Reliability of computational science

Ivo M. Babuska · Fabio Nobile · Raul F. Tempone

55 citations0/0 files storedNumerical Methods for Partial Differential Equations

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Probabilistic and Robust Engineering Design Scientific Measurement and Uncertainty Evaluation Risk and Safety Analysis

Abstract

Abstract Today's computers allow us to simulate large, complex physical problems. Many times the mathematical models describing such problems are based on a relatively small amount of available information such as experimental measurements. The question arises whether the computed data could be used as the basis for decision in critical engineering, economic, and medicine applications. The representative list of engineering accidents occurred in the past years and their reasons illustrate the question. The paper describes a general framework for verification and validation (V&V) which deals with this question. The framework is then applied to an illustrative engineering problem, in which the basis for decision is a specific quantity of interest, namely the probability that the quantity does not exceed a given value. The V&V framework is applied and explained in detail. The result of the analysis is the computation of the failure probability as well as a quantification of the confidence in the computation, depending on the amount of available experimental data. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 753–784, 2007

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References

1998Verification and Validation in Computational Science and Engineering 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations 1967Verification of Computer Simulation Models 2004Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation 1998Validation in Simulation: Various Positions in the Philosophy of Science 2016Probabilistic Techniques in Exposure Assessment 2003SOLVING STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS BASED ON THE EXPERIMENTAL DATA

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2011INTERNATIONAL ASSESSMENT OF RESEARCH AND DEVELOPMENT IN SIMULATION-BASED ENGINEERING AND SCIENCE 2020Stochastic analysis and validation under aleatory and epistemic uncertainties 2011ORTHOGONAL BASES FOR POLYNOMIAL REGRESSION WITH DERIVATIVE INFORMATION IN UNCERTAINTY QUANTIFICATION 2012Static Frame Model Validation with Small Samples Solution Using Improved Kernel Density Estimation and Confidence Level Method 2008New Bayesian Updating Methodology for Model Validation and Robust Predictions Based on Data from Hierarchical Subsystem Tests

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