Stochastic Reconfiguration with Warm-Started SVD
Dexuan Zhou, Huajie Chen, Cheuk Hin Ho, Xin Liu, Christoph Ortner
TL;DR
The paper tackles the computational bottleneck of stochastic reconfiguration in variational Monte Carlo by introducing Warm-Started Stochastic Reconfiguration (WSSR), which leverages warm-started SVD and a low-rank, averaged S-matrix to precondition gradients efficiently. By maintaining history through reduced representations and adaptively selecting rank, WSSR achieves convergence comparable to state-of-the-art SR methods while reducing per-update costs. Numerical experiments on atomic and molecular systems using ACE wavefunctions demonstrate both stable optimization and significant efficiency gains. This approach enhances the scalability of VMC with deep learning wavefunctions, enabling more tractable ground-state calculations for large parameter spaces.
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.