ASSESSING THE RELIABILITY
OF COMPLEX MODELS

img
MATHEMATICAL AND STATISTICAL FOUNDATIONS OF VERIFICATION,
VALIDATION, AND UNCERTAINTY QUANTIFICATION
img

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



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement



Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.

OCR for page R1
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

OCR for page R1
THE NATIONAL ACADEMIES PRESS 500 Fifth Street, NW Washington, DC 20001 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, conclu - sions, 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 Statisti - cal 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

OCR for page R1
The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in sci - entific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Ralph J. Cicerone is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. Charles M. Vest is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Harvey V. Fineberg is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad com - munity of science and technology with the Academy’s purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the gov - ernment, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Ralph J. Cicerone and Dr. Charles M. Vest a re chair and vice chair, respectively, of the National Research Council. www.national-academies.org

OCR for page R1

OCR for page R1
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 v

OCR for page R1
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 vi

OCR for page R1
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 vii

OCR for page R1
viii ACKNOWLEDGMENTS 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

OCR for page R1
Contents SUMMARY 1 1 INTRODUCTION 7 1.1 Overview and Study Charter, 7 1.2 VVUQ Definitions, 8 1.3 Scope of This Study, 9 1.3.1 Focus on Prediction with Physics/Engineering Models, 9 1.3.2 Focus on Mathematical and Quantitative Issues, 9 1.4 VVUQ Processes and Principles, 10 1.4.1 Verification, 10 1.4.2 Validation, 11 1.4.3 Prediction, 11 1.4.4 Uncertainty Quantification, 12 1.4.5 Key VVUQ Principles, 13 1.5 Uncertainty and Probability, 13 1.6 Ball-Drop Case Study, 14 1.6.1 The Physical System, 16 1.6.2 The Model, 16 1.6.3 Verification, 16 1.6.4 Sources of Uncertainty, 16 1.6.5 Propagation of Input Uncertainties, 17 1.6.6 Validation and Prediction, 17 1.6.7 Making Decisions, 17 1.7 Organization of This Report, 18 1.8 References, 18 2 SOURCES OF UNCERTAINTY AND ERROR 19 2.1 Introduction, 19 2.2 Projectile-Impact Example Problem, 20 ix

OCR for page R1
x CONTENTS 2.3 Initial Conditions, 23 2.4 Level of Fidelity, 24 2.5 Numerical Accuracy, 24 2.6 Multiscale Phenomena, 25 2.7 Parametric Settings, 26 2.8 Choosing a Model Form, 26 2.9 Summary, 26 2.10 Climate-Modeling Case Study, 27 2.10.1 Is Formal UQ Possible for Truly Complex Models?, 28 2.10.2 Future Directions for Research and Teaching Involving UQ for Climate Models, 29 2.11 References, 30 3 VERIFICATION 31 3.1 Introduction, 31 3.2 Code Verification, 32 3.3 Solution Verification, 33 3.4 Summary of Verification Principles, 35 3.5 References, 36 4 EMULATION, REDUCED-ORDER MODELING, AND FORWARD PROPAGATION 37 4.1 Approximating the Computational Model, 38 4.1.1 Computer Model Emulation, 38 4.1.2 Reduced-Order Models, 39 4.2 Forward Propagation of Input Uncertainty, 41 4.3 Sensitivity Analysis, 42 4.3.1 Global Sensitivity Analysis, 43 4.3.2 Local Sensitivity Analysis, 44 4.4 Choosing Input Settings for Ensembles of Computer Runs, 46 4.5 Electromagnetic Interference in a Tire Pressure Sensor: Case Study, 46 4.5.1 Background, 46 4.5.2 The Computer Model, 46 4.5.3 Robust Emulators, 48 4.5.4 Representative Result, 49 4.6 References, 49 5 MODEL VALIDATION AND PREDICTION 52 5.1 Introduction, 52 5.1.1 Note Regarding Methodology, 54 5.1.2 The Ball-Drop Example Revisited, 57 5.1.3 Model Validation Statement, 58 5.2 Uncertainties in Physical Measurements, 59 5.3 Model Calibration and Inverse Problems, 60 5.4 Model Discrepancy, 63 5.5 Assessing the Quality of Predictions, 67 5.6 Automobile Suspension Systems Case Study, 70 5.6.1 Background, 70 5.6.2 The Computer Model, 70 5.6.3 The Process Being Modeled and Data, 70 5.6.4 Modeling the Uncertainties, 71 5.6.5 Analysis and Results, 72 5.7 Inference from Multiple Computer Models, 74

OCR for page R1
xi CONTENTS 5.8 Exploiting Multiple Sources of Physical Observations, 75 5.9 PECOS Case Study, 75 5.9.1 Overview, 75 5.9.2 Verification, 76 5.9.3 Code Verification, 76 5.9.4 Solution Verification, 77 5.9.5 Validation, 78 5.10 Rare, High-Consequence Events, 79 5.11 Conclusion, 80 5.12 References, 83 6 MAKING DECISIONS 86 6.1 Overview, 86 6.2 Decisions Within VVUQ Activities, 86 6.3 Decisions Based on VVUQ Information, 87 6.4 Decision Making Informed by VVUQ in the Stockpile Stewardship Program, 88 6.5 Decision Making Informed by VVUQ at the Nevada National Security Site, 90 6.5.1 Background, 90 6.5.2 The Physical System, 91 6.5.3 Computational Modeling of the Physical System, 92 6.5.4 Parameter Estimation, 92 6.5.5 Making (Extrapolative) Predictions and Describing Uncertainty, 93 6.5.6 Reporting Results to Decision Makers and Stakeholders, 93 6.6 Summary, 93 6.7 References, 94 7 NEXT STEPS IN PRACTICE, RESEARCH, AND EDUCATION FOR VERIFICATION, 95 VALIDATION, AND UNCERTAINTY QUANTIFICATION 7.1 VVUQ Principles and Best Practices, 95 7.1.1 Verification Principles and Best Practices, 96 7.1.2 Validation and Prediction Principles and Best Practices, 97 7.2 Principles and Best Practices in Related Areas, 98 7.2.1 Transparency and Reporting, 98 7.2.2 Decision Making, 99 7.2.3 Software, Tools, and Repositories, 99 7.3 Research for Improved Mathematical Foundations, 100 7.3.1 Verification Research, 100 7.3.2 UQ Research, 101 7.3.3 Validation and Prediction Research, 102 7.4 Education Changes for the Effective Integration of VVUQ, 103 7.4.1 VVUQ at the University, 103 7.4.2 Spreading the Word, 106 7.5 Closing Remarks, 106 7.6 References, 106 APPENDIXES A Glossary 109 B Agendas of Committee Meetings 120 C Committee Biographies 124 D Acronyms 130

OCR for page R1