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

Abstract

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.

Final proof for Journal of Computational Physics

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Cited by in corpus (8)

• Ground state phases of the two-dimension electron gas with a unified variational approach
• Second-order optimisation strategies for neural network quantum states
• Design principles of deep translationally-symmetric neural quantum states for frustrated magnets
• Improving neural network performance for solving quantum sign structure
• Simple Fermionic backflow states via a systematically improvable tensor decomposition
• Expressivity of determinantal ansatzes for neural network wave functions
• Assessing Orbital Optimization in Variational and Diffusion Monte Carlo
• Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithm