Accelerating coupled cluster calculations with nonlinear dynamics and supervised machine learning

Abstract

In this paper, the iteration scheme associated with single reference coupled cluster theory has been analyzed using nonlinear dynamics. The phase space analysis indicates the presence of a few significant cluster amplitudes, mostly involving valence excitations, that 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 a polynomial kernel ridge regression model has been employed to express each of the enslaved amplitudes uniquely in terms of the former set of amplitudes. The subsequent coupled cluster iterations are restricted solely to determine those significant excitations, and the enslaved amplitudes are determined through the already established functional mapping. We will show that our hybrid scheme leads to a significant reduction in the computational time without sacrificing the accuracy.

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

“…• The Squared Root Euclidean Distance Matrix (EDM), or what has simply been defined as distance matrix D in our earlier works. 19,22 The elements of the distance matrix D is defined as…”

“…al. 19 Since n L is only a very small fraction even compared to n o n v , this step has a significant reduction in scaling from the usual n 2 o n 4 v of the conventional scheme.…”

“…al. 19 had studied the efficacy of KRR based ML model to represent F . This was studied for a few pilot molecules in their equilibrium and away from equilibrium geometries, and it produced highly accurate energies (of the order of micro-Hartree (µH), compared to the canonical CC calculations).…”

Machine Learning of Coupled Cluster (T)-Energy Corrections via Delta (Δ)-Learning

“…ML-assisted approaches encompass the training of force-fields from ab initio data, prediction of CC amplitudes, and direct energy or property learning using mean-field, correlated, or methods based on density functional theory (DFT) . Using DFT densities, it is possible to predict CC energies by leveraging ML: With an iterative approach, Townsend and Vogiatzis et al were able to predict the converged CC amplitudeshence the CC wave functionby utilizing theoretical properties inherent to Møller–Plesset perturbation theory. , Another iterative hybrid approach by Maitra et al divides the amplitudes into significant and less significant contributions and reduces computational time without loss of accuracy . Often, so-called Δ-learning is employed, in which the objective is not the prediction of the total energy, but rather that of an increment or difference between property values determined at low and high levels of theory .…”

“…10,11 Another iterative hybrid approach by Maitra et al divides the amplitudes into significant and less significant contributions and reduces computational time without loss of accuracy. 12 Often, so-called Δ-learning is employed, in which the objective is not the prediction of the total energy, but rather that of an increment or difference between property values determined at low and high levels of theory. 13 The recent study by Nandi et al presents an example for Δ-learning of potential energy surfaces (PES) from the DFT to the CCSD(T) levels of theory.…”