Metropolis integration schemes for self-adjoint diffusions

Nawaf Bou-Rabee, Aleksandar Donev, Eric Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review


We present explicit methods for simulating diffusions whose generator is self-adjoint with respect to a known (but possibly not normalizable) density. These methods exploit this property and combine an optimized Runge-Kutta algorithm with a Metropolis-Hastings Monte Carlo scheme. The resulting numerical integration scheme is shown to be weakly accurate at finite noise and to gain higher order accuracy in the small noise limit. It also permits the user to avoid computing explicitly certain terms in the equation, such as the divergence of the mobility tensor, which can be tedious to calculate. Finally, the scheme is shown to be ergodic with respect to the exact equilibrium probability distribution of the diffusion when it exists. These results are illustrated in several examples, including a Brownian dynamics simulation of DNA in a solvent. In this example, the proposed scheme is able to accurately compute dynamics at time step sizes that are an order of magnitude (or more) larger than those permitted with commonly used explicit predictor-corrector schemes.

Original languageEnglish (US)
Pages (from-to)781-831
Number of pages51
JournalMultiscale Modeling and Simulation
Issue number2
StatePublished - 2014


  • Brownian dynamics with hydrodynamic interactions
  • DNA simulations
  • Ergodicity
  • Explicit integrators
  • Fluctuation-dissipation theorem
  • Metropolis-hastings algorithm
  • Predictor-corrector schemes
  • Small noise limit

ASJC Scopus subject areas

  • General Chemistry
  • Modeling and Simulation
  • Ecological Modeling
  • General Physics and Astronomy
  • Computer Science Applications


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