Surrogate-based Ensemble Grouping Strategies for Embedded Sampling-based Uncertainty Quantification

TL;DR

This paper introduces a surrogate-based grouping strategy for ensemble sampling in uncertainty quantification, reducing divergence and computational cost by predicting solver iterations to group similar samples.

Contribution

It develops a new surrogate-based grouping method that predicts computational cost to improve ensemble effectiveness in complex simulations.

Findings

Effective grouping reduces ensemble divergence.

Method applies to anisotropic diffusion problems.

Extends previous parameter-based grouping approaches.

Abstract

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.