  In this paper, we consider the development of efficient numerical methods for
linear transport equations with random parameters and under the diffusive
scaling. We extend to the present case the bi-fidelity stochastic collocation
method introduced in [33,50,51]. For the high-fidelity transport model, the
asymptotic-preserving scheme [29] is used for each stochastic sample. We employ
the simple two-velocity Goldstein-Taylor equation as low-fidelity model to
accelerate the convergence of the uncertainty quantification process. The
choice is motivated by the fact that both models, high fidelity and low
fidelity, share the same diffusion limit. Speed-up is achieved by proper
selection of the collocation points and relative approximation of the
high-fidelity solution. Extensive numerical experiments are conducted to show
the efficiency and accuracy of the proposed method, even in non diffusive
regimes, with empirical error bound estimations as studied in [16].
