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We develop a provably efficient importance sampling scheme that estimatesexit probabilities of solutions to small-noise stochastic reaction-diffusionequations from scaled neighborhoods of a stable equilibrium. The moderatedeviation scaling allows for a local approximation of the nonlinear dynamics bytheir linearized version. In addition, we identify a finite-dimensionalsubspace where exits take place with high probability. Using stochastic controland variational methods we show that our scheme performs well both in the zeronoise limit and pre-asymptotically. Simulation studies for stochasticallyperturbed bistable dynamics illustrate the theoretical results.

Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime