Variational Monte Carlo (VMC) is an approach for computing ground-state wavefunctions that has recently become more powerful due to the introduction of neural network-based wavefunction parametrizations. However, efficiently training neural wavefunctions to converge to an energy minimum remains a difficult problem. In this work, we analyze optimization and sampling methods used in VMC and introduce alterations to improve their performance. First, based on theoretical convergence analysis in a noiseless setting, we motivate a new optimizer that we call the Rayleigh-Gauss-Newton method, which can improve upon gradient descent and natural gradient descent to achieve superlinear convergence at no more than twice the computational cost. Second, in order to realize this favorable comparison in the presence of stochastic noise, we analyze the effect of sampling error on VMC parameter updates and experimentally demonstrate that it can be reduced by the parallel tempering method. In particular, we demonstrate that RGN can be made robust to energy spikes that occur when the sampler moves between metastable regions of configuration space. Finally, putting theory into practice, we apply our enhanced optimization and sampling methods to the transverse-field Ising and XXZ models on large lattices, yielding ground-state energy estimates with remarkably high accuracy after just 200 parameter updates.
翻译:蒙特卡洛(VMC)是计算地面状态波子的一种方法,由于引入以神经网络为基础的波子偏差,这一方法最近变得更加强大。然而,高效地训练神经波子以趋同为最低能量仍然是一个难题。在这项工作中,我们分析VMC所使用的优化和取样方法,并采用修改方法来改进其性能。首先,根据无噪音环境下的理论趋同分析,我们鼓励一种新的优化,即我们称之为RayLeleigh-Gaus-Newton方法,该方法可以改进梯度下降和自然梯度下降,以不超过计算成本的两倍实现超线趋同。第二,为了在出现随机噪音的情况下实现这一有利的比较,我们分析了取样错误对VMC参数更新的影响,并实验性地表明,通过平行的调和调节方法,可以减少这种误差。特别是,我们证明RGN能够对采样器在配置空间的元表区域之间移动时出现的能源涨幅变得强大。最后,将理论化为实践,我们将我们的强化的优化和采样方法应用在高水平的地基值的20年和高纬度的地平纬度模型之后,对高水平进行。