Train a neural network potential

In this tutorial, we train a neural network (NN) potential for silicon.

We are going to fit the NN potential to a training set of energies and forces from compressed and stretched diamond silicon structures (the same training set used in Train a Stillinger-Weber potential). Download the training set Si_training_set.tar.gz # (It will be automatically downloaded if it is not present.) The data is stored in extended xyz format, and see Dataset for more information of this format.

Warning

The Si_training_set is just a toy data set for the purpose to demonstrate how to use KLIFF to train potentials. It should not be used to train any potential for real simulations.

Let’s first import the modules that will be used in this example.

from kliff import nn
from kliff.calculators import CalculatorTorch
from kliff.dataset import Dataset
from kliff.dataset.weight import Weight
from kliff.descriptors import SymmetryFunction
from kliff.loss import Loss
from kliff.models import NeuralNetwork
from kliff.utils import download_dataset

Model

For a NN model, we need to specify the descriptor that transforms atomic environment information to the fingerprints, which the NN model uses as the input. Here, we use the symmetry functions proposed by Behler and coworkers.

descriptor = SymmetryFunction(
    cut_name="cos", cut_dists={"Si-Si": 5.0}, hyperparams="set51", normalize=True
)

The cut_name and cut_dists tell the descriptor what type of cutoff function to use and what the cutoff distances are. hyperparams specifies the set of hyperparameters used in the symmetry function descriptor. If you prefer, you can provide a dictionary of your own hyperparameters. And finally, normalize informs that the generated fingerprints should be normalized by first subtracting the mean and then dividing the standard deviation. This normalization typically makes it easier to optimize NN model.

We can then build the NN model on top of the descriptor.

N1 = 10
N2 = 10
model = NeuralNetwork(descriptor)
model.add_layers(
    # first hidden layer
    nn.Linear(descriptor.get_size(), N1),
    nn.Tanh(),
    # second hidden layer
    nn.Linear(N1, N2),
    nn.Tanh(),
    # output layer
    nn.Linear(N2, 1),
)
model.set_save_metadata(prefix="./kliff_saved_model", start=5, frequency=2)

In the above code, we build a NN model with an input layer, two hidden layer, and an output layer. The descriptor carries the information of the input layer, so it is not needed to be specified explicitly. For each hidden layer, we first do a linear transformation using nn.Linear(size_in, size_out) (essentially carrying out , where is the weight matrix of size size_in by size_out, and is a vector of size size_out. Then we apply the hyperbolic tangent activation function nn.Tanh() to the output of the Linear layer (i.e. ) so as to add the nonlinearity. We use a Linear layer for the output layer as well, but unlike the hidden layer, no activation function is applied here. The input size size_in of the first hidden layer must be the size of the descriptor, which is obtained using descriptor.get_size(). For all other layers (hidden or output), the input size must be equal to the output size of the previous layer. The out_size of the output layer must be 1 such that the output of the NN model gives the energy of the atom.

The set_save_metadata function call informs where to save intermediate models during the optimization (discussed below), and what the starting epoch and how often to save the model.

Training set and calculator

The training set and the calculator are the same as explained in Train a Stillinger-Weber potential. The only difference is that we need to use the CalculatorTorch(), which is targeted for the NN model. Also, its create() method takes an argument reuse to inform whether to reuse the fingerprints generated from the descriptor if it is present. To train on gpu, set gpu=True in Calculator.

# training set
dataset_path = download_dataset(dataset_name="Si_training_set")
dataset_path = dataset_path.joinpath("varying_alat")
weight = Weight(forces_weight=0.3)
tset = Dataset(dataset_path, weight)
configs = tset.get_configs()

# calculator
calc = CalculatorTorch(model, gpu=False)
_ = calc.create(configs, reuse=False)

Loss function

KLIFF uses a loss function to quantify the difference between the training data and potential predictions and uses minimization algorithms to reduce the loss as much as possible. In the following code snippet, we create a loss function that uses the Adam optimizer to minimize it. The Adam optimizer supports minimization using mini-batches of data, and here we use 100 configurations in each minimization step (the training set has a total of 400 configurations as can be seen above), and run through the training set for 10 epochs. The learning rate lr used here is 0.001, and typically, one may need to play with this to find an acceptable one that drives the loss down in a reasonable time.

loss = Loss(calc)
result = loss.minimize(method="Adam", num_epochs=10, batch_size=100, lr=0.001)

Out:

Epoch = 0       loss = 7.3307514191e+01
Epoch = 1       loss = 7.2090656281e+01
Epoch = 2       loss = 7.1389846802e+01
Epoch = 3       loss = 7.0744289398e+01
Epoch = 4       loss = 7.0117309570e+01
Epoch = 5       loss = 6.9499519348e+01
Epoch = 6       loss = 6.8886824608e+01
Epoch = 7       loss = 6.8277158737e+01
Epoch = 8       loss = 6.7668614388e+01
Epoch = 9       loss = 6.7058616638e+01
Epoch = 10      loss = 6.6683934212e+01

We can save the trained model to disk, and later can load it back if we want. We can also write the trained model to a KIM model such that it can be used in other simulation codes such as LAMMPS via the KIM API.

model.save("final_model.pkl")
loss.save_optimizer_state("optimizer_stat.pkl")

model.write_kim_model()

Note

Now we have trained an NN for a single specie Si. If you have multiple species in your system and want to use different parameters for different species, take a look at the Train a neural network potential for SiC example.