Reconfigurable computing for Monte Carlo simulations: results and prospects of the Janus project

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Springer Heidelberg
Google Scholar
Research Projects
Organizational Units
Journal Issue
We describe Janus, a massively parallel FPGA-based computer optimized for the simulation of spin glasses, theoretical models for the behavior of glassy materials. FPGAs (as compared to GPUs or many-core processors) provide a complementary approach to massively parallel computing. In particular, our model problem is formulated in terms of binary variables, and floating-point operations can be (almost) completely avoided. The FPGA architecture allows us to run many independent threads with almost no latencies in memory access, thus updating up to 1024 spins per cycle. We describe Janus in detail and we summarize the physics results obtained in four years of operation of this machine; we discuss two types of physics applications: long simulations on very large systems (which try to mimic and provide understanding about the experimental non equilibrium dynamics), and low-temperature equilibrium simulations using an artificial parallel tempering dynamics. The time scale of our non-equilibrium simulations spans eleven orders of magnitude (from picoseconds to a tenth of a second). On the other hand, our equilibrium simulations are unprecedented both because of the low temperatures reached and for the large systems that we have brought to equilibrium. A finite-time scaling ansatz emerges from the detailed comparison of the two sets of simulations. Janus has made it possible to perform spin glass simulations that would take several decades on more conventional architectures. The paper ends with an assessment of the potential of possible future versions of the Janus architecture, based on state-of-the-art technology.
© EDP Sciences, Springer-Verlag 2012. Artículo firmado por 26 autores. We wish to thank several past members of the Janus Collaboration, F. Belletti, M. Cotallo, D. Sciretti and J.L. Velasco, for their important contributions to the project. Over the years, the Janus project has been supported by the EU (FEDER funds, No. UNZA05-33-003, MEC-DGA, Spain), by the MICINN (Spain) (contracts FIS2006- 08533, FIS2009-12648, FIS2007-60977, FIS2010-16587, FPA2004-02602, TEC2010- 19207), by CAM(Spain), by the Junta de Extremadura (GR10158), by UCM-Banco Santander (GR32/10-A/910383), by the Universidad de Extremadura (ACCVII-08) and by the Microsoft Prize 2007. We thank ETHlab for their technical help. E.M. was supported by the DREAM SEED project and by the Computational Platform of IIT (Italy). M.B.-J. and B.S. were supported by the FPU program (Ministerio de Educación, Spain); R.A.B. and J.M.-G. were supported by the FPI program (Diputación de Aragón, Spain); finally J.M.G.-N. was supported by the FPI program (Ministerio de Ciencia e Innovación, Spain).
Unesco subjects
1. See, for instance: C. A. Angell, Science, 267, (1995) 1924 -- P. G. Debenedetti, Metastable liquids (Princeton University Press, Princeton 1997) -- P. G. Debenedetti, F. H. Stillinger, Nature, 410, (2001) 259. 2. L. C. E. Struick, Physical Aging in Amorphous Polymers and Other Materials (Elsevier, Houston, 1978). 3. J. A. Mydosh, Spin Glasses: an Experimental Introduction (Taylor and Francis, London, 1993). 4. A. P. Young (editor), Spin Glasses and Random Fields (World Scientific, Singapore, 1998). 5. A. D. Ogielski, D. A. Huse, Phys. Rev. Lett., 56, (1986) 1298-1301. 6. P. A. Boyle, et al., IBM J. of Research and Development, 49, (2005) 351-365. 7. F. Belletti, et al., Computing in Science & Engineering, 8, (2006) 18-29. 8. G. Goldrian, et al., Computing in Science & Engineering, 10, (2008) 46-54 -- H. Baier, et al., Computer Science - Research and Development, 25, (2010) 149-154. 9. J. Makino, et al., A 1.349 Tflops Simulation of Black Holes in a Galactic Center on GRAPE-6, Proceedings of the 2000 ACM/IEEE conference on Supercomputing (2000) Article n. 43. 10. J. Pech, et al., Comp. Phys. Comm., 106, (1997) 10-20 -- A. Cruz, et al., Comp. Phys. Comm., 133, (2001) 165-176. 11. S. F. Edwards, P. W. Anderson, J. Phys. F: Metal Phys., 5, (1975) 965-974 -- ibid. 6, (1976) 1927-1937. 12. J. Barahona., J. Phys. A: Math. Gen., 15, (1982) 3241-3253. 13. M. Mézard, G. Parisi, M. Virasoro, Spin-Glass Theory and Beyond, (World Scientific, Singapore, 1987). 14. M. Mézard, G. Parisi, R. Zecchina, Science, 297, (2002) 812-815 -- R. Zecchina, Statistical Mechanics and Combinatorial Problems in Encyclopedia of Mathematical Physics, J. -P. Fran¸coise, G. L. Naber and T. S. Tsun (eds.) (Elsevier, Oxford, 2006). 15. K. Gunnarsson, et al., Phys. Rev. B, 43, (1991) 8199-8203. See also P. Norblad and P. Svendlidh Experiments on Spin-Glasses in [4]. 16. H. G. Ballesteros, et al., Phys. Rev. B, 62, (2000) 14237-14245. 17. F. Bert, et al., Phys. Rev. Lett., 92, (2004) 167203. 18. See for instance D. J. Amit and V. Martín-Mayor, Field Theory, the Renormalization Group and Critical Phenomena, (World Scientific, Singapore, 3rd edition, 2005). 19. M. E. J. Newman, G. Barkema, Monte Carlo Methods in Statistical Physics (Oxford University Press, 1999). 20. H. Hukushima, K. Nemoto, J. Phys. Soc. Japan, 65, (1996) 1604 -- E. Marinari, in Advances in Computer Simulation, J. Kerstéz, I. Kondor (eds.) (Springer-Verlag, 1998). 21. H.G. Katzgraber, Introduction to Monte Carlo methods, lecture at Modern Computation Science, (Oldenburg, 2009). 22. F. Belletti, et al., Comp. Phys. Comm., 178, (2008) 208-216. 23. F. Belletti, et al., IANUS: Scientific Computing on an FPGA-based Architecture, in Proceedings of ParCo2007, Parallel Computing: Architectures, Algorithms and Applications (NIC Series Vol. 38, 2007) 553-560. 24. F. Belletti, et al., Computing in Science & Engineering, 8, (2006) 41-49. 25. F. Belletti, et al., Computing in Science & Engineering, 11, (2009) 48-58. 26. V. Parisi, cited in G. Parisi and F. Rapuano, Phys. Lett. B, 157, (1985) 301-302. 27. H. G. Ballesteros, V. Martín-Mayor, Phys.Rev.E, 58 (1998) 6787-6791. 28. P. Contucci, C. Giardinà, C. Giberti, G. Parisi, C. Vernia, Phys. Rev. Lett, 99 (2007) 057206. 29. S. Jiménez, V. Martín-Mayor, G. Parisi, A. Tarancón, J. Phys. A: Math. and Gen, 36, (2003) 10755-10771. 30. F. Belletti, et al., Phys. Rev. Lett., 101, (2008) 157201. 31. F. Belletti, et al., J. Stat. Phys., 135, (2009) 1121-1158. 32. L. A. Fernández, et al., Phys. Rev. B, 80, (2009) 024422. 33. R. A. Baños, et al., J. Stat. Mech., (2010) P06026. 34. R. A. Baños, et al., Phys. Rev. B, 84, (2011) 174209. 35. A. Billoire, et al., J. Stat. Mech, (2011) P10019. 36. R. A. Baños, et al., Phys. Rev. Lett., 105, (2010) 177202. 37. M. Mézard, G. Parisi, M.A. Virasoro, Spin Glass Theory and Beyond (World Scientifi, Singapore, 1987). 38. D.S. Fisher, D.A. Huse, Phys. Rev. Lett., 56, (1986) 1601 -- ibid, Phys. Rev. B, 38, (1988) 373 -- ibid, Phys. Rev. B, 38, (1988) 386. 39. F. Krzakala, O. C. Martin, Phys. Rev. Lett., 85, (2000) 3013 -- M. Palassini, A.P.Young, Phys. Rev. Lett., 85, (2000) 3017. 40. J. R. L. de Almeida, D. J. Thouless, J. Phys. A, 11, (1978) 983. 41. R. A. Baños, et al., Proc. Natl. Acad. Sci. USA, (in press) (2012) doi:10.1073/pnas.1203295109. Preprint arXiv:1202.5593. 42. D. J. Gross, I. Kanter, H. Sompolinsky, Phys. Rev. Lett., 55, (1985) 304-307. 43. A. Cruz, et al. Phys. Rev. B, 79, (2009) 184408. 44. R. A. Baños, et al., J. Stat. Mech., (2010) P05002. 45. J.T. Chayes, L. Chayes, D.S. Fischer, T. Spencer, Phys. Rev. Lett., 57, (1986) 2999 -- A. Maiorano, V. Martín-Mayor, J.J. Ruiz-Lorenzo, A. Tarancón, Phys. Rev. B, 76, (2007) 064435. 46. M. Guidetti, et al., Spin Glass Monte Carlo Simulations on the Cell Broadband Engine in Proc. of PPAM09, (Lecture Notes on Computer Science (LNCS) 6067, Springer 2010) 467-476. 47. M. Guidetti, et al., Monte Carlo Simulations of Spin Systems on Multi-core Processors (Lecture Notes on Computer Science (LNCS) 7133 K. Jonasson (ed.), Springer, Heidelberg 2010) 220-230.