Active learning a coarse-grained neural network model for bulk water from sparse training data

Abstract

Neural network (NN) based potentials represent flexible alternatives to pre-defined functional forms. Well-trained NN potentials are transferable and provide a high level of accuracy on-par with the reference model used for training. Despite their tremendous potential and interest in them, there are at least two challenges that need to be addressed – (1) NN models are interpolative, and hence trained by generating large quantities (∼10⁴ or greater) of structural data in hopes that the model has adequately sampled the energy landscape both near and far-from-equilibrium. It is desirable to minimize the number of training data, especially if the underlying reference model is expensive. (2) NN atomistic potentials (like any other classical atomistic model) are limited in the time scales they can access. Coarse-grained NN potentials have emerged as a viable alternative. Here, we address these challenges by introducing an active learning scheme that trains a CG model with a minimal amount of training data. Our active learning workflow starts with a sparse training data set (∼1 to 5 data points), which is continually updated via a nested ensemble Monte Carlo scheme that iteratively queries the energy landscape in regions of failure and improves the network performance. We demonstrate that with ∼300 reference data, our AL-NN is able to accurately predict both the energies and the molecular forces of water, within 2 meV per molecule and 40 meV Å⁻¹ of the reference (coarse-grained bond-order potential) model. The AL-NN water model provides good prediction of several structural, thermodynamic, and temperature dependent properties of liquid water, with values close to those obtained from the reference model. The AL-NN also captures the well-known density anomaly of liquid water observed in experiments. Although the AL procedure has been demonstrated for training CG models with sparse reference data, it can be easily extended to develop atomistic NN models against a minimal amount of high-fidelity first-principles data.