Assessing the Performance of Nonlinear Regression based Machine Learning Models to Solve Coupled Cluster Theory

TL;DR

This paper introduces a machine learning hybrid approach to coupled cluster theory that uses regression models to efficiently predict auxiliary amplitudes, significantly reducing computational effort while maintaining accuracy.

Contribution

The study presents a novel machine learning-based hybrid scheme that solves for principal amplitudes explicitly and predicts auxiliary amplitudes via regression, enhancing efficiency in quantum chemistry calculations.

Findings

Significant reduction in computation time achieved.

Regression models accurately predict auxiliary amplitudes.

Scheme effective for molecules in various geometries.

Abstract

The iteration dynamics of the coupled cluster equations exhibits a synergistic relationship among the cluster amplitudes. The iteration scheme may be viewed as a multivariate discrete-time propagation of nonlinearly coupled equations, which is dictated by only a few principal cluster amplitudes. These principal amplitudes usually correspond to only a few valence excitations, whereas all other cluster amplitudes are enslaved, and behave as auxiliary variables. Staring with a few trial iterations, we employ a supervised machine learning strategy to establish a mapping of the principal and auxiliary amplitudes. We introduce a machine learning-coupled cluster hybrid scheme where the coupled cluster equations are solved only to determine the principal amplitudes, which saves significant computation time. The auxiliary amplitudes, on the other hand, are determined via regression. Few different regression techniques have been introduced to express the auxiliary amplitudes as functions of the principal amplitudes. The scheme has been applied to several molecules in their equilibrium and stretched geometries, and our scheme, with both the regression models, shows a significant reduction in computation time without unduly sacrificing the accuracy.