A Computational Infrastructure for Reliable Computer Simulations

Abstract

Abstract. The reliability of computer simulations of physical events or of engineering systems has emerged as the single most critical issue facing advancements in computational engineering and science. Without concrete and quantifiable measures of reliability, the confidence and usefulness of computer predictions are severely limited and the value of computer simulation, in general, is greatly diminished. This paper describes a mathematical and computational infrastructure for the systematic validation of computer simulations of complex physical systems and presents procedures for the integration of computer-based verification and validation processes into simulations. A general class of applications characterized by variational boundary-value problems in continuum mechanics is considered, but the approach is valid for virtually all types of models used in simulations. To simulate a particular feature or attribute of a physical event, four basic concepts are used: 1) hierarchical modeling and a posteriori estimation of modeling error, 2) a posteriori error estimation of approximation error, 3) quantification of uncertainty in the data and in the predicted response, and 4) the development of dynamic a data management paradigm, based on code composition of associated code interfaces and use of annotated source code. The result is a computational framework for computing bounds on, and estimating accuracy of, computer predictions of user-specified features of the response of physical systems.

A General Strategy for Physics-Based Model Validation Illustrated with Earthquake Phenomenology, Atmospheric Radiative Transfer, and Computational Fluid Dynamics

“…It may actually be advantageous to develop a hierarchical modeling framework. In this respect, Oden et al [116] proposed to use hierarchical modeling as a mathematical structure that can be useful in directing validation studies. In this construction, a class of models of events of interest is defined in which one identifies a "fine" model that possesses a level of sophistication high enough to adequately capture the event of interest with good accuracy.…”

“…Using the fine model output as a datum, the error in the solution of ever coarser models can be estimated and controlled, with the goal of obtaining a model best suited for the simulation goal at hand. The essential components of this program are the following [116]:…”

On Error Estimators and Bayesian Approaches in Computational Model Validation

“…Surveys of the extensive literature existing on error estimation for finite element methods can be found in (Noor & Babuška, 1987) (Olgierd C. Zienkiewicz & Taylor, 1994) (J. Tinsley Oden & Demkowicz, 1989) (Zhu, 1997) (Ainsworth & Oden, 1997). Mostly, the literature deals with discretization error, and the development of methods for estimating modeling error has appeared very recently (J. Tinsley Oden & Vemaganti, 2000) (J. Tinsley et al, 2003.…”