Random Batch Algorithms for Quantum Monte Carlo simulations
Random Batch Algorithms for Quantum Monte Carlo simulations
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DOI：
10.4208/cicp.oa-2020-0168
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发表时间：
2020-06
期刊：
影响因子：
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通讯作者：
Shi Jin;Xiantao Li
中科院分区：
文献类型：
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作者：
Shi Jin;Xiantao Li
随机批量算法是为量子蒙特卡罗模拟构建的。主要目标是减轻与二体相互作用计算相关的计算成本，包括势能中的成对相互作用以及贾斯特罗因子中的二体项。在变分蒙特卡罗方法的框架下，基于过阻尼朗之万动力学构建随机批量算法，因此更新$N$粒子系统中每个粒子的位置仅需要$\mathcal{O}(1)$操作，因此对于每个时间步，$N$粒子的计算成本从$\mathcal{O}(N^2)$减少到$\mathcal{O}(N)$。对于扩散蒙特卡罗方法，随机批量算法使用能量分解来避免分支步骤中总能量的计算。使用与石墨表面相互作用的液体 ${}^4$He 原子系统证明了随机批量方法的有效性。
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.