Mathematical understanding of detailed balance condition violation and its application to Langevin dynamics

8th STATPHYS-KOLKATA

Ohzeki, Masayuki^1 ; Ichiki, Akihisa^2

Department of Systems Science, Graduate School of Informatics, Kyoto University, 36-1 Yoshida Hon-machi, Sakyo-ku, Kyoto

606-8501, Japan^1

Green Mobility Collaborative Research Center, Nagoya University, Fro-cho, Nagoya

464-8603, Japan^2

关键词: Artificial forces;    Correlation time;    Detailed balance;    Efficient sampling;    ITS applications;    Langevin dynamics;    Numerical implementation;    Transition probabilities;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/638/1/012003/pdf
DOI  :  10.1088/1742-6596/638/1/012003

来源: IOP

【 摘 要 】

We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined distribution such as the Gibbs- Boltzmann one is performed under the detailed balance condition. In the present study, we propose a modified Langevin dynamics violating the detailed balance condition on the transition- probability formulation. We confirm that the numerical implementation of the proposed method actually demonstrates two major beneficial improvements: acceleration of the relaxation to the predetermined distribution and reduction of the correlation time between two different realizations in the steady state.