论文标题
量子蒙特卡洛模拟的随机批处理算法
Random Batch Algorithms for Quantum Monte Carlo simulations
论文作者
论文摘要
为量子蒙特卡洛模拟构建了随机批次算法。主要目的是减轻与两体相互作用的计算相关的计算成本，包括势能中的成对相互作用以及jastrow因子中的两体项。在变异蒙特卡洛方法的框架中，基于过度抑制的langevin动力学构建随机批次算法，因此更新每个粒子在$ n $ - 零件系统中的位置仅需要$ \ mathcal {o}（o}（o}（o}（o}（1）$ $ \ MATHCAL {O}（N）$。对于扩散的蒙特卡洛方法，随机批处理算法使用能量分解来避免分支步骤中总能量的计算。使用液体$ {}^4 $ He原子与石墨表面相互作用的液体$ {}^4 $ He原子的系统来证明随机批处理方法的有效性。
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.
