Defining predictive maturity for validated numerical simulations

The increasing reliance on computer simulations in decision-making motivates the need to formulate a commonly accepted definition for ''predictive maturity.'' The concept of predictive maturity involves quantitative metrics that could prove useful while allocating resources for physical testing and code development. Such metrics should be able to track progress (or lack thereof) as additional knowledge becomes available and is integrated into the simulations for example, through the addition of new experimental datasets during model calibration, and/or through the implementation of better physics models in the codes. This publication contributes to a discussion of attributes that a metric of predictive maturity should exhibit. It is contended that the assessment of predictive maturity must go beyond the goodness-of-fit of the model to the available test data. We firmly believe that predictive maturity must also consider the ''knobs,'' or ancillary variables, used to calibrate the model and the degree to which physical experiments cover the domain of applicability. The emphasis herein is placed on translating the proposed attributes into mathematical properties, such as the degree of regularity and asymptotic limits of the maturity function. Altogether these mathematical properties define a set of constraints that the predictive maturity function must satisfy. Based on these constraints, we propose a Predictive Maturity Index (PMI). Physical datasets are used to illustrate how the PMI quantifies the maturity of the non-linear, Preston-Tonks-Wallace model of plastic deformation applied to beryllium, a light-weight, high-strength metal. The question ''does collecting additional data improve predictive power?'' is answered by computing the PMI iteratively as additional experimental datasets become available. The results obtained reflect that coverage of the validation domain is as important to predictive maturity as goodness-of-fit. The example treated also indicates that the stabilization of predictive maturity can be observed, provided that enough physical experiments are available.

[1]  François M. Hemez,et al.  ANSWERING THE QUESTION OF SUFFICIENCY: HOW MUCH UNCERTAINTY IS ENOUGH? , 2007 .

[2]  Osman Balci,et al.  A collaborative evaluation environment for credibility assessment of modeling and simulation applications , 2002, Proceedings of the Winter Simulation Conference.

[3]  François M. Hemez,et al.  Info-gap robustness for the correlation of tests and simulations of a non-linear transient , 2004 .

[4]  Dean L. Preston,et al.  Model of plastic deformation for extreme loading conditions , 2003 .

[5]  R W Logan,et al.  Verification & Validation: Goals, Methods, Levels, and Metrics , 2003 .

[6]  A. O'Hagan,et al.  Predicting the output from a complex computer code when fast approximations are available , 2000 .

[7]  D. Higdon,et al.  Computer Model Calibration Using High-Dimensional Output , 2008 .

[8]  John E. Mottershead,et al.  Model Updating In Structural Dynamics: A Survey , 1993 .

[9]  R. Logan,et al.  Verification & validation : Process and levels leading to qualitative or quantitative validation statements , 2004 .

[10]  F. Hemez,et al.  REVIEW AND ASSESSMENT OF MODEL UPDATING FOR NON-LINEAR, TRANSIENT DYNAMICS , 2001 .

[11]  Matthew F. Barone,et al.  Measures of agreement between computation and experiment: Validation metrics , 2004, J. Comput. Phys..

[12]  Brian Williams,et al.  A Bayesian calibration approach to the thermal problem , 2008 .

[13]  Timothy G. Trucano,et al.  Verification and validation. , 2005 .

[14]  Timothy G. Trucano,et al.  Predictive Capability Maturity Model for computational modeling and simulation. , 2007 .

[15]  François M. Hemez,et al.  A BRIEF TUTORIAL ON VERIFICATION AND VALIDATION , 2003 .

[16]  Vicente J. Romero,et al.  Description of the Sandia Validation Metrics Project , 2001 .

[17]  François M. Hemez,et al.  AND ASSESSMENT OF MODEL UPDATING FOR NONLINEAR , TRANSIENT DYNAMICS , 1999 .

[18]  Leonard E. Schwer,et al.  An overview of the PTC 60/V&V 10: guide for verification and validation in computational solid mechanics , 2007, Engineering with Computers.

[19]  Didier Sornette,et al.  A General Strategy for Physics-Based Model Validation Illustrated with Earthquake Phenomenology, Atmospheric Radiative Transfer, and Computational Fluid Dynamics , 2007, 0710.0317.