Active Learning the Coarse-Grained Energy Landscape For Water Clusters From Sparse Training Data

TL;DR

This paper introduces an active learning method to train neural networks for water cluster energy landscapes using only 426 structures, achieving high accuracy with minimal data and enabling efficient molecular simulations.

Contribution

The study presents a novel active learning workflow that significantly reduces training data requirements for accurate energy landscape modeling of water clusters.

Findings

Achieved ~2 meV/molecule MAE in energy predictions

Accurately captured cluster structures and free energies

Demonstrated effective training with only 426 structures

Abstract

ANNs are currently trained by generating large quantities (On the order of $10^{4}$ or greater) of structural data in hopes that the ANN has adequately sampled the energy landscape both near and far-from-equilibrium. This can, however, be a bit prohibitive when it comes to more accurate levels of quantum theory. As such it is desirable to train a model using the absolute minimal data set possible, especially when costs of high-fidelity calculations such as CCSD and QMC are high. Here, we present an Active Learning approach that iteratively trains an ANN model to faithfully replicate the coarse-grained energy surface of water clusters using only 426 total structures in its training data. Our active learning workflow starts with a sparse training dataset which is continually updated via a Monte Carlo scheme that sparsely queries the energy landscape and tests the network performance. Next, the network is retrained with an updated training set that includes failed configurations/energies from previous iteration until convergence is attained. Once trained, we generate an extensive test set of ~100,000 configurations sampled across clusters ranging from 1 to 200 molecules and demonstrate that the trained network adequately reproduces the energies (within mean absolute error (MAE) of ~ 2 meV/molecule) and forces (MAE ~ 40 meV/{\r{A}}) compared to the reference model. More importantly, the trained ANN model also accurately captures both the structure as well as the free energy as a function of the various cluster sizes. Overall, this study reports a new active learning scheme with promising strategy to develop accurate force-fields for molecular simulations using extremely sparse training data sets.