TY - JOUR

T1 - Random batch algorithms for quantum monte carlo simulations

AU - Jin, Shi

AU - Li, Xiantao

N1 - Funding Information:
Jin’s research is partly supported by NSFC grant No. 11871297. Li’s research is supported by NSF under grant DMS-1819011 and DMS-1953120.
Publisher Copyright:
© 2020 Global-Science Press
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/11

Y1 - 2020/11

N2 - 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 O(1) operations, thus for each time step the computational cost for N particles is reduced from O(N2) to 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 4He atoms interacting with a graphite surface.

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 O(1) operations, thus for each time step the computational cost for N particles is reduced from O(N2) to 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 4He atoms interacting with a graphite surface.

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U2 - 10.4208/CICP.OA-2020-0168

DO - 10.4208/CICP.OA-2020-0168

M3 - Article

AN - SCOPUS:85097473446

VL - 28

SP - 1907

EP - 1936

JO - Communications in Computational Physics

JF - Communications in Computational Physics

SN - 1815-2406

IS - 5

ER -