Rare event sampling

Rare event sampling is an umbrella term for a group of computer simulation methods intended to selectively sample 'special' regions of the dynamic space of systems which are unlikely to visit those special regions through brute-force simulation. A familiar example of a rare event in this context would be nucleation of a raindrop from over-saturated water vapour: although raindrops form every day, relative to the length and time scales defined by the motion of water molecules in the vapour phase, the formation of a liquid droplet is extremely rare.

Due to the wide use of computer simulation across very different domains, articles on the topic arise from quite disparate sources and it is difficult to make a coherent survey of rare event sampling techniques.[1] Contemporary methods include transition-path sampling (TPS),[2] replica exchange transition interface sampling (RETIS),[3] repetitive simulation trials after reaching thresholds (RESTART),[4] forward flux sampling (FFS),[5][6] generalized splitting,[7][8] adaptive multilevel splitting (AMS),[9] stochastic-process rare-event sampling (SPRES),[10] line sampling,[11] subset simulation,[12] and weighted ensemble (WE).[13][14] The first published rare event technique was by Herman Kahn and Theodore Edward Harris in 1951,[15] who in turn referred to an unpublished technical report by John von Neumann and Stanislaw Ulam.

  1. ^ Morio, J.; Balesdent, M. (2014). "A survey of rare event simulation methods for static input–output models" (PDF). Simulation Modelling Practice and Theory. 49 (4): 287–304. doi:10.1016/j.simpat.2014.10.007.
  2. ^ Cite error: The named reference acj2002 was invoked but never defined (see the help page).
  3. ^ Riccardi, Enrico; Dahlen, Oda; van Erp, Titus S. (2017-09-06). "Fast Decorrelating Monte Carlo Moves for Efficient Path Sampling". The Journal of Physical Chemistry Letters. 8 (18): 4456–4460. doi:10.1021/acs.jpclett.7b01617. hdl:11250/2491276. ISSN 1948-7185. PMID 28857565.
  4. ^ Cite error: The named reference wsc1994 was invoked but never defined (see the help page).
  5. ^ Allen, Rosalind J.; Warren, Patrick B.; ten Wolde, Pieter Rein (2005). "Sampling Rare Switching Events in Biochemical Networks". Physical Review Letters. 94 (1): 018104. arXiv:q-bio/0406006. Bibcode:2005PhRvL..94a8104A. doi:10.1103/PhysRevLett.94.018104. PMID 15698138. S2CID 7998065.
  6. ^ Allen, Rosalind J.; ten Wolde, Pieter Rein; Rein Ten Wolde, Pieter (2009). "Forward flux sampling for rare event simulations". Journal of Physics: Condensed Matter. 21 (46): 463102. arXiv:0906.4758. Bibcode:2009JPCM...21T3102A. doi:10.1088/0953-8984/21/46/463102. PMID 21715864. S2CID 10222109.
  7. ^ Botev, Z. I.; Kroese, D. P. (2008). "Efficient Monte Carlo simulation via the generalized splitting method". Methodology and Computing in Applied Probability. 10 (4): 471–505. CiteSeerX 10.1.1.399.7912. doi:10.1007/s11009-008-9073-7. S2CID 1147040.
  8. ^ Botev, Z. I.; Kroese, D. P. (2012). "Efficient Monte Carlo simulation via the generalized splitting method". Statistics and Computing. 22 (1): 1–16. doi:10.1007/s11222-010-9201-4. S2CID 14970946.
  9. ^ Cerou., Frédéric; Arnaud Guyader (2005). Adaptive multilevel splitting for rare event analysis (Technical report). INRIA. RR-5710.
  10. ^ Berryman, Joshua T.; Schilling, Tanja (2010). "Sampling rare events in nonequilibrium and nonstationary systems". The Journal of Chemical Physics. 133 (24): 244101. arXiv:1001.2456. Bibcode:2010JChPh.133x4101B. doi:10.1063/1.3525099. PMID 21197970. S2CID 34154184.
  11. ^ Schueller, G. I.; Pradlwarter, H. J.; Koutsourelakis, P. (2004). "A critical appraisal of reliability estimation procedures for high dimensions". Probabilistic Engineering Mechanics. 19 (4): 463–474. doi:10.1016/j.probengmech.2004.05.004.
  12. ^ Au, S.K.; Beck, James L. (October 2001). "Estimation of small failure probabilities in high dimensions by subset simulation". Probabilistic Engineering Mechanics. 16 (4): 263–277. CiteSeerX 10.1.1.131.1941. doi:10.1016/S0266-8920(01)00019-4.
  13. ^ Zuckerman, Daniel M.; Chong, Lillian T. (2017-05-22). "Weighted Ensemble Simulation: Review of Methodology, Applications, and Software". Annual Review of Biophysics. 46 (1): 43–57. doi:10.1146/annurev-biophys-070816-033834. ISSN 1936-122X. PMC 5896317. PMID 28301772.
  14. ^ Huber, G.A.; Kim, S. (January 1996). "Weighted-ensemble Brownian dynamics simulations for protein association reactions". Biophysical Journal. 70 (1): 97–110. Bibcode:1996BpJ....70...97H. doi:10.1016/S0006-3495(96)79552-8. PMC 1224912. PMID 8770190.
  15. ^ Kahn, H.; Harris, T.E. (1951). "Estimation of particle transmission by random sampling". National Bureau of Standards Appl. Math. Series. 12: 27–30.