  We present a new method for sampling rare and large fluctuations in a
non-equilibrium system governed by a stochastic partial differential equation
(SPDE) with additive forcing. To this end, we deploy the so-called instanton
formalism that corresponds to a saddle-point approximation of the action in the
path integral formulation of the underlying SPDE. The crucial step in our
approach is the formulation of an alternative SPDE that incorporates knowledge
of the instanton solution such that we are able to constrain the dynamical
evolutions around extreme flow configurations only. Finally, a reweighting
procedure based on the Girsanov theorem is applied to recover the full
distribution function of the original system. The entire procedure is
demonstrated on the example of the one-dimensional Burgers equation.
Furthermore, we compare our method to conventional direct numerical simulations
as well as to Hybrid Monte Carlo methods. It will be shown that the
instanton-based sampling method outperforms both approaches and allows for an
accurate quantification of the whole probability density function of velocity
gradients from the core to the very far tails.
