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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.


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

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.:

pip install --upgrade jax jaxlib==0.1.57+cuda110 -f

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:

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


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.

ferminet --config ferminet/configs/ --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 with a bond-length of 1.63999 angstroms 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/

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:

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 get_config():
  # Get default options.
  cfg = base_config.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/

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

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.get_absl_handler() = sys.stdout

# 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


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

from pyscf import gto
mol = gto.Mole()
    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

from ferminet import base_config
from ferminet import train

# Add H2 molecule
cfg = base_config.default()
cfg.system.pyscf_mol = mol

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


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.


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.

Pretrained Models

A collection of pretrained models trained with KFAC can be found on Google Cloud here. These are all systems from the original PRResearch paper: carbon and neon atoms, and nitrogen, ethene, methylamine, ethanol and bicyclobutane molecules. Each folder contains samples from the wavefunction in walkers.npy, parameters in parameters.npz and geometries for the molecule in geometry.npz. To load the models and evaluate the local energy, run:

import numpy as np
import jax
from functools import partial
from ferminet import networks, train

with open('params.npz', 'rb') as f:
  params = dict(np.load(f, allow_pickle=True))
  params = params['arr_0'].tolist()

with open('walkers.npy', 'rb') as f:
  data = np.load(f)

with open('geometry.npz', 'rb') as f:
  geometry = dict(np.load(f, allow_pickle=True))

signed_network = partial(networks.fermi_net, envelope_type='isotropic', full_det=False, **geometry)
# networks.fermi_net gives the sign/log of the wavefunction. We only care about the latter.
network = lambda p, x: signed_network(p, x)[1]
batch_network = jax.vmap(network, (None, 0), 0)
loss = train.make_loss(network, batch_network, geometry['atoms'], geometry['charges'], clip_local_energy=5.0)

print(loss(params, data)[0])  # For neon, should give -128.94165

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:

  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},
  issue = {3},
  doi = {10.1103/PhysRevResearch.2.033429},
  url = {}

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

  title={Better, Faster Fermionic Neural Networks},
  author={James S. Spencer and David Pfau and Aleksandar Botev and W. M.C. Foulkes},
  url = {}

This repository can be cited using:

  author = {James S. Spencer, David Pfau and FermiNet Contributors},
  title = {{FermiNet}},
  url = {},
  year = {2020},


This is not an official Google product.


An implementation of the Fermionic Neural Network for ab-initio electronic structure calculations







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