ASSESSING THE RELIABILITY
OF COMPLEX MODELS
MATHEMATICAL AND STATISTICAL FOUNDATIONS OF VERIFICATION,
VALIDATION, AND UNCERTAINTY QUANTIFICATION
Committee on Mathematical Foundations of Verification, Validation, and Uncertainty Quantification
Board on Mathematical Sciences and Their Applications
Division on Engineering and Physical Sciences
NATIONAL RESEARCH COUNCIL
OF THE NATIONAL ACADEMIES
THE NATIONAL ACADEMIES PRESS
Washington, D.C.
www.nap.edu
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NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences and with regard for appropriate balance.
This project was supported by the Department of Energy under Contracts DE-AT01-07NA78285 and DE-DT0001857, Task Order 9, and by the Air Force Office of Scientific Research under Contract FA9550-10-1-0435. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the organizations or agencies that provided support for the project.
Cover image credit: The galaxy image at the bottom is of white dwarf stars in globular cluster NGC 6397—Hubble Space Telescope. Courtesy of NASA, ESA, and H. Riches, University of British Columbia.
International Standard Book Number-13: 978-0-309-25634-6
International Standard Book Number-10: 0-309-25634-8
Additional copies of this report are available from the National Academies Press, 500 Fifth Street, NW, Keck 360, Washington, DC 20001; (800) 624-6242 or (202) 334-3313; http://www.nap.edu.
Suggested citation: National Research Council. 2012. Assessing the Reliability of Complex Models: Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification. Washington, D.C.: The National Academies Press.
Copyright 2012 by the National Academy of Sciences. All rights reserved.
Printed in the United States of America
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Advisers to the Nation on Science, Engineering, and Medicine
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COMMITTEE ON MATHEMATICAL FOUNDATIONS OF VERIFICATION, VALIDATION, AND UNCERTAINTY QUANTIFICATION
MARVIN L. ADAMS, Texas A&M University, Co-Chair
DAVID M. HIGDON, Los Alamos National Laboratory, Co-Chair
JAMES O. BERGER, Duke University
DEREK BINGHAM, Simon Fraser University
WEI CHEN, Northwestern University
ROGER GHANEM, University of Southern California
OMAR GHATTAS, University of Texas at Austin
JUAN MEZA, University of California, Merced
ERIC MICHIELSSEN, University of Michigan
VIJAYAN N. NAIR, University of Michigan
CHARLES W. NAKHLEH, Sandia National Laboratories
DOUGLAS NYCHKA, National Center for Atmospheric Research
STEPHEN M. POLLOCK, University of Michigan (retired)
HOWARD A. STONE, Princeton University
ALYSON G. WILSON, Institute for Defense Analyses
MICHAEL R. ZIKA, Lawrence Livermore National Laboratory
Staff
NEAL GLASSMAN, Study Director
MICHELLE SCHWALBE, Associate Program Officer
BARBARA WRIGHT, Administrative Assistant
BOARD ON MATHEMATICAL SCIENCES AND THEIR APPLICATIONS
C. DAVID LEVERMORE, University of Maryland, Chair
TANYA STYBLO BEDER, SBCC, Inc.
PATRICIA FLATLEY BRENNAN, University of Wisconsin-Madison
GERALD G. BROWN, U.S. Naval Postgraduate School
LOUIS ANTHONY COX, JR., Cox Associates
BRENDA L. DIETRICH, IBM T.J. Watson Research Center
CONSTANTINE GATSONIS, Brown University
DARRYLL HENDRICKS, UBS Investment Bank
KENNETH L. JUDD, The Hoover Institution
DAVID MAIER, Portland State University
JAMES C. McWILLIAMS, University of California, Los Angeles
JUAN MEZA, University of California, Merced
JOHN W. MORGAN, Stony Brook University
VIJAYAN N. NAIR, University of Michigan
CLAUDIA NEUHAUSER, University of Minnesota, Rochester
J. TINSLEY ODEN, University of Texas at Austin
DONALD G. SAARI, University of California, Irvine
J.B. SILVERS, Case Western Reserve University
GEORGE SUGIHARA, University of California, San Diego
EVA TARDOS, Cornell University
KAREN VOGTMANN, Cornell University
BIN YU, University of California, Berkeley
Staff
SCOTT WEIDMAN, Director
NEAL GLASSMAN, Senior Program Officer
MICHELLE SCHWALBE, Associate Program Officer
BARBARA WRIGHT, Administrative Assistant
Acknowledgments
This report has been reviewed in draft form by individuals chosen for their diverse perspectives and technical expertise, in accordance with procedures approved by the National Research Council’s Report Review Committee. The purpose of this independent review is to provide candid and critical comments that will assist the institution in making its published report as sound as possible and to ensure that the report meets institutional standards for objectivity, evidence, and responsiveness to the study charge. The review comments and draft manuscript remain confidential to protect the integrity of the deliberative process. We wish to thank the following individuals for their review of this report:
Andrew Booker, Boeing Corporation
Donald Haynes, Los Alamos National Laboratory
Max Morris, Iowa State University
William Oberkampf, WLO Consulting
J. Tinsley Oden, University of Texas at Austin
Elaine Oren, Naval Research Laboratory
Naomi Oreskes, University of California, San Diego
Susan Sanchez, Naval Postgraduate School
Kaspar Willam, University of Colorado at Boulder
Although the reviewers listed above have provided many constructive comments and suggestions, they were not asked to endorse the conclusions or recommendations nor did they see the final draft of the report before its release. The review of this report was overseen by Ali Mosleh. Appointed by the National Research Council, he was responsible for making certain that an independent examination of this report was carried out in accordance with institutional procedures and that all review comments were carefully considered. Responsibility for the final content of this report rests entirely with the authoring committee and the institution.
The committee also acknowledges the valuable contribution of the following individuals, who provided input at the meetings on which this report is based:
Mark Anderson, Los Alamos National Laboratory
Bilal Ayyub, University of Maryland
Chris Barrett, Virginia Tech
Louis Anthony Cox, Cox Associates
Andrew Dienstfrey, National Institute of Standards and Technology
Michael Eldred, Sandia National Laboratories
Peter Gleckler, Lawrence Livermore National Laboratory
Thuc Hoang, National Nuclear Security Administration
Richard Klein, Lawrence Livermore National Laboratory
Alex Levis, George Mason University
J. Tinsley Oden, University of Texas at Austin
Mikel Petty, University of Alabama in Huntsville
Bruce Robinson, Los Alamos National Laboratory
Susan Sanchez, Naval Postgraduate School
Christopher Sims, Princeton University
Timothy Trucano, Sandia National Laboratories
The co-chairs also thank the following individuals for their helpful discussions over the course of this study:
Donald Estep, Colorado State University
Elizabeth Keating, Los Alamos National Laboratory
James McWilliams, University of California, Los Angeles
Robert Moser, University of Texas at Austin
Habib Najm, Sandia National Laboratories
Leonard Smith, London School of Economics
Karen Willcox, Massachusetts Institute of Technology
Contents
1.1 Overview and Study Charter
1.3.1 Focus on Prediction with Physics/Engineering Models
1.3.2 Focus on Mathematical and Quantitative Issues
1.4 VVUQ Processes and Principles
1.4.4 Uncertainty Quantification
1.5 Uncertainty and Probability
1.6.5 Propagation of Input Uncertainties
1.6.6 Validation and Prediction
1.7 Organization of This Report
2.10 Climate-Modeling Case Study
2.10.1 Is Formal UQ Possible for Truly Complex Models?
2.10.2 Future Directions for Research and Teaching Involving UQ for Climate Models
3.4 Summary of Verification Principles
4 EMULATION, REDUCED-ORDER MODELING, AND FORWARD PROPAGATION
4.1 Approximating the Computational Model
4.1.1 Computer Model Emulation
4.2 Forward Propagation of Input Uncertainty
4.3.1 Global Sensitivity Analysis
4.3.2 Local Sensitivity Analysis
4.4 Choosing Input Settings for Ensembles of Computer Runs
4.5 Electromagnetic Interference in a Tire Pressure Sensor: Case Study
5 MODEL VALIDATION AND PREDICTION
5.1.1 Note Regarding Methodology
5.1.2 The Ball-Drop Example Revisited
5.1.3 Model Validation Statement
5.2 Uncertainties in Physical Measurements
5.3 Model Calibration and Inverse Problems
5.5 Assessing the Quality of Predictions
5.6 Automobile Suspension Systems Case Study
5.6.3 The Process Being Modeled and Data
5.8 Exploiting Multiple Sources of Physical Observations
5.10 Rare, High-Consequence Events
6.2 Decisions Within VVUQ Activities
6.3 Decisions Based on VVUQ Information
6.4 Decision Making Informed by VVUQ in the Stockpile Stewardship Program
6.5 Decision Making Informed by VVUQ at the Nevada National Security Site
6.5.3 Computational Modeling of the Physical System
6.5.5 Making (Extrapolative) Predictions and Describing Uncertainty
6.5.6 Reporting Results to Decision Makers and Stakeholders
7.1 VVUQ Principles and Best Practices
7.1.1 Verification Principles and Best Practices
7.1.2 Validation and Prediction Principles and Best Practices
7.2 Principles and Best Practices in Related Areas
7.2.1 Transparency and Reporting
7.2.3 Software, Tools, and Repositories
7.3 Research for Improved Mathematical Foundations
7.3.3 Validation and Prediction Research
7.4 Education Changes for the Effective Integration of VVUQ
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