Comparing machine learning potentials for water: Kernel-based regression and Behler-Parrinello neural networks

TL;DR

This study compares kernel-based regression and Behler-Parrinello neural networks in predicting water's thermodynamic properties, highlighting the importance of database quality and comprehensive testing over fitting method differences.

Contribution

It provides a systematic comparison of two machine learning potentials for water, emphasizing the role of training data quality and advocating for multiple models to ensure reliable predictions.

Findings

High agreement between MLPs on key observables.

Training dataset size significantly impacts accuracy.

Limitations of RMS errors highlighted, advocating comprehensive testing.

Abstract

In this paper we investigate the performance of different machine learning potentials (MLPs) in predicting key thermodynamic properties of water using RPBE+D3. Specifically, we scrutinize kernel-based regression and high-dimensional neural networks trained on a highly accurate dataset consisting of about 1,500 structures, as well as a smaller data set, about half the size, obtained using only on-the-fly learning. The study reveals that despite minor differences between the MLPs, their agreement on observables such as the diffusion constant and pair-correlation functions is excellent, especially for the large training dataset. Variations in the predicted density isobars, albeit somewhat larger, are also acceptable, particularly given the errors inherent to approximate density functional theory. Overall, the study emphasizes the relevance of the database over the fitting method. Finally, the study underscores the limitations of root mean square errors and the need for comprehensive testing, advocating the use of multiple MLPs for enhanced certainty, particularly when simulating complex thermodynamic properties that may not be fully captured by simpler tests.