  The embedded ensemble propagation approach introduced in [49] has been
demonstrated to be a powerful means of reducing the computational cost of
sampling-based uncertainty quantification methods, particularly on emerging
computational architectures. A substantial challenge with this method however
is ensemble-divergence, whereby different samples within an ensemble choose
different code paths. This can reduce the effectiveness of the method and
increase computational cost. Therefore grouping samples together to minimize
this divergence is paramount in making the method effective for challenging
computational simulations. In this work, a new grouping approach based on a
surrogate for computational cost built up during the uncertainty propagation is
developed and applied to model diffusion problems where computational cost is
driven by the number of (preconditioned) linear solver iterations. The approach
is developed within the context of locally adaptive stochastic collocation
methods, where a surrogate for the number of linear solver iterations,
generated from previous levels of the adaptive grid generation, is used to
predict iterations for subsequent samples, and group them based on similar
numbers of iterations. The effectiveness of the method is demonstrated by
applying it to highly anisotropic diffusion problems with a wide variation in
solver iterations from sample to sample. It extends the parameter-based
grouping approach developed in [17] to more general problems without requiring
detailed knowledge of how the uncertain parameters affect the simulation's
cost, and is also less intrusive to the simulation code.
