论文标题
深层蒙特卡洛中的固定节点极限的收敛
Convergence to the fixed-node limit in deep variational Monte Carlo
论文作者
论文摘要
变异量子蒙特卡洛（QMC）是一种用于求解原则上准确但受到实践中可用ansatzes的灵活性的电子schrödinger方程的Ab-Initio方法。最近引入的深度QMC方法，特别是两个深神经网络Ansatzes Paulinet和Ferminet，使变异QMC达到扩散QMC的准确性，但几乎没有理解有关此类Ansatzes的收敛行为。在这里，我们分析了深层QMC如何随着网络尺寸的增加接近固定节点限制。首先，我们证明了深层神经网络可以克服小基础集的局限性并达到平均田间完整基础限制。然后，转到电子相关性，我们对LIH和H $ _4 $的深jastrow系数进行了广泛的高参数扫描，并发现可以通过足够大的网络获得固定节点极限的变异能量。 Finally, we benchmark mean-field and many-body ansatzes on H$_2$O, increasing the fraction of recovered fixed-node correlation energy of single-determinant Slater--Jastrow-type ansatzes by half an order of magnitude compared to previous variational QMC results and demonstrate that a single-determinant Slater--Jastrow--backflow version of the ansatz overcomes the fixed-node限制。与在各个理论层面上的传统试验波函数相比，该分析有助于理解深度变异ansatzes的出色准确性，并将指导深QMC中神经网络体系结构的未来改进。
Variational quantum Monte Carlo (QMC) is an ab-initio method for solving the electronic Schrödinger equation that is exact in principle, but limited by the flexibility of the available ansatzes in practice. The recently introduced deep QMC approach, specifically two deep-neural-network ansatzes PauliNet and FermiNet, allows variational QMC to reach the accuracy of diffusion QMC, but little is understood about the convergence behavior of such ansatzes. Here, we analyze how deep variational QMC approaches the fixed-node limit with increasing network size. First, we demonstrate that a deep neural network can overcome the limitations of a small basis set and reach the mean-field complete-basis-set limit. Moving to electron correlation, we then perform an extensive hyperparameter scan of a deep Jastrow factor for LiH and H$_4$ and find that variational energies at the fixed-node limit can be obtained with a sufficiently large network. Finally, we benchmark mean-field and many-body ansatzes on H$_2$O, increasing the fraction of recovered fixed-node correlation energy of single-determinant Slater--Jastrow-type ansatzes by half an order of magnitude compared to previous variational QMC results and demonstrate that a single-determinant Slater--Jastrow--backflow version of the ansatz overcomes the fixed-node limitations. This analysis helps understanding the superb accuracy of deep variational ansatzes in comparison to the traditional trial wavefunctions at the respective level of theory, and will guide future improvements of the neural network architectures in deep QMC.
