Arclength parametrized hamilton's equations for the calculation of instantons

T. Grafke, R. Grauer, T. Schäfer, E. Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review

Abstract

A method is presented to compute minimizers (instantons) of action functionals using arclength parametrization of Hamilton's equations. This method can be interpreted as a local variant of the geometric minimum action method introduced to compute minimizers of the Freidlin-Wentzell action functional that arises in the context of large deviation theory for stochastic differential equations. The method is particularly well suited to calculate expectations dominated by noiseinduced excursions from deterministically stable fixpoints. Its simplicity and computational efficiency are illustrated here using several examples: a finite-dimensional stochastic dynamical system (an Ornstein-Uhlenbeck model) and two models based on stochastic partial differential equations: the f4-model and the stochastically driven Burgers equation.

Original languageEnglish (US)
Pages (from-to)566-580
Number of pages15
JournalMultiscale Modeling and Simulation
Volume12
Issue number2
DOIs
StatePublished - 2014

Keywords

  • Burgers equation
  • Freidlin-wentzell action
  • Geometric minimum action method
  • Instantons

ASJC Scopus subject areas

  • Chemistry(all)
  • Modeling and Simulation
  • Ecological Modeling
  • Physics and Astronomy(all)
  • Computer Science Applications

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