arXiv 2008.129902020-08-29physics.comp-phcs.NAmath.NA

量子蒙特卡罗模拟的随机批处理算法

Random Batch Algorithms for Quantum Monte Carlo simulations

Shi Jin, Xiantao Li

摘要：

构造了量子蒙特卡罗模拟的随机批处理算法。主要目标是减轻与计算两体相互作用相关的计算成本，包括势能中的成对相互作用和Jastrow因子中的两体项。在变分Monte Carlo方法的框架下，基于过阻尼Langevin动力学构造了随机批处理算法，使得$N$ -粒子系统中每个粒子的位置更新只需要$\mathcal{O}(1)$操作，从而使每个时间步的$N$粒子的计算量从$\mathcal{O}(N^2)$减少到$\mathcal{O}(N)$ .对于扩散蒙特卡罗方法，随机批处理算法使用能量分解以避免在分支步骤中计算总能量。使用液体${}^4$ He原子与石墨表面相互作用的系统证明了随机批处理方法的有效性。

英文摘要：

Random batch algorithms are constructed for quantum Monte Carlo simulations. The main objective is to alleviate the computational cost associated with the calculations of two-body interactions, including the pairwise interactions in the potential energy, and the two-body terms in the Jastrow factor. In the framework of variational Monte Carlo methods, the random batch algorithm is constructed based on the over-damped Langevin dynamics, so that updating the position of each particle in an $N$-particle system only requires $\mathcal{O}(1)$ operations, thus for each time step the computational cost for $N$ particles is reduced from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$. For diffusion Monte Carlo methods, the random batch algorithm uses an energy decomposition to avoid the computation of the total energy in the branching step. The effectiveness of the random batch method is demonstrated using a system of liquid ${}^4$He atoms interacting with a graphite surface.

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