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Speaker: Hidemaro Suwa (Department of Physics, The University of Tokyo)
Time & Date: 13:00 – 14:00, April 11 (Thr), 2024 (JST)
Place: Hybrid (Room A614, ISSP / Zoom meeting)
Title: Probability control nonreversible Markov chain Monte Carlo
Abstract:
In recent developments, Monte Carlo methods that strategically break
detailed balance to manipulate the flow of probabilities have emerged
[1]. These methods include optimizing the transition probabilities
during state updates. We developed an optimization algorithm designed
to minimize the rejection probability and successfully applied it to
various statistical mechanical models, such as the Potts model and
quantum spin systems [2]. Further, we introduced an algorithm capable
of controlling the rejection rate through a single parameter,
revealing that reducing the rejection rate leads to an exponential
increase in computational efficiency [3]. Another intriguing strategy
for breaking detailed balance is the concept of lifting, which expands
the state space to introduce probability flow in the enlarged state
space. The lifting technique is particularly effective in particle
systems, as demonstrated by the event chain Monte Carlo method [4]. In
this talk, reviewing these approaches to constructing nonreversible
Markov chains, we will present the lifted directed-worm algorithm
[5,6] and the multi-replica swap optimization of the replica exchange
method (namely, parallel tempering). These probability control
nonreversible Markov chains significantly improve the computational
efficiency of Monte Carlo sampling.
[1] H. Suwa and S. Todo, Butsuri 77(11) 731-739 (2022).
[2] H. Suwa and S. Todo, Phys. Rev. Lett. 105, 120603 (2010).
[3] H. Suwa, Physica A 633, 129368 (2024).
[4] W. Krauth, Front. Phys. 9:663457 (2021).
[5] H. Suwa, Phys. Rev. E 103, 013308 (2021).
[6] H. Suwa, Phys. Rev. E 106, 055306 (2022).
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—
Satoshi Morita (森田 悟史)
Graduate School of Science and Technology, Keio University
smorita.github.io/
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