Accelerating Coupled Cluster Calculations with Nonlinear Dynamics and Shallow Machine Learning

TL;DR

This paper introduces a novel approach combining phase space analysis and shallow machine learning to reduce the computational cost of coupled cluster calculations by focusing on key amplitudes and modeling others, maintaining accuracy.

Contribution

It presents a new method that uses phase space analysis and polynomial Kernel Ridge Regression to accelerate coupled cluster computations by reducing dimensionality.

Findings

Significant cluster amplitudes primarily involve valence excitations.

Enslaved amplitudes can be accurately modeled using supervised machine learning.

The proposed scheme drastically reduces computational time without losing accuracy.

Abstract

The dynamics associated with the time series of the iteration scheme of coupled cluster theory has been analysed. The phase space analysis indicates the presence of a few significant cluster amplitudes, mostly involving valence excitations, which dictate the dynamics, while all other amplitudes are enslaved. Starting with a few initial iterations to establish the inter-relationship among the cluster amplitudes, a supervised Machine Learning scheme with polynomial Kernel Ridge Regression model has been employed to express each of the enslaved variables uniquely in terms of the master amplitudes. The subsequent coupled cluster iterations are restricted to a reduced dimension only to determine those significant excitations, and the enslaved variables are determined through the already established functional mapping. We will show that our scheme leads to tremendous reduction in computational time without sacrificing the accuracy.