Adaptivity, High Dimensionality and Randomness

The overall goal of this workshop is to initiate new and groundbreaking research in algorithm design and mathematical analysis in scientific computing. The focus is directed at the numerical approximation of partial differential equations (PDEs for short), when randomness is involved either in the input data of the modeling equations or in the approximation algorithms themselves.

Rather than a tight focus on a highly specialized, clearly delineated research field, the workshop aims at cross-fertilization of several recently emerged research directions in applied and computational mathematics around the numerical solution of PDEs. This comprises, in particular, mathematically justified paradigms for the design of adaptive algorithms, the recently strongly advanced understanding of randomized and number-theoretic algorithms such as Monte-Carlo (MC), quasi-Monte Carlo (QMC) and Markov Chain MC (MCMC), sparse and high dimensional approximation, tensor-formatted computations, deep neural network approximation and machine learning algorithms.

The workshop will be held in hybrid mode.
 

April 4, 2022
09:00 — 10:00
Registration and Coffee
10:00 — 10:15
Welcome
12:00 — 13:30
Lunch Break
13:30 — 14:20
Chris Oates (U Newcastle upon Tyne)
Optimal Thinning of MCMC Output
15:10 — 15:30
Coffee Break
15:30 — 16:20
16:20 — 17:10
April 5, 2022
09:00 — 09:50
Wolfgang Dahmen (U of South Carolina, Columbia)
Some Thoughts on PINN - Prediction Capability
09:50 — 10:20
Coffee Break
10:20 — 11:10
Giovanni Migliorati (Sorbonne U, Paris)
Adaptive approximation by weighted least-squares methods
12:00 — 13:30
Lunch Break
15:10 — 15:30
Coffee Break
April 6, 2022
09:50 — 10:20
Coffee Break
10:20 — 11:10
Tabea Tscherpel (U of Bielefeld)
Interpolation operators on negative Sobolev spaces
11:10 — 12:00
12:00 — 13:30
Lunch Break
13:30 — 14:20
14:20 — 15:10
15:10 — 15:30
Coffee Break
15:30 — 16:20
Ricardo Nochetto (U of Maryland)
Adaptive Virtual Element Methods
April 7, 2022
09:50 — 10:20
Coffee Break
11:10 — 12:00
12:00 — 13:30
Lunch Break
15:10 — 15:30
Coffee Break
15:30 — 16:20
Elisabeth Ullmann (TU Munich)
Rare event estimation with PDE-based models
April 8, 2022
09:50 — 10:20
Coffee Break
10:20 — 11:10
12:00 — 12:15
Closing

Organizers

Name Affiliation
Carsten Carstensen Humboldt University
Albert Cohen Sorbonne University
Michael Feischl Technical University of Vienna
Christoph Schwab ETH Zürich

Attendees

Name Affiliation
Markus Bachmayr Johannes-Gutenberg Universität Mainz
Andrea Barth University of Stuttgart
Alex Bespalov University of Birmingham
Wolfgang Dahmen University of South Carolina
Bruno Després Sorbonne University
Josef Dick University of New South Wales
Hieu Do Paris Dauphine University
Matthieu Dolbeault Sorbonne University
Martin Eigel Weierstrass Institut Berlin
Markus Faustmann Technische Universitaet Wien
Sara Fraschini University of Vienna
Dietmar Gallistl University of Jena
Lars Grasedyck RWTH Aachen
Michael Griebel Institute for Numerical Simulation
Philipp Grohs University of Vienna
Cosmas Heiss Technical University Berlin
Clemens Karner University Vienna
Vladimir Kazeev University of Vienna
Arbaz Khan Indian Institute of Technology Roorkee
Christian Kreuzer Technical University Dortmund
Peter Kritzer Johann-Radon Institute
Frances Kuo University of New South Wales, Sydney
Gitta Kutyniok Ludwig-Maximilians-University Munich
Marcello Longo ETH Zürich
Jens Markus Melenk Technical University of Vienna
Fabian Merle University of Tübingen
Giovanni Migliorati Sorbonne University
Olga Mula Hernandez Paris Dauphine University
Fabio Nobile EPFL Lausanne
Ricardo Nochetto University of Maryland
Monica Nonino University of Vienna
Anthony Nouy Centrale Nantes
Chris Oates University of Newcastle upon Tyne
Joost Opschoor ETH Zürich
Ivan Oseledets -
Houman Owhadi California Institute of Technology, Pasadena
Ilaria Perugia University of Vienna
Daniel Peterseim University Augsburg
Philipp Petersen University of Vienna
Friedrich Pillichshammer Johannes Kepler Universität
Catherine Powell University of Manchester
Davide Pradovera University of Vienna
Dirk Praetorius Technical University of Vienna
Andreas Prohl University of Tübingen
Holger Rauhut RWTH Aachen
Michele Ruggeri University of Strathclyde
Andrea Scaglioni Technische Universitaet Wien
Mira Schedensack University of Leipzig
Anna Shalova Technical University Eindhoven
Andreas Stein ETH Zurich
Rob Stevenson University of Amsterdam
Tim Sullivan University of Warwick
Leila Taghizadeh Technical University of Munich
Aretha Teckentrup University of Edinburgh
Tabea Tscherpel Bielefeld University
Elisabeth Ullmann Technical University of Munich
Barbara Verfürth Karlsruhe Institute of Technology
Clayton Webster University of Texas at Austin
Marco Zank University of Vienna
Jakob Zech University of Heidelberg
Preview of Chris Oates - Optimal Thinning of MCMC Output
Chris Oates (U Newcastle upon Tyne): Optimal Thinning of MCMC Output
April 4, 2022 13:30 — 14:20
Preview of Aretha Teckentrup - Convergence and Robustness of Gaussian Process Regression
Aretha Teckentrup (U Edinburgh): Convergence and Robustness of Gaussian Process Regression
April 4, 2022 15:30 — 16:20
Preview of Markus Faustmann - Adaptive FEM for fractional diffusion
Markus Faustmann (TU Wien): Adaptive FEM for fractional diffusion
April 6, 2022 11:10 — 12:00
Preview of Christian Kreuzer - On the threshold condition for Dörfler marking
Christian Kreuzer (TU Dortmund): On the threshold condition for Dörfler marking
April 6, 2022 14:20 — 15:10
Preview of Arbaz Khan - Mixed finite element approximation for poroelasticity
Arbaz Khan (IIT Roorkee): Mixed finite element approximation for poroelasticity
April 6, 2022 16:20 — 17:10
Preview of Michele Ruggeri - Convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM
Michele Ruggeri (U Strathclyde, Glasgow): Convergence and rate optimality of adaptive multilevel stochastic Galerkin FEM
April 7, 2022 10:20 — 11:10
Preview of Barbara Verfürth - Offline-online strategy for multiscale problems with random defects
Barbara Verfürth (KIT, Karlsruhe): Offline-online strategy for multiscale problems with random defects
April 7, 2022 11:10 — 12:00
At a glance
Type:
Workshop
When:
April 4, 2022 — April 8, 2022
Where:
ESI Boltzmann Lecture Hall
Organizer(s):
Carsten Carstensen (HU Berlin)
Albert Cohen (Sorbonne U, Paris)
Michael Feischl (TU Vienna)
Christoph Schwab (ETH Zürich)