HOME    »    PROGRAMS/ACTIVITIES    »    Annual Thematic Program
Fall 1999
IMA Hot Topics Workshop
Decision Making under Uncertainty: Assessment of the Reliability of Mathematical Models
September 16-17, 1999

Partially supported by General Motors.


James Cavendish
Research and Development Center
General Motors Corporation


James M. Hyman
Los Alamos National Laboratory

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:

  • Sources of uncertainty
  • Sensitivity analysis
  • Stability and robustness
  • Experimental validation
  • Statistical analysis of computer experiments
  • A posteori error estimation

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.


All talks are in the IMA EAST Seminar Room, Lind Hall 409 unless otherwise noted.
Thursday Friday
8:30 am Coffee and Registration IMA East Lind Hall 400
9:10 am Willard Miller, Fadil Santosa, Fred Dulles,
and James Cavendish
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
3:50-4:30 pm Discussion
6:00 pm Workshop Dinner
Bona Restaurant
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 California-Santa 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)

3:50-5:00 pm Discussion

Thursday Friday


as of 9/16/99
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 Kimberly-Clark 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 California-Santa 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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