Effective Many-body Interactions in Reduced-Dimensionality Spaces Through Neural Network Models

TL;DR

This paper presents a neural network framework that reduces computational costs in many-body quantum chemistry calculations by efficiently modeling downfolded Hamiltonians, enabling accurate predictions across different molecular geometries.

Contribution

It introduces a combined approach integrating active-space coupled cluster downfolded Hamiltonians with neural networks to efficiently approximate complex many-body interactions.

Findings

Neural networks can accurately interpolate and extrapolate effective Hamiltonians for different molecular geometries.

The approach reduces the computational overhead of evaluating multidimensional tensor contractions.

Demonstrated on small molecules like H2O and HF, showing promising results for larger systems.

Abstract

Accurately describing properties of challenging problems in physical sciences often requires complex mathematical models that are unmanageable to tackle head-on. Therefore, developing reduced dimensionality representations that encapsulate complex correlation effects in many-body systems is crucial to advance the understanding of these complicated problems. However, a numerical evaluation of these predictive models can still be associated with a significant computational overhead. To address this challenge, in this paper, we discuss a combined framework that integrates recent advances in the development of active-space representations of coupled cluster (CC) downfolded Hamiltonians with neural network approaches. The primary objective of this effort is to train neural networks to eliminate the computationally expensive steps required for evaluating hundreds or thousands of Hugenholtz diagrams, which correspond to multidimensional tensor contractions necessary for evaluating a many-body form of downfolded/effective Hamiltonians. Using small molecular systems (the H2O and HF molecules) as examples, we demonstrate that training neural networks employing effective Hamiltonians for a few nuclear geometries of molecules can accurately interpolate/ extrapolate their forms to other geometrical configurations characterized by different intensities of correlation effects. We also discuss differences between effective interactions that define CC downfolded Hamiltonians with those of bare Hamiltonians defined by Coulomb interactions in the active spaces.