Computation of Sobol' indices using embedded variance deconvolution

Sobol' sensitivity indices (SI) provide robust and accurate measures of how much uncertainty in output quantities is caused by different uncertain input parameters. These allow analysts to prioritize future work to either reduce or better quantify the effects of the most important uncertain parameters. One of the most common approaches to computing SI requires Monte Carlo (MC) sampling of uncertain parameters and full physics code runs to compute the response for each of these samples. In the case that the physics code is a MC radiation transport code, this traditional approach to computing SI presents a workflow in which the MC transport calculation must be sufficiently resolved for each MC uncertain parameter sample. This process can be prohibitively expensive, especially since thousands or more particle histories are often required on each of thousands or so uncertain parameter samples. We propose a process for computing SI in which only a few MC radiation transport histories are simulated before sampling new uncertain parameter values. We use Embedded Variance Deconvolution (EVADE) to parse the desired parametric variance from the MC transport variance on each uncertain parameter sample. To provide a relevant benchmark, we propose a new radiation transport benchmark problem and derive analytic solutions for its outputs, including SI. The new EVADE-based approach is found to converge with MC convergence behavior and be at least an order of magnitude more precise for the same computational cost than the traditional approach for several SI on our test problem. (authors)