Abstract
Population annealing is a novel Monte Carlo algorithm designed for simulations of systems of statistical mechanics with rugged free-energy landscapes. We discuss a realization of the algorithm for the use on a hybrid computing architecture combining CPUs and GPGPUs. The particular advantage of this approach is that it is fully scalable up to many thousands of threads. We report on applications of the developed realization to several interesting problems, in particular the Ising and Potts models, and review applications of population annealing to further systems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Kitaev, A.Yu.: Fault-tolerant quantum computation by anyons. Annals Phys. 303, 2–30 (2003)
Iba, Y.: Population Monte Carlo algorithms. Trans. Jpn. Soc. Artif. Intell. 16, 279–286 (2001)
Hukushima, K., Iba, Y.: Population annealing and its application to a spin glass. In: AIP Conference Proceedings, vol. 690, pp. 200–206 (2003)
Machta, J.: Population annealing with weighted averages: a Monte Carlo method for rough free-energy landscapes. Phys. Rev. E 82, 026704 (2010)
Weigel, M.: Monte Carlo methods for massively parallel computers. In: Holovatch, Yu. (ed.) Order, Disorder and Criticality, vol. 5, pp. 271–340. World Scientific, Singapore (2018)
Barash, L.Yu., Weigel, M., Borovský, M., Janke, W., Shchur, L.N.: GPU accelerated population annealing algorithm. Comp. Phys. Comm. 220, 341–350 (2017)
Weigel, M., Barash, L.Yu., Shchur, L.N., Janke, W.: Understanding population annealing Monte Carlo simulations (in preparation)
Amey, C., Machta, J.: Analysis and optimization of population annealing. Phys. Rev. E 97, 033301 (2018)
Ferrenberg, A.M., Swendsen, R.H.: Optimized Monte Carlo data analysis. Phys. Rev. Lett. 63, 1195–1198 (1989)
Kumar, S., Bouzida, D., Swendsen, R.H., Kollman, P.A., Rosenberg, J.M.: The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method. J. Comp. Chem. 13, 1011–1021 (1992)
Kumar, S., Rosenberg, J.M., Bouzida, D., Swendsen, R.H., Kollman, P.A.: Mu1tidimensional free-energy calculations using the weighted histogram analysis method. J. Comp. Chem. 16, 1339–1350 (1995)
Code repository for the GPU accelerated PA algorithm is located at: https://github.com/LevBarash/PAising
Weigel, M.: Performance potential for simulating spin models on GPU. J. Comput. Phys. 231, 3064–3082 (2012)
Yavors’kii, T., Weigel, M.: Optimized GPU simulation of continuous-spin glass models. Eur. Phys. J. Special Topics 210, 159–173 (2012)
McCool, M., Reinders, J., Robison, A.: Structured Parallel Programming: Patterns for Efficient Computation. Morgan Kaufman, Waltham (2012)
Salmon, J.K., Moraes, M.A., Dror, R.O., Shaw, D.E.: Parallel random numbers: as easy as 1, 2, 3. In: Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2011, article no. 16. ACM, New York (2011)
Manssen, M., Weigel, M., Hartmann, A.K.: Random number generators for massively parallel simulations on GPU. Eur. Phys. J. Special Topics 210, 53–71 (2012)
Barash, L.Yu., Shchur, L.N.: RNGSSELIB: program library for random number generation, SSE2 realization. Comp. Phys. Comm. 182, 1518–1526 (2011)
Barash, L.Yu., Shchur, L.N.: RNGSSELIB: program library for random number generation. More generators, parallel streams of random numbers and Fortran compatibility. Comp. Phys. Comm. 184, 2367–2369 (2013)
Guskova, M.S., Barash, L.Yu., Shchur, L.N.: RNGAVXLIB: program library for random number generation, AVX realization. Comp. Phys. Comm. 200, 402–405 (2016)
Barash, L.Yu., Shchur, L.N.: PRAND: GPU accelerated parallel random number generation library: using most reliable algorithms and applying parallelism of modern GPUs and CPUs. Comp. Phys. Comm. 185, 1343–1353 (2014)
Kramers, H.A., Wannier, G.H.: Statistics of the two-dimensional ferromagnet. Part I. Phys. Rev. 60, 252–262 (1941)
Onsager, L.: Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev. 65, 117–149 (1944)
Baxter, R.J.: Potts model at the critical temperature. J. Phys. C Solid State Phys. 6, L445–L448 (1973)
Wu, F.Y.: The Potts model. Rev. Mod. Phys. 54, 235–268 (1982). ibid 55, 315 (1983). Erratum
Binder, K., Heermann, D.: Monte Carlo Simulation in Statistical Physics. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-03163-2
Janke, W.: First-order phase transitions. In: Dünweg, B., Landau, D.P., Milchev, A.I. (eds.) Computer Simulations of Surfaces and Interfaces, NATO Science Series, II. Mathematics, Physics and Chemistry, vol. 114, pp. 111–135. Kluwer, Dordrecht (2003)
Borgs, C., Janke, W.: An explicit formula for the interface tension of the 2D Potts model. J. Physique I 2, 2011–2018 (1992)
Barash, L.Yu., Weigel, M., Shchur, L.N., Janke, W.: Exploring first-order phase transitions with population annealing. Eur. Phys. J. Special Topics 226, 595–604 (2017)
Borovský, M., Weigel, M., Barash, L.Yu., Žukovič, M.: GPU-accelerated population annealing algorithm: frustrated Ising antiferromagnet on the stacked triangular lattice. In: EPJ Web of Conferences, vol. 108, p. 02016 (2016)
Wang, W., Machta, J., Katzgraber, H.G.: Comparing Monte Carlo methods for finding ground states of Ising spin glasses: population annealing, simulated annealing, and parallel tempering. Phys. Rev. E 92, 013303 (2015)
Wang, W., Machta, J., Katzgraber, H.G.: Evidence against a mean-field description of short-range spin glasses revealed through thermal boundary conditions. Phys. Rev. B 90, 184412 (2014)
Wang, W., Machta, J., Katzgraber, H.G.: Chaos in spin glasses revealed through thermal boundary conditions. Phys. Rev. B 92, 094410 (2015)
Wang, W., Machta, J., Munoz-Bauza, H., Katzgraber, H.G.: Number of thermodynamic states in the three-dimensional Edwards-Anderson spin glass. Phys. Rev. B 96, 184417 (2017)
Callaham, J., Machta, J.: Population annealing simulations of a binary hard-sphere mixture. Phys. Rev. E 95, 063315 (2017)
Odriozola, G., Berthier, L.: Equilibrium equation of state of a hard sphere binary mixture at very large densities using replica exchange Monte Carlo simulations. J. Chem. Phys. 134, 054504 (2011)
Christiansen, H., Weigel, M., Janke, W.: Population annealing for molecular dynamics simulations of biopolymers. Preprint arXiv:1806.06016
Acknowledgment
This work was partially supported by the grant 14-21-00158 from the Russian Science Foundation and by the Landau Institute for Theoretical Physics in the framework of the tasks from the Federal Agency of Scientific Organizations. The authors acknowledge support from the European Commission through the IRSES network DIONICOS under Contract No. PIRSES-GA-2013-612707.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Shchur, L., Barash, L., Weigel, M., Janke, W. (2019). Population Annealing and Large Scale Simulations in Statistical Mechanics. In: Voevodin, V., Sobolev, S. (eds) Supercomputing. RuSCDays 2018. Communications in Computer and Information Science, vol 965. Springer, Cham. https://doi.org/10.1007/978-3-030-05807-4_30
Download citation
DOI: https://doi.org/10.1007/978-3-030-05807-4_30
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-05806-7
Online ISBN: 978-3-030-05807-4
eBook Packages: Computer ScienceComputer Science (R0)