  Runaway electrons (RE) generated during magnetic disruptions present a major
threat to the safe operation of plasma nuclear fusion reactors. A critical
aspect of understanding RE dynamics is to calculate the runaway probability,
i.e., the probability that an electron in the phase space will runaway on, or
before, a prescribed time. Such probability can be obtained by solving the
adjoint equation of the underlying Fokker-Planck equation that controls the
electron dynamics. In this effort, we present a sparse-grid probabilistic
scheme for computing the runaway probability. The key ingredient of our
approach is to represent the solution of the adjoint equation as a conditional
expectation, such that discretizing the differential operator reduces to the
approximation of a set of integrals. Adaptive sparse grid interpolation is
utilized to approximate the map from the phase space to the runaway
probability. The main novelties of this effort are the integration of the
sparse-grid method into the probabilistic numerical scheme for computing escape
probability, as well as the demonstration in computing RE probabilities. Two
numerical examples are given to illustrate that the proposed method can achieve
$\mathcal{O}(\Delta t)$ convergence, as well as the adaptive refinement
strategy can effectively handle the sharp transition layer between the runaway
and non-runaway regions.
