Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions

TL;DR

This paper compares permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in modeling water interactions using many-body expansions, showing similar accuracy levels and highlighting the synergy with physically sound, transferable potentials.

Contribution

It introduces and evaluates three analytical potential energy functions based on different machine learning and polynomial methods within a many-body expansion framework for water.

Findings

All three methods achieve similar accuracy in reproducing reference data.

The methods effectively model two-body and three-body water interactions.

Machine learning techniques complement physically sound many-body potentials.

Abstract

The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enable routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, BPNN-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms.