Gradient domain machine learning with composite kernels: improving the accuracy of PES and force fields for large molecules

TL;DR

This paper enhances gradient domain machine learning models for molecular potential energy surfaces and force fields by introducing composite kernels, leading to improved accuracy with fewer training data for large molecules.

Contribution

It extends GDML with composite kernels optimized via a greedy Bayesian approach, significantly reducing generalization errors for complex molecular systems.

Findings

Composite kernels improve model accuracy.

Models trained on fewer data achieve high precision.

Successful application to large molecules like aspirin.

Abstract

The generalization accuracy of machine learning models of potential energy surfaces (PES) and force fields (FF) for large polyatomic molecules can be generally improved either by increasing the number of training points or by improving the models. In order to build accurate models based on expensive high-level ab initio calculations, much of recent work has focused on the latter. In particular, it has been shown that gradient domain machine learning (GDML) models produce accurate results for high-dimensional molecular systems with a small number of ab initio calculations. The present work extends GDML to models with composite kernels built to maximize inference from a small number of molecular geometries. We illustrate that GDML models can be improved by increasing the complexity of underlying kernels through a greedy search algorithm using Bayesian information criterion as the model selection metric. We show that this requires including anisotropy into kernel functions and produces models with significantly smaller generalization errors. The results are presented for ethanol, uracil, malonaldehyde and aspirin. For aspirin, the model with composite kernels trained by forces at 1000 randomly sampled molecular geometries produces a global 57-dimensional PES with the mean absolute accuracy 0.177 kcal/mol (61.9 cm$^{-1}$) and FFs with the mean absolute error 0.457 kcal/mol {\AA}$^{-1}$.