Permutationally invariant polynomial regression for energies and gradients, using reverse differentiation, achieves orders of magnitude speed-up with high precision compared to other machine learning methods

TL;DR

This paper introduces a highly efficient permutationally invariant polynomial regression method with reverse differentiation, achieving 10 to 1000 times faster energy and gradient evaluations with high accuracy, enabling improved molecular simulations.

Contribution

The authors develop a reverse gradient approach for PIP regression, significantly accelerating gradient calculations and improving the efficiency of potential energy surface fitting.

Findings

PIP method achieves comparable accuracy to other ML methods.

Gradient evaluation speed is increased by 10 to 1000 times.

New ethanol PES enables successful Diffusion Monte Carlo simulations.

Abstract

Permutationally invariant polynomial (PIP) regression has been used to obtain machine-learned (ML) potential energy surfaces, including analytical gradients, for many molecules and chemical reactions. Recently, the approach has been extended to moderate size molecules and applied to systems up to 15 atoms. The algorithm, including "purification of the basis", is computationally efficient for energies; however, we found that the recent extension to obtain analytical gradients, despite being a remarkable advance over previous methods, could be further improved. Here we report developments to compact further a purified basis and, more significantly, to use the reverse gradient approach to greatly speed up gradient evaluation. We demonstrate this for our recent 4-body water interaction potential. Comparisons of training and testing precision on the MD17 database of energies and gradients (forces) for ethanol against GP-SOAP, ANI, sGDML, PhysNet, pKREG, KRR, and other methods, which were recently assessed by Dral and co-workers, are given. The PIP fits are as precise as those using these methods, but the PIP computation time for energy and force evaluation is shown to be 10 to 1000 times faster. Finally, a new PIP PES is reported for ethanol based on a more extensive dataset of energies and gradients than in the MD17 database. Diffusion Monte Carlo calculations which fail on MD17-based PESs are successful using the new PES.