A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions
This work addresses a bottleneck in applying neural network wavefunctions to larger atomic and molecular systems, representing an incremental improvement over existing optimization methods.
The paper tackles the high computational cost of optimizing neural network wavefunctions for electronic structure calculations by proposing the SPRING optimizer, which reduces training iterations needed for chemical accuracy, achieving it in 40,000 iterations on the oxygen atom compared to over 100,000 for baseline methods.
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.