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arXiv · 1309.5175

Arclength parametrized Hamilton's equations for the calculation of instantons

Tobias Grafke·Rainer Grauer·Tobias Schäfer·Eric Vanden-Eijnden
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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 (gMAM) 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 noise-induced 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 $ϕ^4$-model and the stochastically driven Burgers equation.

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Tobias Grafke, Rainer Grauer, Tobias Schäfer, Eric Vanden-Eijnden. 2013-09-20. Arclength parametrized Hamilton's equations for the calculation of instantons. https://doi.org/10.1137/130939158

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