  Extreme events play a crucial role in fluid turbulence. Inspired by methods
from field theory, these extreme events, their evolution and probability can be
computed with help of the instanton formalism as minimizers of a suitable
action functional. Due to the high number of degrees of freedom in
multi-dimensional fluid flows, traditional global minimization techniques
quickly become prohibitive in their memory requirements. We outline a novel
method for finding the minimizing trajectory in a wide class of problems that
typically occurs in turbulence setups, where the underlying dynamical system is
a non-gradient, non-linear partial differential equation, and the forcing is
restricted to a limited length scale. We demonstrate the efficiency of the
algorithm in terms of performance and memory by computing high resolution
instanton field configurations corresponding to viscous shocks for 1D and 2D
compressible flows.
