A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions

Neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce highly accurate results for the electronic structure of atoms and small molecules, but the high cost of optimizing such wavefunctions prevents their application to larger systems. We propose th...

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Bibliographic Details
Published in:	Journal of computational physics Vol. 516; p. 113351
Main Authors:	Goldshlager, Gil, Abrahamsen, Nilin, Lin, Lin
Format:	Journal Article
Language:	English
Published:	United States Elsevier Inc 01.11.2024 Elsevier
ISSN:	0021-9991
Online Access:	Get full text
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Summary:	Neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce highly accurate results for the electronic structure of atoms and small molecules, but the high cost of optimizing such wavefunctions prevents their application to larger systems. We propose the Subsampled Projected-Increment Natural Gradient Descent (SPRING) optimizer to reduce this bottleneck. SPRING combines ideas from the recently introduced minimum-step stochastic reconfiguration optimizer (MinSR) and the classical randomized Kaczmarz method for solving linear least-squares problems. We demonstrate that SPRING outperforms both MinSR and the popular Kronecker-Factored Approximate Curvature method (KFAC) across a number of small atoms and molecules, given that the learning rates of all methods are optimally tuned. For example, on the oxygen atom, SPRING attains chemical accuracy after forty thousand training iterations, whereas both MinSR and KFAC fail to do so even after one hundred thousand iterations. •SPRING algorithm accelerates the optimization of neural network wavefunctions.•Enables faster and more accurate variational Monte Carlo simulations.•Outperforms KFAC and MinSR when learning rates are tuned optimally.•Easy to implement and incorporate into any codebase.
Bibliography:	USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) USDOE AC02-05CH11231; SC0023112
ISSN:	0021-9991
DOI:	10.1016/j.jcp.2024.113351