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Uncertainty Quantification with Multi-Level and Multi-Index methods

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UNQW02 - Surrogate models for UQ in complex systems

We start by recalling the Monte Carlo and Multi-level Monte Carlo (MLMC) methods for computing statistics of the solution of a Partial Differential Equation with random data. Then, we present the Multi-Index Monte Carlo (MIMC) and Multi-Index Stochastic Collocation (MISC) methods. MIMC is both a stochastic version of the combination technique introduced by Zenger, Griebel and collaborators and an extension of the MLMC method first described by Heinrich and Giles. Instead of using first-order differences as in MLMC , MIMC uses mixed differences to reduce the variance of the hierarchical differences dramatically, thus yielding improved convergence rates. MISC is a deterministic combination technique that also uses mixed differences to achieve better complexity than MIMC , provided enough regularity. During the presentation, we will showcase the behavior of the numerical methods in applications, some of them arising in the context of Regression based Surrogates and Optimal Experimental Design. Coauthors: J. Beck, L. Espath (KAUST), A.-L. Haji-Ali (Oxford), Q. Long (UT), F. Nobile (EPFL), M. Scavino (UdelaR), L. Tamellini (IMATI), S. Wolfers (KAUST) Webpages: https://stochastic_numerics.kaust.edu.sa https://sri-uq.kaust.edu.sa

This talk is part of the Isaac Newton Institute Seminar Series series.

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