Multilevel and multifidelity sampling methods in UQ for PDEs

Online Workshop 1 of the Thematic Programme:
"Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data"


Due to the Covid-19 pandemic, the thematic program "Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data" has been canceled and will be re-proposed from May 2 to June 24, 2022 with the same workshop structure, including also an opening workshop on "Multilevel and multifidelity sampling methods in UQ for PDEs” as originally planned.

As a precursor for this event in 2022, we propose, however, a reduced version of this opening workshop to be held online on May 4-5, 2020 at 14-19 CET, with the aim of initiating a 2-year collaborative ESI research effort in analysis and computation for UQ.

The reduced online version of the workshop includes 8 speakers and one recorded talk:

Tiangang Cui (Monash University, Melbourne).
Josef Dick (UNSW Sydney)
Alex Gorodetsky (University of Michigan)
Abdul-Lateef Haji-Ali (Herriot-Watt University, Edinburgh),
Dirk Nuyens (KU Leuven)
Benjamin Peherstorfer (Courant Institute)
Raul Tempone (RWTH Aachen & KAUST)
Elisabeth Ullmann (TU Munich)
Matti Vihola (University of Jyväskylä)

as well as some "round table" online discussion and interaction.

Follow-Up Session & Collaboration Kick-Off on May 13, 2020, 15:30 - 16:30

Desription of the Workshop

This workshop will cover multilevel and multifidelity sampling methods in uncertainty quantification for PDEs, with a particular focus on moving beyond forward propagation of uncertainty.

A powerful and attractive way for uncertainty propagation and for Bayesian inference in random and parametric PDEs are multilevel sampling approaches, such as multilevel Monte Carlo, multilevel quasi-Monte Carlo, multilevel stochastic collocation, to name but a few. These methods exploit the natural hierarchies of numerical approximations (mesh size, polynomial degree, truncations of expansions, regularisations, model order reduction) to efficiently tackle the arising high- or infinite-dimensional quadrature problems. Their efficiency is based on variance reduction through a systematic use of control variates and importance sampling (in the stochastic setting) and of the sparse grid recombination idea (in the deterministic setting). The variance reduction is intrinsically tied to a priori and a posteriori error control in the numerical approximations, which in turn has spawned a resurgence in fundamental research in the mathematical and numerical analysis of PDEs with spatiotemporally heterogeneous data.

A related body of work has focused on combining models of varying fidelity (such as 1D and 3D models, reduced-order models, differing physical assumptions, data-fit surrogate models, and look-up tables of experimental results) in multifidelity uncertainty quantification methods. These methods similarly use control variate formulations (the multifidelity Monte Carlo method) and importance sampling. This multifidelity setting differs from the multilevel setting above because the different models do not need to form a fixed hierarchy. The relationships among the models are typically unknown a priori and are learned adaptively as the computation advances.

All these methodologies have most notably been developed in the context of forward propagation of uncertainty, or quadrature with respect to a known (prior) distribution, but they have also been extended to inverse problems and intractable (posterior) distributions that arise when incorporating data in a Bayesian inference framework, and to in optimization under uncertainty. 

May 4, 2020
08:00 — 12:00
14:00 — 14:10
14:55 — 15:35
15:35 — 16:00
Coffee Break
16:45 — 17:25
Elisabeth Ullmann (TU Munich)
On Multilevel Best Linear Unbiased Estimators
17:25 — 17:40
Short Break
17:40 — 17:45
Introduction to the Discussion Session
17:45 — 18:30
Breakout Room Discussions
18:30 — 19:15
Feedback from Breakout Rooms
May 5, 2020
14:00 — 14:40
14:45 — 15:25
15:25 — 15:50
Coffee Break
15:50 — 16:30
17:15 — 17:30
Short Break
17:30 — 17:35
Intoduction to the Discussion Session
17:35 — 18:20
Breakout Room Discussions
18:20 — 19:05
Feedback from Breakout Rooms
19:00 — 19:15
Closing Statements
May 13, 2020
15:30 — 16:30
Follow-Up Session & Collaboration Kick-Off
This event has no subevents associated to it.


Name Affiliation
Kody Law University of Manchester
Fabio Nobile EPFL, Lausanne
Robert Scheichl University of Heidelberg
Karen Willcox University of Texas at Austin


Name Affiliation
Terrence Alsup New York University
Quentin Ayoul-Guilmard EPFL, Lausanne
Andrea Barth University of Stuttgart
Francesca Bonizzoni University Augsburg
Lukas Brencher University of Stuttgart
Anirban Chaudhuri MIT
Mariana Clare Imperial College London
Albert Cohen Sorbonne University
Colin Cotter Imperial College London
Matteo Croci University of Texas at Austin
Tiangang Cui Monash University
Josef Dick University of New South Wales
Adrian Ebert Radon Institute, RICAM
Michael Feischl Technical University of Vienna
Sundar Ganesh Subramaniam EPFL, Lausanne
Alfredo Garbuno Inigo California Institute of Technology, Pasadena
Fatemeh Ghoreishi Northeastern University
Alexander Gilbert University of Heidelberg
Mike Giles University of Oxford
Alex Gorodetsky University of Michigan
Abdul-Lateef Haji-Ali Heriot-Watt University
Lukas Herrmann Johann-Radon Institute
John Jakeman Sandia National Laboratories
Yoshihito Kazashi Heidelberg University
Parisa Khodabakhshi University of Texas at Austin
Amirreza Khodadadian University of Hannover
Kristin Kirchner Technical University Delft
Peter Kritzer Johann-Radon Institute
Frances Kuo University of New South Wales, Sydney
Annika Lang Chalmers University of Technology
Jonas Latz University of Cambridge
Juan Pablo Madrigal Cianci EPFL, Lausanne
Hermann Matthies Technical University Braunschweig
Sean McBane University of Texas at Austin
Robin Merkle University of Stuttgart
Dirk Nuyens KU Leuven
Iason Papaioannou Technical University of Munich
Benjamin Peherstorfer Courant Institute of Mathematical Sciences
Chiara Piazzola Istituto di Matematica Applicata e Tecnologie Informatiche
Elizabeth Qian California Institute of Technology, Pasadena
Daniel Schaden Technical University of Munich
Christoph Schwab ETH Zürich
Linus Seelinger University of Heidelberg
Yang Shangda University of Manchester
Aretha Teckentrup University of Edinburgh
Raul Tempone RWTH Aachen
Panagiotis Tsilifis General Electric Research
Elisabeth Ullmann Technical University of Munich
Matti Vihola University of Jyväskylä
Umberto Villa Washington University in St. Louis
Jakob Zech University of Heidelberg
At a glance
Online Workshop
May 4, 2020 — May 13, 2020
Erwin Schrödinger Institute - virtual
Part of:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data - postponed (Thematic Programme)
Kody Law (U Manchester)
Fabio Nobile (EPFL, Lausanne)
Robert Scheichl (U Heidelberg)
Karen Willcox (U of Texas, Austin)