Stochastic potential switching algorithm for Monte Carlo simulations of complex systems

Mak, C. H.

doi:10.1063/1.1925273

Cited by 30 publications

(33 citation statements)

References 27 publications

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“…15,16) We hereafter consider a lattice system with pairwise long-range interactions described by the Hamiltonian…”

Section: Stochastic Cutoff (Sco) Methodsmentioning

confidence: 99%

“…15,16) To our knowledge, this is the first method for general long-range interacting systems that greatly reduces computational time without any approximation. This method is applicable to any lattice system with long-range interactions.…”

Section: Conclusion Remarksmentioning

confidence: 99%

“…In this method, we stochastically switch long-range interactions V ij to either zero or a pseudointeractionV ij by use of the stochastic potential switching algorithm. 15,16) Then the system is mapped on that with onlyV ij . The potential switching is performed every several steps.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Cutoff Method for Long-Range Interacting Systems

Sasaki

Matsubara

2008

J. Phys. Soc. Jpn.

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“…15,16) We hereafter consider a lattice system with pairwise long-range interactions described by the Hamiltonian…”

Section: Stochastic Cutoff (Sco) Methodsmentioning

confidence: 99%

Section: Conclusion Remarksmentioning

confidence: 99%

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Stochastic Cutoff Method for Long-Range Interacting Systems

Sasaki

Matsubara

2008

J. Phys. Soc. Jpn.

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“…Moreover, [14] have shown that the algorithm's performance depends on the tightness of the bound; it only achieves significant gains when computational light and tight bounds are applicable. The idea of using lower bounds to reduce the cost of MCMC has been exploited previously in [24]; [11] (Section 4.3) propose construction of the lower bound that avoids specifying a resampling fraction, but it requires the integrals of the exponents of the lower bound functions to be tractable.…”

Section: Custom-precision Firefly Mcmc (Cf-mcmc)mentioning

confidence: 99%

An Unbiased MCMC FPGA-Based Accelerator in the Land of Custom Precision Arithmetic

Liu

Mingas

Bouganis

2017

IEEE Trans. Comput.

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Abstract-Markov Chain Monte Carlo (MCMC) based methods have been the main tool used for Bayesian Inference by practitioners and researchers due to their flexibility and theoretical properties that guarantee unbiased sampling-based estimates. Nevertheless, with the availability of large data sets and the constant need to develop more complex models that better capture the targeted problem, significant computational challenges have been presented. Current approaches, based on multi-core CPUs, GPUs, and FPGAs, aim to accelerate the execution time of the MCMC methods using subsampling techniques or custom precision arithmetic, resulting to biased estimates. In this work, a novel FPGA-based construction is proposed that utilises the custom precision support of FPGA devices in order to accelerate the computations, guaranteeing at the same time asymptotically unbiased estimates. Key to this approach is the extension of the parameter space by an extra parameter that indicates the required precision in the computation of the likelihood of a data point. The work proposes an FPGA architecture for the above algorithm, as well as discuss its tuning for maximising the performance of the system. The performance of the FPGA-mapped sampler is evaluated using two Bayesian logistic regression case studies of varying complexity, which show significant speedups compared to existing FPGA-and CPU-based works that utilise double floating point arithmetic, without any bias on the sampling-based estimates.

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“…13,14) The switching probability to 0 and that toV ij are P ij and 1 − P ij , respectively. Since the pseudointeractionV ij and switching probability P ij are chosen properly in the SPS algorithm, the SCO method strictly satisfies the detailed balance condition concerning the original Hamiltonian.…”

Section: )mentioning

confidence: 99%

An Efficient Monte-Carlo Method for Calculating Free Energy in Long-Range Interacting Systems

Watanabe

Sasaki

2011

J. Phys. Soc. Jpn.

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We present an efficient Monte-Carlo method for long-range interacting systems to calculate free energy as a function of an order parameter. In this method, a variant of the Wang-Landau method regarding the order parameter is combined with the stochastic cutoff method, which has recently been developed for long-range interacting systems. This method enables us to calculate free energy in long-range interacting systems with reasonable computational time despite the fact that no approximation is involved. This method is applied to a three-dimensional magnetic dipolar system to measure free energy as a function of magnetization. By using the present method, we can calculate free energy for a large system size of 16 3 spins despite the presence of long-range magnetic dipolar interactions. We also discuss the merits and demerits of the present method in comparison with the conventional Wang-Landau method in which free energy is calculated from the joint density of states of energy and order parameter.KEYWORDS: Monte Carlo, long-range interacting system, Wang-Landau method, free energy measurement, magnetic dipolar systemIn general, Monte Carlo (MC) simulations in longrange interacting systems are much more difficult than those in short-range interacting systems because we have to take a large number of interactions into consideration. For example, in the case of systems with pairwise interactions, the number of interactions is proportional to N 2 , where N is the number of elements of the system. Therefore, if a naive MC simulation is carried out in such systems, the computational time per MC step rapidly increases in proportion to N 2 , which is in contrast to that in the case of short-range interacting systems in which the computational time increases in proportion to N . In order to overcome this difficulty, many simulation methods have been proposed. 1-11)Recently, one of the authors and Matsubara have developed an efficient MC method called the stochastic cutoff (SCO) method for long-range interacting systems. 12)In the SCO method, each of the pairwise interactions V ij is stochastically switched to either 0 or a pseudointeractionV ij by the stochastic potential switching (SPS) algorithm. 13,14) The switching probability to 0 and that toV ij are P ij and 1 − P ij , respectively. Since the pseudointeractionV ij and switching probability P ij are chosen properly in the SPS algorithm, the SCO method strictly satisfies the detailed balance condition concerning the original Hamiltonian. [13][14][15] This means that the SCO method does not involve any approximation. Furthermore, since most of the distant and weak interactions are switched to 0 and an efficient method to switch potentials has been developed, 12) the SCO method enables us to reduce the computational time of long-range interactions markedly. For example, in the case of threedimensional dipolar systems, to which our new method will be applied later, the computational time is reduced from O(N 2 ) to O(N log N ) by the SCO method. 12) We can measure internal...

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Stochastic potential switching algorithm for Monte Carlo simulations of complex systems

Cited by 30 publications

References 27 publications

Stochastic Cutoff Method for Long-Range Interacting Systems

Stochastic Cutoff Method for Long-Range Interacting Systems

An Unbiased MCMC FPGA-Based Accelerator in the Land of Custom Precision Arithmetic

An Efficient Monte-Carlo Method for Calculating Free Energy in Long-Range Interacting Systems

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