Rare but extreme events are known to have dramatic influence on the statistics of turbulent flows, but are notoriously hard to handle analytically. Large deviation theory is often the right theoretical framework to understand their effects. At the core of the theory lies the minimization of an action functional, which in many cases of interest has to be computed by numerical means. In this talk, the theoretical and numerical aspect behind these calculations are discussed. The presented family of algorithms is capable to predict the large deviation minimizer in examples from fluid dynamics, and atmosphere/ocean sciences. In particular, it can be used to calculate expectations dominated by noise-induced excursions from deterministically stable fixpoints in hydrodynamical equations, as well as rare transitions between metastable fixed points of the dynamics, to gain knowledge on statistics of rare events and the interplay between the nonlinear dynamics and the stochastic forcing.
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