T. Grafke, R. Grauer, T. Schaefer and E. Vanden-Eijnden, Multiscale Model. Simul., 12 (2014), 2, 566–580.
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 \(\phi^4\)-model and the stochastically driven Burgers equation.