Uncertainty Quantification

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Uncertainty Quantification

 24 - 28 May 2010
 Royal Society of Edinburgh, 22-26 George Street Edinburgh

Scientific Organisers:

  • Andrew Cliffe, University of Nottingham

  • Max Gunzburger, Florida State University

  • Paul Houston, University of Nottingham

  • Catherine Powell, University of Manchester

In deterministic modelling, complete knowledge of input parameters is assumed; this leads to simplified, tractable computations and produces simulations of outputs that correspond to specific choices of inputs. However, most physical, biological, social, economic and financial processes, etc, involve some degree of uncertainty. Uncertainty quantification (UQ) is the task of determining statistical information about the outputs of a process of interest, given only statistical (i.e., incomplete) information about the inputs. It has long been recognised that mathematical models need to account for uncertainty. The science of UQ has been in its infancy in any application areas until relatively recently but is now rapidly developing.  This workshop will concentrate on UQ for processes that are governed by partial differential equations (PDEs).

Speakers:

  • Max Gunzburger, Florida State University - Numerical Methods for Partial Differential Equations Having Random Inputs

  • Ian Sloan, University of New South Wales - Sparse Sampling Techniques

  • Andrea Saltelli, JRC ISPRA - Sensitivity Analysis and Dimension Reduction

  • Ed Allen, Texas Tech University - Derivation of SPDEs for Randomly Varying Problems in Physics, Biology or Finance

  • Olivier Le Maitre, LIMSI - Multi-Resolution for Stochastic Hyperbolic Systems

  • Keith Worden, University of Sheffield - Bayesian Sensitivity Analysis of a Heart Valve Model

  • Simon Tavener, Colorado State University - Sensitivity Analysis for Parametrized Nonlinear Maps and O.d.e.s

  • Daniel Tartakovsky, University of California - PDF Methods for Uncertainty Quantification 

  • Hilmi Kurt-Elli, Rolls Royce - Vibration Related Examples of Uncertainty Issues in the Design and Validation of Gas Turbine Components and Systems 

  • Erik von Schwerin, KAUST - Adaptive Multi-Level Monte Carlo Simulation

  • David Holton, SERCO - Uncertainty Quantification Issues in Radioactive Waste Disposal

  • Hermann Matthies, TU Braunschweig - Low Rank-Representation Numerical Methods for Uncertainty Quantification Equations

  • David Kerridge, BGS - Earthquakes, Volcanoes and Space Weather; Dealing with Unpredictable Natural Hazards 

  • Joakim Hove, Statoil - Uncertainty in the Petroleum Industry 

  • Des Higham, University of Strathclyde - Statistical Inference in a Zombie Outbreak Model

  • Angela Kunoth, Universitaet Paderborn - Multiscale Methods for the Valuation of American Options with Stochastic Volatility 

  • Peter Challenor, University of Southampton - Using Emulators to Account for Uncertainty in Climate Models

  • Sebastien Boyaval, Université Paris Est - The Reduced-Basis Method for Uncertainty Quantification

  • Rob Scheichl, University of Bath - Novel Monte Carlo Type Methods for Elliptic PDEs with Random Coefficients

  • Aretha Teckentrup, University of Bath - Multilevel Monte Carlo for Partial Differential Equations with Random Coefficients 

  • Eric Phipps, Sandia Labs - Intrusive Stochastic Galerkin Methods for Uncertainty Quantification of Nonlinear Stochastic PDEs

  • Nathaniel Burch, Colorado State University - Sensitivity Analysis for Solutions of Elliptic PDEs on Domains with Randomly Perturbed Boundaries

  • Mike Christie, Heriot-Watt University - Uncertainty Quantification in Reservoir Modelling

  • Andrew Gordon, University of Manchester - Solving Stochastic Collocation Systems with Algebraic Multigrid

  • Ivan Graham, University of Bath - Quasi-Monte Carlo Methods for Flow in Porous Media with Random Data 

  • Andrew Stuart, University of Warwick - Bayesian Well-Posedness for Inverse Problems

  • Masoumeh Dashti, University of Warwick - Bayesian Approach to an Elliptic Inverse Problem

  • Oliver Ernst, TU Freiberg - Efficient Solution of Large-Scale Covariance Eigenproblems

  • Houman Owhadi, CalTech - Optimal Uncertainty Quantification

  • Julia Charrier, ENS Cachan - A Weak Error Estimate for the Solution of an Elliptic Partial Differential Equation with Random Coefficients 

  • Tim Barth, NASA - Propagation of Statistical Model Parameter Uncertainty in Compressible Flow Simulations 

  • Sondipon Adhikari, University of Swansea - Elliptic Stochastic Partial Differential Equations: An Orthonormal Vector Basis Approach

  • Michael Goldstein, University of Durham - Bayesian Uncertainty Analysis for Complex Physical Models 

  • Marta D'Elia, Emory University - A Data Assimilation Technique for Including Noisy Velocity Measurements into Navier-Stokes Simulations 

  • Habib Najm, Sandia Labs - Uncertainty Quantification in Reacting Flow

  • Elisabeth Ullmann, TU Freiberg - Iterative Solvers for Stochastic Galerkin Discretizations of PDEs with Random Data

  • Tuhin Sahai, United Technologies Research Center - Uncertainty Quantification of Hybrid Dynamical Systems 

  • Chad Liebermann, MIT - Optimal Design Under Uncertainty

  • Clayton Webster, Florida State University - The Analysis and Applications of Sparse Grid Stochastic Collocation Techniques Within the Context of Uncertainty Quantification

  • Yanzhao Cao, Auburn University - Sparse Grid Collocation Method for Stochastic Integral Equations

  • Nicholas Zabaras, Cornell University - Model Reduction for Stochastic PDEs 

  • Doug Allaire, MIT - A Bayesian-Based Approach to Multi-Fidelity Multidisciplinary Design Optimization

  • Howard Elman, University of Maryland - Numerical Solution Algorithms for Discrete Partial Differential Equations with Random Data 

  • Junping Wang, NSF - Mathematics and Computation of Sediment Transport in Open Channels

  • John Burkhardt, Virginia Tech - Sparse Grids for Anisotropic Problems 

  • Dongbin Xiu, Purduee University - Uncertainty Analysis for Complex Systems: Algorithms and Data

  • Jim Hall, University of Newcastle - Calibration of Flood Models for Risk Analysis

  • Fabio Nobile, Politecnico di Milano - Stochastic Galerkin and Collocation Methods for PDEs with Random Coefficients

  • Jon Helton, Sandia National Laboratories - Uncertainty and Sensitivity Analysis in the 2008 Performance Assessment for the Proposed Yucca Mountain Repository for High-Level Radioactive Waste

  • Alexander Labovsky, Florida State University - Effects of Approximate Deconvolution Models on the Solution Models on the Solution of the Stochastic Navier-Stokes Equations

  • Tarek El Moselhy, MIT - A Dominant Singular Vectors Approach for Stochastic Partial Differential Equations

  • Miroslav Stoyanov, Florida State University - Stochastic Peridynamics and Finite Temperature Molecular Dynamics

  • Alberto Giovanni Busetto, ETH Zurich - Active Uncertainty Reduction for Dynamical Systems

  • Hyung-Chun Lee, Ajou University - Approximation of an Optimal Control Problem for Stochastic PDEs 

  • Youssef Marzouk, MIT - Tractable Bayesian Inference and Experimental Design in Complex Physical Systems

  • Tony Shardlow, University of Manchester - Milstein Method for Stochastic Delay Differential Equations

 

We wish to thank the following organisations for their kind support: ICMS, LMS, the US National Science Foundation and the European Office of Aerospace Research and Development, the Air Force Office of Scientific Research and the United States Air Force Research Labratory.

Presentations

Teckentrup1, Aretha
Multilevel Monte Carlo for partial differential equations with random coefficients
View Abstract
When solving partial differential equations (PDEs) with random coefficients numerically, one is usually interested in finding the expected value of a certain statistic of the solution. A common way to obtain estimates is to use Monte Carlo methods combined with spatial discretisations of the PDE on sufficiently fine grids. However, standard Monte Carlo methods have a rather slow rate of convergence with respect to the number of samples used, and individual samples of the solution are usually costly to compute numerically. In this talk we introduce the multilevel Monte Carlo method, with the aim of achieving the same accuracy of standard Monte Carlo at a much lower computational cost. The method exploits the linearity of expectation, by expressing the quantity of interest on a fine spatial grid in terms of the same quantity on a coarser grid and some “correction” terms. It has been extensively studied in the context of stochastic differential equations in the area of financial mathematics by Mike Giles and co-authors. We will give an outline of the method applied to elliptic PDEs with random coefficients, and also show some numerical results on the reduction of the computational cost resulting from it. The efficiency of the multilevel method is assessed by comparing it to standard Monte Carlo.

Participants

Name
Institution
Sondipon, AdhikariSwansea University
Douglas, AllaireMIT
Ed, AllenTexas Tech University
Tim, BarthNASA Ames Reseach Center
Sebastien, BoyavalUniversité Paris Est
Nathanial, BurchColorado State University
John, BurkardtVirginia Tech
Alberto Giovanni, BusettoETH Zurich
Yanzhao, CaoAuburn University
Peter, ChallenorUniversity of Exeter
Julia, CharrierAix Marseille Université
Mike, ChristieHeriot-Watt University
Andrew, CliffeUniversity of Nottingham
Joe, CollisUniversity of Nottingham
Marta, D'EliaEmory University
Masoumeh, DashtiUniversity of Sussex
Tarek, El MoselhyMIT
Howard, ElmanUniversity of Maryland
Oliver, ErnstTU Bergakademie Freiberg
Fariba, FahrooAFOSR
Michael, GoldsteinDurham University
Andrew, GordonUniversity Of Manchester
Ivan, GrahamUniversity of Bath
Max, GunzburgerFlorida State University
Jim, HallNewcastle University
Jon, HeltonSandia National Laboratories
Des, HighamUniversity of Strathclyde
David, HoltonSerco
Paul, HoustonUniversity of Nottingham
Joakim, HoveStatoil
Angela, KunothUniversitaet Paderborn
Hilmi, Kurt-ElliRolls Royce
Alexander, LabovskyFlorida State University
Kody, LawKAUST
Olivier, Le MaitreLIMSI
Hyung-Chun, LeeAjou University
Chad, LiebermanMIT
Gabriel, LordHeriot-Watt University
Youssef, MarzoukMIT
Hermann, MatthiesTU Braunschweig
Habib, NajmSandia National Laboratories
Fabio, NobilePolitecnico di Milano
Houman, OwhadiCalifornia Institute of Technology
Eric, PhippsSandia National Laboratories
Catherine, PowellUniversity of Manchester
Tuhin, SahaiUnited Technologies Research Center
Andrea, SaltelliJRC Ispra
Rob, ScheichlUniversity of Bath
Tony, Shardlow
David, SilvesterUniversity of Manchester
Ian, SloanUniversity of New South Wales
Miroslav, StoyanovFlorida State University
Andrew, StuartCalTech
Daniel, TartakovskyUniversity of California at San Diego
Simon, TavenerColorado State University
Phillip, TaylorUniversity of Manchester
Aretha, TeckentrupUniversity of Edinburgh
Elisabeth, UllmannTU Freiberg
Hans-Werner, Van WykVirginia Tech
Erik, von SchwerinKAUST
Junping, WangNSF
Clayton, WebsterOak Ridge National Laboratory
Karen, WillcoxMIT
Keith, WordenUniversity of Sheffield
Dongbin, XiuPurdue University
Nicholas, ZabarasCornell University