Validation of physical models in the presence of uncertainty

Abstract

As the field of computational modeling continues to mature and simulation results are used to inform more critical decisions, validation of the physical models that form the basis of these simulations takes on increasing importance. While model validation is not a new concept, traditional techniques such as visual comparison of model outputs and experimental observations without accounting for uncertainties are insufficient for assessing model validity, particularly for the case where the intended purpose of the model is to make extrapolative predictions. This work provides an overview of validation of physical models in the presence of uncertainty. In particular, two issues are discussed: Comparison of model outputs and observational data when both the model and observations are uncertain, and the process of building confidence in extrapolative predictions. For comparing uncertain model outputs and data, a Bayesian probabilistic perspective is adopted in which the problem of assessing the consistency of the model and the observations becomes one of Bayesian model checking. A broadly applicable approach to Bayesian model checking for physical models is described. For validating extrapolative predictions, a recently developed process termed predictive validation is discussed. This process relies on the ideas of Bayesian model checking but goes beyond comparison of model and data to assess the conditions necessary for reliable extrapolation using physics-based models.