Efficient control variates for uncertainty quantification of radiation transport

•Control variate Monte Carlo is used to propagate uncertainties in radiative transfer.•Control variates based on the diffusion approximation and discrete ordinates are introduced.•Metrics of variance reduction and computational efficiency are introduced.•Problems with stochastic inputs are solved comparing Monte Carlo and control variate Monte Carlo.•Control variates based on low order approximations are able to provide efficiency improvements.

Numerical simulations of problems involving radiation transport are challenging because of the associated computational cost; moreover, it is typically difficult to describe the optical properties of the system very precisely, and therefore uncertainties abound. We aim to represent the uncertainties explicitly and to characterize their impact on the output of interest. While stochastic collocation and polynomial chaos methods have been applied previously, these methods can suffer from the curse of dimensionality and fail in cases where the system response is discontinuous or highly non-linear. Monte Carlo methods are more robust, but they converge slowly. To that end, we apply the control variate method to uncertainty propagation via Monte Carlo. We leverage the modeling hierarchy of radiation transport to use low fidelity models such as the diffusion approximation and coarse angular discretizations to reduce the confidence interval on the quantity of interest. The efficiency of the control variate method is demonstrated in several problems involving stochastic media, thermal emission, and radiation properties with different quantities of interest. The control variates are able to provide significant variance reduction and efficiency increase in all problems considered. We conclude our study with a discussion of choosing optimal control variates and other extensions of Monte Carlo methods.