Embracing the Epistemic: A Practical VVUQ Framework

Most model validation paradigms presume that uncertainty quantification will be informed by data with sufficient sample size to generate probability density functions. Thus, most frameworks assume aleatory uncertainty as fundamental. We argue that this is rare in many engineering applications, where model inputs are more likely to be informed by sparse data, i.e. epistemic uncertainty. As such, there is a need for a practical framework that acknowledges this reality. In this study, we propose a framework in which all uncertainty is treated as epistemic, represented by mathematical intervals. This unconventional choice has several advantages. Among these are the possibility of efficient uncertainty propagation using optimization algorithms rather than sampling methods. Given that model form and numerical uncertainties are usually considered epistemic by nature, our approach leads to a self-consistent treatment of uncertainty in the validation process. We explore several possible interval-based validation metrics that are appropriate for this methodology. A hypothetical example problem is used to demonstrate the approach and compare the performance of the metrics.