A Kernel-based Machine Learning Approach to Computing Quasiparticle Energies within Many-Body Green's Functions Theory

TL;DR

This paper introduces a machine learning approach combining Kernel Ridge Regression and Genetic Algorithms to efficiently compute quasiparticle energies in many-body Green's functions theory, significantly reducing computational cost while maintaining accuracy.

Contribution

The authors develop a novel KRR-GA method that transforms the quasiparticle energy calculation into a global optimization problem, improving efficiency and physical relevance.

Findings

Achieves less than 0.01 eV accuracy compared to standard methods.

Reduces the number of self-energy evaluations by about ten times.

Successfully applied to challenging molecules from the GW100 dataset.

Abstract

We present a Kernel Ridge Regression (KRR) based supervised learning method combined with Genetic Algorithms (GAs) for the calculation of quasiparticle energies within Many-Body Green's Functions Theory. These energies representing electronic excitations of a material are solutions to a set of non-linear equations, containing the electron self-energy (SE) in the $GW$ approximation. Due to the frequency-dependence of this SE, standard approaches are computationally expensive and may yield non-physical solutions, in particular for larger systems. In our proposed model, we use KRR as a self-adaptive surrogate model which reduces the number of explicit calculations of the SE. Transforming the standard fixed-point problem of finding quasiparticle energies into a global optimization problem with a suitably defined fitness function, application of the GA yields uniquely the physically relevant solution. We demonstrate the applicability of our method for a set of molecules from the $GW$100 dataset, which are known to exhibit a particularly problematic structure of the SE. Results of the KRR-GA model agree within less than 0.01 eV with the reference standard implementation, while reducing the number of required SE evaluations roughly by a factor of ten.