A Differentiable Neural-Network Force Field for Ionic Liquids

We present NeuralIL, a model for the potential energy
of an ionic liquid that accurately reproduces first-principles results
with orders-of-magnitude savings in computational cost. Built on the
basis of a multilayer perceptron and spherical Bessel descriptors
of the atomic environments, NeuralIL is implemented in such
a way as to be fully automatically differentiable. It can thus be
trained on ab initio forces instead of just energies, to make the
most out of the available data, and can efficiently predict arbitrary
derivatives of the potential energy. Using ethylammonium nitrate as
the test system, we obtain out-of-sample accuracies better than 2
meV atom–1 (<0.05 kcal mol–1) in the energies and 70 meV Å–1 in the forces.
We show that encoding the element-specific density in the spherical
Bessel descriptors is key to achieving this. Harnessing the information
provided by the forces drastically reduces the amount of atomic configurations
required to train a neural network force field based on atom-centered
descriptors. We choose the Swish-1 activation function and discuss
the role of this choice in keeping the neural network differentiable.
Furthermore, the possibility of training on small data sets allows
for an ensemble-learning approach to the detection of extrapolation.
Finally, we find that a separate treatment of long-range interactions
is not required to achieve a high-quality representation of the potential
energy surface of these dense ionic systems.