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James Cavendish
Research and Development Center
General Motors Corporation
jcavendi@hp.ma.gmr.com
and
James M. Hyman
Los Alamos National Laboratory
mac@morita.lanl.gov
Mathematical modeling, particularly in the form of numerical simulation, has become increasingly important in engineering and industrial applications. The ability to model and predict behavior of systems has allowed engineers to design products without building prototypes, and therefore shortening the length of the design cycle. The approach has the added advantage that it reduces the cost of a design process, while allowing the engineer to explore many designs in a short time span.
While there are a number of successful products that have been designed with the aid of mathematical modeling, what is less clear is the extent to which a designer can rely on a mathematical model. There are several sources of uncertainty in a numerical simulation. For example the parameters entering a given model, such as geometrical description, material properties, excitations, are usually known only up to some level of accuracy. Moreover, there are situations when parameters in a problem of interest are beyond the range in which we can "trust" a mathematical model. Many computer simulations are approximate solutions to an underlying continuous system. While we often can validate an approximate solution for a given problem by comparing the output with carefully obtained experimental data, there are clear limitations to the discretization level in the approximation, and hence the ultimate accuracy of a simulation. These factors suggest that most numerical simulations must be used carefully in any decision process, and that uncertainty in the simulations can be introduced by a variety of sources.
This workshop has been organized to address the question of how to assess the reliability of a mathematical model. The participants will be researchers from academia and industry with expertise in numerical analysis and scientific computing, experimental validation, applied statistics. It is meant to provide a forum for discussion of sources of uncertainty, and ways of assessing their impact on a numerical model. The workshop will bring leading researchers who have made contribution to the understanding of uncertainty in several areas of application.
Topics that will be addressed in this workshop are:
The goal of the workshop is to produce a document which articulates the
problems arising in the assessment of uncertainty, and set research
directions. It is hoped that future research will result in methods and
procedures for quantitative assessment of reliability of mathematical
models.
Thursday  Friday 
THURSDAY, SEPTEMBER 16  

8:30 am  Coffee and Registration  IMA East Lind Hall 400 
9:10 am 
Willard Miller, Fadil Santosa, Fred Dulles, and James Cavendish 
Introduction 
9:30 am  James M. Hyman
Los Alamos National Laboratory 
Quantifying Uncertainty and Predictability in Mathematical Models 
10:10 am  Kenneth F. Alvin
Sandia National Laboratories 
Methodologies for Treating Model Uncertainty and Discretization Error in Modeling and Simulation of Physical Systems 
10:50 am  Break  IMA East Lind Hall 400 
11:20 am  12:00 pm  Timothy G.
Trucano
Sandia National Laboratories 
Code Validation as a Reliability Problem 
2:00 pm  Timothy K.
Hasselman
ACTA Incorporated 
Effect of Total Modeling Uncertainty on the Accuracy of Numerical Simulations 
2:40 pm  Break  IMA East Lind Hall 400 
3:10 pm  Robert V. Lust
General Motors Research & Development and Planning 
Uncertainty in Mode Shape Data and its Influence on the Comparison of Test and Analysis Models 
3:504:30 pm  Discussion


6:00 pm  Workshop
Dinner

Bona Restaurant 
FRIDAY, SEPTEMBER 17  
9:15 am  Coffee  IMA East Lind Hall 400 
9:30 am  Gregory J. McRae
Massachusetts Institute of Technology 
Direct Treatment of Uncertainties in Complex Models and Decision
Making
pdf (484K) 
10:10 am  Linda R. Petzold
University of CaliforniaSanta Barbara 
Model Reduction and Assessment for Nonlinear Networked Systems 
10:50 am  Break  IMA East Lind Hall 400 
11:20 am  12:00 pm  James Glimm
SUNY at Stony Brook 
Predictability and the Quantification of Uncertainty 
2:00 pm  Max D. Morris
Iowa State University 
A Sequential Computer Experiment for Input Screening and Model Approximation 
2:40 pm  Break  IMA East Lind Hall 400 
3:10 pm  John A. Burns
Virginia Polytechnic 
Numerical Methods for Sensitivity Computations
Talk pdf (1MB) 
3:505:00 pm  Discussion

Thursday  Friday 
Name  Department  Affiliation 

Kenneth Alvin  Structural Dynamics & Vibration Control  Sandia National Laboratories 
Richard Benson  Corporate Research  Cargill Inc. 
John Burns  Mathematics  Virginia Polytechnic 
John Cafeo  General Motors Research  General Motors Corporation 
James Cavendish  Research & Development Center  General Motors Corporation 
Ben H. Chan  Commercial Insurance Research  The Hartford Financial Services Group 
Fred Dulles  Institute for Mathematics and its Applications  
James Glimm  Applied Mathematics and Statistics  SUNY at Stony Brook 
Joseph Grcar  Combustion Research Laboratory  Sandia National Laboratory 
Timothy Hasselman  ACTA Inc.  
James Hyman  Los Alamos Laboratory  
Elizabeth J. Kelly  Statistical Sciences  Los Alamos National Laboratory 
John Kerins  R&E  KimberlyClark Corporation 
Steven L. Lee  Center for Applied Scientific Computing  Lawrence Livermore National Laboratory 
Robert Lust  Electrical & Controls Integration Lab  General Motors Corporation 
Gregory McRae  Chemical Engineering  Massachusetts Institute of Technology 
Willard Miller  Institute for Mathematics and its Applications  
Alexander Morgan  GM Research & Development Center  
Max Morris  Statistics  Iowa State University 
Mark A. Oedekoven  Central Research  Cargil 
Linda Petzold  Mechanical & Environmental Engineering  University of CaliforniaSanta Barbara 
James Reneke  Mathematical Sciences  Clemson University 
Fadil Santosa  MCIM  IMA & Minnesota Center for Industrial Math 
Fred Torcaso  Applied Business Research  The Hartford Financial Services Group 
Timothy G. Trucano  Computational Physics Research & Dev., 9231  Sandia National Laboratories 
Cheng Wang  Chemical Engineering  MIT 
Yijun Wang  Mechanical Engineering  University of Illinois 
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