Volume 28, Issue 5
Random Batch Algorithms for Quantum Monte Carlo Simulations

Shi JinXiantao Li

Commun. Comput. Phys., 28 (2020), pp. 1907-1936.

Published online: 2020-11

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  • Abstract

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.

  • Keywords

Quantum Monte Carlo method, random batch methods, Langevin equation.

  • AMS Subject Headings

65C05, 81Q05, 82C31

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-28-1907, author = {Jin , Shi and Li , Xiantao}, title = {Random Batch Algorithms for Quantum Monte Carlo Simulations}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {5}, pages = {1907--1936}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0168}, url = {http://global-sci.org/intro/article_detail/cicp/18400.html} }
TY - JOUR T1 - Random Batch Algorithms for Quantum Monte Carlo Simulations AU - Jin , Shi AU - Li , Xiantao JO - Communications in Computational Physics VL - 5 SP - 1907 EP - 1936 PY - 2020 DA - 2020/11 SN - 28 DO - http://doi.org/10.4208/cicp.OA-2020-0168 UR - https://global-sci.org/intro/article_detail/cicp/18400.html KW - Quantum Monte Carlo method, random batch methods, Langevin equation. AB -

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.

Shi Jin & Xiantao Li. (2020). Random Batch Algorithms for Quantum Monte Carlo Simulations. Communications in Computational Physics. 28 (5). 1907-1936. doi:10.4208/cicp.OA-2020-0168
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