Random sampling versus active learning algorithms for machine learning potentials of quantum liquid water

TL;DR

This study compares random sampling and active learning for training neural network potentials of quantum liquid water, finding that random sampling often yields smaller test errors and that the training process is robust to the data selection method.

Contribution

It demonstrates that random sampling can outperform active learning in certain contexts for training machine learning potentials of quantum water.

Findings

Random sampling leads to smaller test errors than active learning at the same data set size.

All trained models accurately reproduce structural properties of quantum liquid water.

A small initial data set is crucial for effective active learning to avoid exploring irrelevant configurations.

Abstract

Training accurate machine learning potentials requires electronic structure data comprehensively covering the configurational space of the system of interest. As the construction of this data is computationally demanding, many schemes for identifying the most important structures have been proposed. Here, we compare the performance of high-dimensional neural network potentials (HDNNPs) for quantum liquid water at ambient conditions trained to data sets constructed using random sampling as well as various flavors of active learning based on query by committee. Contrary to the common understanding of active learning, we find that for a given data set size, random sampling leads to smaller test errors for structures not included in the training process. In our analysis we show that this can be related to small energy offsets caused by a bias in structures added in active learning, which can be overcome by using instead energy correlations as an error measure that is invariant to such shifts. Still, all HDNNPs yield very similar and accurate structural properties of quantum liquid water, which demonstrates the robustness of the training procedure with respect to the training set construction algorithm even when trained to as few as 200 structures. However, we find that for active learning based on preliminary potentials, a reasonable initial data set is important to avoid an unnecessary extension of the covered configuration space to less relevant regions.