Configuration Interaction Guided Sampling with Interpretable Restricted Boltzmann Machine

TL;DR

This paper introduces a machine learning approach using a Restricted Boltzmann Machine to efficiently identify significant configurations in quantum chemistry, achieving high accuracy with fewer determinants and providing interpretable insights into electron distributions.

Contribution

It presents a novel RBM-guided sampling method with a taboo list to improve efficiency and interpretability in configuration interaction calculations.

Findings

Achieves up to 99.99% of correlation energy with significantly fewer determinants.

Reduces computational cost by up to four orders of magnitude compared to full CI.

Learns electron distribution patterns that resemble Radial Distribution Functions.

Abstract

We propose a data-driven approach using a Restricted Boltzmann Machine (RBM) to solve the Schr\"odinger equation in configuration space. Traditional Configuration Interaction (CI) methods construct the wavefunction as a linear combination of Slater determinants, but this becomes computationally expensive due to the factorial growth in the number of configurations. Our approach extends the use of a generative model such as the RBM by incorporating a taboo list strategy to enhance efficiency and convergence. The RBM is used to efficiently identify and sample the most significant determinants, thus accelerating convergence and substantially reducing computational cost. This method achieves up to 99.99% of the correlation energy while using up to four orders of magnitude fewer determinants compared to full CI calculations and up to two orders of magnitude fewer than previous state of the art methods. Beyond efficiency, our analysis reveals that the RBM learns electron distributions over molecular orbitals by capturing quantum patterns that resemble Radial Distribution Functions (RDFs) linked to molecular bonding. This suggests that the learned pattern is interpretable, highlighting the potential of machine learning for explainable quantum chemistry