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.

翻译：利用变分蒙特卡洛方法优化的神经网络波函数已被证明能够为原子和小分子电子结构提供高精度结果，但此类波函数的高昂优化成本阻碍了其在更大系统中的应用。我们提出子采样投影增量自然梯度下降（SPRING）优化器以减少这一瓶颈。SPRING结合了近期提出的最小步长随机重配置优化器（MinSR）与经典随机Kaczmarz方法求解线性最小二乘问题的思想。实验表明，在多种小原子和小分子体系上，当所有方法的学习率经过最优调参时，SPRING的性能均优于MinSR及流行的克罗内克因子近似曲率方法（KFAC）。以氧原子为例，SPRING在四万次训练迭代后即达到化学精度，而MinSR与KFAC即使经过十万次迭代仍无法实现该精度。