FermiNet: Fermionic Neural Networks

FermiNet is a neural network for learning highly accurate ground state wavefunctions of atoms and molecules using a variational Monte Carlo approach.

This repository contains an implementation of the algorithm and experiments first described in "Ab-Initio Solution of the Many-Electron Schroedinger Equation with Deep Neural Networks", David Pfau, James S. Spencer, Alex G de G Matthews and W.M.C. Foulkes, Phys. Rev. Research 2, 033429 (2020), along with subsequent research and developments.

WARNING: This is a research-level release of a JAX implementation and is under active development. The original TensorFlow implementation can be found in the tf branch.

Installation

pip install -e . will install all required dependencies. This is best done inside a virtual environment.

shell virtualenv ~/venv/ferminet source ~/venv/ferminet/bin/activate pip install -e .

If you have a GPU available (highly recommended for fast training), then you can install JAX with CUDA support, using e.g.:

shell pip install --upgrade jax jaxlib==0.1.57+cuda110 -f https://storage.googleapis.com/jax-releases/jax_releases.html

Note that the jaxlib version must correspond to the existing CUDA installation you wish to use. Please see the JAX documentation for more details.

The tests are easiest run using pytest:

shell pip install -e '.[testing]' python -m pytest

Usage

ferminet uses the ConfigDict from ml_collections to configure the system. A few example scripts are included under ferminet/configs/. These are mostly for testing so may need additional settings for a production-level calculation.

shell ferminet --config ferminet/configs/atom.py --config.system.atom Li --config.batch_size 256 --config.pretrain.iterations 100

or

shell python3 ferminet/main.py --config ferminet/configs/atom.py --config.system.atom Li --config.batch_size 256 --config.pretrain.iterations 100

will train FermiNet to find the ground-state wavefunction of the Li atom using a batch size of 1024 MCMC configurations ("walkers" in variational Monte Carlo language), and 100 iterations of pretraining (the default of 1000 is overkill for such a small system). The system and hyperparameters can be controlled by modifying the config file or (better, for one-off changes) using flags. See the ml_collections' documentation for further details on the flag syntax. Details of all available config settings are in ferminet/base_config.py.

Other systems can easily be set up, by creating a new config file or ferminet, or writing a custom training script. For example, to run on the H2 molecule, you can create a config file containing:

```python from ferminet import base_config from ferminet.utils import system

Settings in a config files are loaded by executing the the get_config

function.

def getconfig(): # Get default options. cfg = baseconfig.default() # Set up molecule cfg.system.electrons = (1,1) cfg.system.molecule = [system.Atom('H', (0, 0, -1)), system.Atom('H', (0, 0, 1))]

# Set training hyperparameters cfg.batch_size = 256 cfg.pretrain.iterations = 100

return cfg ```

and then run it using

ferminet --config /path/to/h2_config.py

or equivalently write the following script (or execute it interactively):

```python import sys

from absl import logging from ferminet.utils import system from ferminet import base_config from ferminet import train

Optional, for also printing training progress to STDOUT.

If running a script, you can also just use the --alsologtostderr flag.

logging.getabslhandler().pythonhandler.stream = sys.stdout logging.setverbosity(logging.INFO)

Define H2 molecule

cfg = base_config.default() cfg.system.electrons = (1,1) # (alpha electrons, beta electrons) cfg.system.molecule = [system.Atom('H', (0, 0, -1)), system.Atom('H', (0, 0, 1))]

Set training parameters

cfg.batch_size = 256 cfg.pretrain.iterations = 100

train.train(cfg) ```

Alternatively, you can directly pass in a PySCF 'Molecule'. You can create PySCF Molecules with the following:

python from pyscf import gto mol = gto.Mole() mol.build( atom = 'H 0 0 1; H 0 0 -1', basis = 'sto-3g', unit='bohr')

Once you have this molecule, you can pass it directly into the configuration by running

```python from ferminet import base_config from ferminet import train

Add H2 molecule

cfg = baseconfig.default() cfg.system.pyscfmol = mol

Set training parameters

cfg.batch_size = 256 cfg.pretrain.iterations = 100

train.train(cfg) ```

Note: to train on larger atoms and molecules with large batch sizes, multi-GPU parallelisation is essential. This is supported via JAX's pmap. Multiple GPUs will be automatically detected and used if available.

Inference

After training, it is useful to run calculations of the energy and other observables over many time steps with the parameters fixed to accumulate low-variance estimates of physical quantities. To do this, just re-run the same command used for training with the flag --config.optim.optimizer 'none'. Make sure that either the value of cfg.log.save_path is the same, or that the value of cfg.log.restore_path is set to the value of cfg.log.save_path from the original training run.

It can also be useful to accumulate statistics about observables at inference time which were not included in the original training run. Spin magnitude, dipole moments and density matrices can be tracked by adding --config.observables.s2, --config.observables.dipole and --config.observables.density to the command line if they are not set to true in the config file.

Excited States

Excited state properties of systems can be calculated using either the Natural Excited States for VMC (NES-VMC) algorithm or an ensemble penalty method. To enable the calculation of k states of a system, simply set cfg.system.states=k in the config file. By default, NES-VMC is used, but to enable the ensemble penalty method, add cfg.optim.objective='vmc_overlap' to the config. NES-VMC does not have any parameters to set, but the ensemble penalty method has a free choice of weights on the energies and overlap penalty, which can be set in cfg.optim.overlap. If the weights are not set for the energies in the config, they are automatically set to 1/k for state k. We have found that NES-VMC is generally more accurate than the ensemble penalty method, but include both for completeness. Config files for all experiments from the paper which introduced NES-VMC can be found in the folder configs/excited, and all experiments can be tested (on smaller networks) by running tests/excited_test.py.

Output

The results directory contains train_stats.csv which contains the local energy and MCMC acceptance probability for each iteration, and the checkpoints directory, which contains the checkpoints generated during training. When computing observables of excited states or the density matrix for the ground state, .npy files are also saved to the same folder. A single NumPy array is saved for every iteration of optimization into the same file. An example Colab notebook analyzing these outputs is given in notebooks/excited_states_analysis.ipynb.

Giving Credit

If you use this code in your work, please cite the associated papers. The initial paper details the architecture and results on a range of systems:

@article{pfau2020ferminet, title={Ab-Initio Solution of the Many-Electron Schr{\"o}dinger Equation with Deep Neural Networks}, author={D. Pfau and J.S. Spencer and A.G. de G. Matthews and W.M.C. Foulkes}, journal={Phys. Rev. Research}, year={2020}, volume={2}, issue = {3}, pages={033429}, doi = {10.1103/PhysRevResearch.2.033429}, url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.033429} }

and a NeurIPS Workshop Machine Learning and Physics paper describes the JAX implementation:

@misc{spencer2020better, title={Better, Faster Fermionic Neural Networks}, author={James S. Spencer and David Pfau and Aleksandar Botev and W. M.C. Foulkes}, year={2020}, eprint={2011.07125}, archivePrefix={arXiv}, primaryClass={physics.comp-ph}, url={https://arxiv.org/abs/2011.07125} }

The PsiFormer architecture is detailed in an ICLR 2023 paper:

@misc{vonglehn2023psiformer, title={A Self-Attention Ansatz for Ab-initio Quantum Chemistry}, author={Ingrid von Glehn and James S Spencer and David Pfau}, journal={ICLR}, year={2023}, }

Periodic boundary conditions were originally introduced in a Physical Review Letters article:

@article{cassella2023discovering, title={Discovering quantum phase transitions with fermionic neural networks}, author={Cassella, Gino and Sutterud, Halvard and Azadi, Sam and Drummond, ND and Pfau, David and Spencer, James S and Foulkes, W Matthew C}, journal={Physical review letters}, volume={130}, number={3}, pages={036401}, year={2023}, publisher={APS} }

Wasserstein QMC (thanks to Kirill Neklyudov) is described in a NeurIPS 2023 article:

@article{neklyudov2023wasserstein, title={Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the Quantum Many-Body Schr{\"o}dinger Equation}, author={Neklyudov, Kirill and Nys, Jannes and Thiede, Luca and Carrasquilla, Juan and Liu, Qiang and Welling, Max and Makhzani, Alireza}, journal={NeurIPS}, year={2023} }

Natural excited states was introduced in this article, which is also the first paper from our group using pseudopotentials

@article{pfau2024excited, title={Accurate computation of quantum excited states with neural networks}, author={Pfau, David and Axelrod, Simon and Sutterud, Halvard and von Glehn, Ingrid and Spencer, James S}, journal={Science}, volume={385}, number={6711}, pages={eadn0137}, year={2024}, url={https://doi.org/10.1126/science.adn0137}, }

This repository can be cited using:

@software{ferminet_github, author = {James S. Spencer, David Pfau and FermiNet Contributors}, title = {{FermiNet}}, url = {http://github.com/deepmind/ferminet}, year = {2020}, }

Disclaimer

This is not an official Google product.