Stochastic Reconfiguration with Warm-Started SVD

TL;DR

This paper introduces a warm-started stochastic reconfiguration method that leverages SVD techniques to efficiently improve variational Monte Carlo calculations in quantum many-body systems.

Contribution

It proposes a novel WSSR method combining warm-start SVD with stochastic reconfiguration to handle large parameter spaces efficiently.

Findings

WSSR improves convergence in VMC ground-state calculations.

The method reduces computational costs for large covariance matrices.

Numerical experiments demonstrate enhanced accuracy and efficiency.

Abstract

The combination of the variational Monte Carlo (VMC) method with deep learning wave function architectures has led to several successes in ground-state calculations of quantum many-body systems in recent years. However, commonly used stochastic gradient-based methods often perform poorly on these parameter training problems and typically lack convergence guarantees. The stochastic reconfiguration (SR) method provides a robust preconditioner of the stochastic gradient, whose computational cost becomes prohibitive for large parameter spaces owing to the repeated inversion of large covariance matrices. To overcome this bottleneck, we propose a warm-started stochastic reconfiguration (WSSR) method, which integrates warm-start techniques from singular value decomposition (SVD) to refine low-rank approximations of the preconditioning matrix iteratively. Numerical experiments on typical atomic and molecular systems highlight the effectiveness of the WSSR method within VMC calculations.