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IMA Data Science Seminar - Matteo Croci
Speaker: Matteo Croci
Title: Flexible multi-output multifidelity uncertainty quantification via MLBLUE
Abstract: A central task in forward uncertainty quantification (UQ) is estimating the expectation of one or more quantities of interest (QoIs). In computational engineering UQ problems often involve multiple QoIs, and extremely
eterogeneous models, both in terms of how they are constructed (varying grids, equations, or dimensions, different physics, surrogate and reduced-order models...) & in terms of their input-output structure (different models might have different uncertain inputs and yield different QoIs). In this complex scenario it is crucial to design estimators that are as flexible and as efficient as possible. Multilevel (or multifidelity) Monte Carlo (MLMC) methods are often the go-to methods for estimating expectations as they are able to exploit the correlations between models to significantly reduce the estimation cost. However, multi-output strategies in MLMC methods are either sub-optimal, or non-existent.
In this talk we focus on multilevel best linear unbiased estimators (MLBLUEs, Schaden & Ullmann, SIAM/ASA JUQ, 2021).MLBLUEs are extremely flexible and have the appealing property of being provably optimal among all multilevel linear unbiased estimators, making them, in our opinion, one of the most powerful MLMC methods available in the literature. Nevertheless, MLBLUEs have two limitations: 1) their setup requires solving their model selection and sample allocation problem (MOSAP), which is a non-trivial nonlinear optimization procedure, and 2) they can only work with one scalar QoI at a time.
In this talk we show how the true potential of MLBLUEs can be unlocked:
1) We present a new formulation of their MOSAP that can be solved almost as easily & efficiently as a linear program.
2) We extend MLBLUEs to the multi- & infinite-dimensional output case.
3) We provide multi-output MLBUE MOSAP formulations that can be solved efficiently a consistent.

Sep 20, 2022 01:25 PM in Central Time (US and Canada)

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