# 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

### Participants

Name | Institution |
---|---|

Sondipon, Adhikari | Swansea University |

Douglas, Allaire | MIT |

Ed, Allen | Texas Tech University |

Tim, Barth | NASA Ames Reseach Center |

Sebastien, Boyaval | Université Paris Est |

Nathanial, Burch | Colorado State University |

John, Burkardt | Virginia Tech |

Alberto Giovanni, Busetto | ETH Zurich |

Yanzhao, Cao | Auburn University |

Peter, Challenor | University of Exeter |

Julia, Charrier | Aix Marseille Université |

Mike, Christie | Heriot-Watt University |

Andrew, Cliffe | University of Nottingham |

Joe, Collis | University of Nottingham |

Marta, D'Elia | Emory University |

Masoumeh, Dashti | University of Sussex |

Tarek, El Moselhy | MIT |

Howard, Elman | University of Maryland |

Oliver, Ernst | TU Bergakademie Freiberg |

Fariba, Fahroo | AFOSR |

Michael, Goldstein | Durham University |

Andrew, Gordon | University Of Manchester |

Ivan, Graham | University of Bath |

Max, Gunzburger | Florida State University |

Jim, Hall | Newcastle University |

Jon, Helton | Sandia National Laboratories |

Des, Higham | University of Strathclyde |

David, Holton | Serco |

Paul, Houston | University of Nottingham |

Joakim, Hove | Statoil |

Angela, Kunoth | Universitaet Paderborn |

Hilmi, Kurt-Elli | Rolls Royce |

Alexander, Labovsky | Florida State University |

Kody, Law | KAUST |

Olivier, Le Maitre | LIMSI |

Hyung-Chun, Lee | Ajou University |

Chad, Lieberman | MIT |

Gabriel, Lord | Heriot-Watt University |

Youssef, Marzouk | MIT |

Hermann, Matthies | TU Braunschweig |

Habib, Najm | Sandia National Laboratories |

Fabio, Nobile | Politecnico di Milano |

Houman, Owhadi | California Institute of Technology |

Eric, Phipps | Sandia National Laboratories |

Catherine, Powell | University of Manchester |

Tuhin, Sahai | United Technologies Research Center |

Andrea, Saltelli | JRC Ispra |

Rob, Scheichl | University of Bath |

Tony, Shardlow | |

David, Silvester | University of Manchester |

Ian, Sloan | University of New South Wales |

Miroslav, Stoyanov | Florida State University |

Andrew, Stuart | CalTech |

Daniel, Tartakovsky | University of California at San Diego |

Simon, Tavener | Colorado State University |

Phillip, Taylor | University of Manchester |

Aretha, Teckentrup | University of Edinburgh |

Elisabeth, Ullmann | TU Freiberg |

Hans-Werner, Van Wyk | Virginia Tech |

Erik, von Schwerin | KAUST |

Junping, Wang | NSF |

Clayton, Webster | Oak Ridge National Laboratory |

Karen, Willcox | MIT |

Keith, Worden | University of Sheffield |

Dongbin, Xiu | Purdue University |

Nicholas, Zabaras | Cornell University |