recommended to check the jax docs for the installation guide. The basic installation command is given below:

pip install --upgrade pip

# NVIDIA CUDA 12 installation
# Note: wheels only available on linux.
pip install --upgrade "jax[cuda12]"

install required packages

pip install -r requirements.txt

Available Weights

We release the weights of the model trained on the MP-20 dataset and Alex-20 dataset. More details can be seen in the model folder.

How to run

train

python ./main.py --folder ./data/ --train_path YOUR_PATH/mp_20/train.csv --valid_path YOUR_PATH/mp_20/val.csv

• folder: the folder to save the model and logs
• train_path: the path to the training dataset
• valid_path: the path to the validation dataset
• test_path: the path to the test dataset

sample

python ./main.py --optimizer none --test_path YOUR_PATH/mp_20/test.csv --restore_path YOUR_MODEL_PATH --spacegroup 160 --num_samples 1000  --batchsize 1000 --temperature 1.0

• optimizer: the optimizer to use, none means no training, only sampling
• restore_path: the path to the model weights
• spacegroup: the space group number to sample
• num_samples: the number of samples to generate
• batchsize: the batch size for sampling
• temperature: the temperature for sampling

You can also use the elements to sample the specific element. For example, --elements La Ni O will sample the structure with La, Ni, and O atoms. The sampling results will be saved in the output_LABEL.csv file, where the LABEL is the space group number g specified in the command --spacegroup.

The input for the elements can be also the json file which specifies the atom mask in each Wyckoff site and the constraints. An example atoms.json file can be seen in the data folder. There are two keys in the atoms.json file:

• atom_mask: set the atom list for each Wyckoff position, the element can only be selected from the list in the corresponding Wyckoff position
• constraints: set the constraints for the Wyckoff sites in the sampling, you can specify the pair of Wyckoff sites that should have the same elements

evaluate

Before evaluating the generated structures, you need to transform the generated g, W, A, X, L to the cif format. You can use the following command to transform the generated structures to the cif format and save as the csv file:

python ./scripts/awl2struct.py --output_path YOUR_PATH --label SPACE_GROUP  --num_io_process 40

• output_path: the path to read the generated L, W, A, X and save the cif files
• label: the label to save the cif files, which is the space group number g
• num_io_process: the number of processes

Calculate the structure and composition validity of the generated structures:

python ./scripts/compute_metrics.py --root_path YOUR_PATH --filename YOUR_FILE --num_io_process 40

• root_path: the path to the dataset
• filename: the filename of the generated structures
• num_io_process: the number of processes

Calculate the novelty and uniqueness of the generated structures:

python ./scripts/compute_metrics_matbench.py --train_path TRAIN_PATH --test_path TEST_PATH --gen_path GEN_PATH --output_path OUTPUT_PATH --label SPACE_GROUP --num_io_process 40

• train_path: the path to the training dataset
• test_path: the path to the test dataset
• gen_path: the path to the generated dataset
• output_path: the path to save the metrics results
• label: the label to save the metrics results, which is the space group number g
• num_io_process: the number of processes

Note that the training, test, and generated datasets should contain the structures within the same space group g which is specified in the command --label.

More details about the post-processing can be seen in the scripts folder.

Reinforcement Fine-tuning

Important

Before running the reinforcement fine-tuning, please make sure you have installed the corresponding machine learning force field model or property prediction model. The mlff_model and mlff_path arguments in the command line should be set according to the model you are using. Now we support theorb and MACE models for the $E_{hull}$ reward, and the matgl model for the dielectric FoM reward.

$E_{hull}$ Reward

train_ppo --folder ./data/\
          --restore_path YOUR_PATH\
          --valid_path YOUR_PATH/alex_20/val.csv\
          --test_path YOUR_PATH/alex_20/train.csv\
          --reward ehull\
          --convex_path YOUR_PATH/convex_hull_pbe_2023.12.29.json.bz2\
          --mlff_model orb\
          --mlff_path YOUR_PATH/orb-v2-20241011.ckpt

• folder: the folder to save the model and logs
• restore_path: the path to the pre-trained model weights
• valid_path: the path to the validation dataset
• test_path: the path to the test dataset. The space group distribution will be loaded from this dataset and used for the sampling in the reinforcement learning fine-tuning
• reward: the reward function to use, ehull means the energy above the convex hull
• convex_path: the path to the convex hull data, which is used to calculate the $E_{hull}$. Only used when the reward is ehull
• mlff_model: the machine learning force field model to predict the total energy. We support orb and MACE models for the $E_{hull}$ reward
• mlff_path: the path to load the checkpoint of the machine learning force field model

Dielectric FoM Reward

train_ppo --folder ./data/\
          --restore_path YOUR_PATH\
          --valid_path YOUR_PATH/alex_20/val.csv\
          --test_path YOUR_PATH/alex_20/train.csv\
          --reward dielectric\
          --mlff_model matgl\
          --mlff_path YOUR_PATH/model1,YOUR_PATH/model2

• folder: the folder to save the model and logs
• restore_path: the path to the pre-trained model weights
• valid_path: the path to the validation dataset
• test_path: the path to the test dataset. The space group distribution will be loaded from this dataset and used for the sampling in the reinforcement learning fine-tuning
• reward: the reward function to use, dielectric means the dielectric figure of merit (FoM), which is the product of the total dielectric constant and the band gap
• mlff_model: the machine learning force field model to predict the total energy. We only support models in matgl for the dielectric reward
• mlff_path: the path to load the checkpoint of the machine learning force field model. Note that you need to provide the model paths for the total dielectric constant and band gap, separated by the ,

How to cite

@article{cao2024space,
      title={Space Group Informed Transformer for Crystalline Materials Generation}, 
      author={Zhendong Cao and Xiaoshan Luo and Jian Lv and Lei Wang},
      year={2024},
      eprint={2403.15734},
      archivePrefix={arXiv},
      primaryClass={cond-mat.mtrl-sci}
}

@article{cao2025crystalformerrl,
      title={CrystalFormer-RL: Reinforcement Fine-Tuning for Materials Design}, 
      author={Zhendong Cao and Lei Wang},
      year={2025},
      eprint={2504.02367},
      archivePrefix={arXiv},
      primaryClass={cond-mat.mtrl-sci},
      url={https://arxiv.org/abs/2504.02367}, 
}

Note: This project is unrelated to https://github.com/omron-sinicx/crystalformer with the same name.