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Surrogate-based ensemble grouping strategies for embedded sampling-based uncertainty quantification. (English) Zbl 1455.62158
D’Elia, Marta (ed.) et al., Quantification of uncertainty: improving efficiency and technology. QUIET. Selected contributions based on the presentations at the international workshop, Trieste, Italy, July 18–21, 2017. Cham: Springer. Lect. Notes Comput. Sci. Eng. 137, 41-66 (2020).
Summary: The embedded ensemble propagation approach introduced in [E. Phipps et al., SIAM J. Sci. Comput. 39, No. 2, C162–C193 (2017; Zbl 1365.65017)] 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 advection-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 advection-dominated diffusion problems with a wide variation in solver iterations from sample to sample. It extends the parameter-based grouping approach developed in [M. D’Elia et al., SIAM/ASA J. Uncertain. Quantif. 6, 87–117 (2018; Zbl 1390.60229)] 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.
For the entire collection see [Zbl 1454.62013].
MSC:
62L20 Stochastic approximation
62-08 Computational methods for problems pertaining to statistics
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
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