A sparse-sampling approach for the fast computation of matrices: application to molecular vibrations

TL;DR

This paper introduces a sparse-sampling method leveraging compressed sensing to efficiently compute matrices, significantly accelerating molecular vibration calculations in computational chemistry.

Contribution

The paper presents a novel sparse-sampling approach that reduces computational cost and improves scaling in matrix calculations for molecular vibrations.

Findings

Achieved up to 3x speed-up in molecular vibration computations

Reduced reliance on expensive high-accuracy calculations

Provided a general framework for combining low- and high-accuracy simulations

Abstract

This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes the computational bottleneck. We apply this new method to an important problem in computational chemistry: the determination of molecular vibrations from electronic structure calculations, where our results show that the overall scaling of the procedure can be improved in some cases. Moreover, our method provides a general framework for bootstrapping cheap low-accuracy calculations in order to reduce the required number of expensive high-accuracy calculations, resulting in a significant 3x speed-up in actual calculations.