Tensor Hypercontraction Error Correction Using Regression

TL;DR

This paper introduces machine learning-based error correction for tensor hypercontraction approximations in quantum chemistry, significantly improving the accuracy of THC-approximated MP3 energies.

Contribution

It demonstrates the use of regression models to correct THC errors in MP3 calculations, enhancing accuracy for molecular and reaction energies.

Findings

Non-linear regression models reduce RMS errors 6-9 times for total energies.

Regression improves THC-MP3 accuracy, approaching canonical MP3 results.

Method shows promise for scalable, accurate quantum chemical calculations.

Abstract

Wavefunction-based quantum methods are some of the most accurate tools for predicting and analyzing the electronic structure of molecules, in particular for accounting for dynamical electron correlation. However, most methods of including dynamical correlation beyond the simple second-order M{\o}ller-Plesset perturbation theory (MP2) level are too computationally expensive to apply to large molecules. Approximations which reduce scaling with system size are a potential remedy, such as the tensor hyper-contraction (THC) technique of Hohenstein et al., but also result in additional sources of error. In this work, we correct errors in THC-approximated methods using machine learning. Specifically, we apply THC to third-order M{\o}ller-Plesset theory (MP3) as a simplified model for coupled cluster with single and double excitations (CCSD), and train several regression models on observed THC errors from the Main Group Chemistry Database (MGCDB84). We compare performance of multiple linear regression models and non-linear Kernel Ridge regression models. We also investigate correlation procedures using absolute and relative corrections and evaluate the corrections for both molecule and reaction energies. We discuss the potential for using regression techniques to correct THC-MP3 errors by comparing it to the "canonical" MP3 reference values and find the optimum technique based on accuracy. We find that non-linear regression models reduced root mean squared errors between THC- and canonical MP3 by a factor of 6-9$\times$ for total molecular energies and 2-3$\times$ for reaction energies.