Hybrid Monte Carlo algorithm for sampling rare events in space-time histories of stochastic fields

G. Margazoglou, L. Biferale, R. Grauer, K. Jansen, D. Mesterházy, T. Rosenow, and R. Tripiccione
Phys. Rev. E 99, 053303 – Published 7 May 2019

Abstract

We introduce a variant of the Hybrid Monte Carlo (HMC) algorithm to address large-deviation statistics in stochastic hydrodynamics. Based on the path-integral approach to stochastic (partial) differential equations, our HMC algorithm samples space-time histories of the dynamical degrees of freedom under the influence of random noise. First, we validate and benchmark the HMC algorithm by reproducing multiscale properties of the one-dimensional Burgers equation driven by Gaussian and white-in-time noise. Second, we show how to implement an importance sampling protocol to significantly enhance, by orders of magnitudes, the probability to sample extreme and rare events, making it possible to estimate moments of field variables of extremely high order (up to 30 and more). By employing reweighting techniques, we map the biased configurations back to the original probability measure in order to probe their statistical importance. Finally, we show that by biasing the system towards very intense negative gradients, the HMC algorithm is able to explore the statistical fluctuations around instanton configurations. Our results will also be interesting and relevant in lattice gauge theory since they provide unique insights into reweighting techniques.

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  • Received 5 August 2018
  • Revised 27 January 2019

DOI:https://doi.org/10.1103/PhysRevE.99.053303

©2019 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsStatistical Physics & ThermodynamicsNonlinear Dynamics

Authors & Affiliations

G. Margazoglou1,2, L. Biferale1, R. Grauer3, K. Jansen4, D. Mesterházy5,*, T. Rosenow6, and R. Tripiccione7

  • 1Department of Physics, University of Rome Tor Vergata and INFN-Tor Vergata, 00133 Rome, Italy
  • 2Computation-based Science and Technology Research Center, Cyprus Institute, 2121 Nicosia, Cyprus
  • 3Institut für Theoretische Physik I, Ruhr-University Bochum, 44780 Bochum, Germany
  • 4NIC, DESY, 15738 Zeuthen, Germany
  • 5Institute for Theoretical Physics, University of Bern, 3012 Bern, Switzerland
  • 6Institut für Physik, Brandenburg University of Technology Cottbus-Senftenberg, 03046 Cottbus, Germany
  • 7Department of Physics, Università di Ferrara and INFN-Ferrara, 44122 Ferrara, Italy

  • *Corresponding author: mesterh@itp.unibe.ch

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Vol. 99, Iss. 5 — May 2019

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