Model Validation in Scientific Computing: Considering Robustness to Non-probabilistic Uncertainty in the Input Parameters

The origin of the term validation traces to the Latin valere, meaning worth. In the context of scientific computing, validation aims to determine the worthiness of a model in regard to its support of critical decision making. This determination of worthiness must occur in the face of unavoidable idealizations in the mathematical representation of the phenomena the model is intended to represent. These models are often parameterized further complicating the validation problem due to the need to determine appropriate parameter values for the imperfect mathematical representations. The determination of worthiness then becomes assessing whether an unavoidably imperfect mathematical model, subjected to poorly known input parameters, can predict sufficiently well to serve its intended purpose. To achieve this, we herein evaluate the agreement between a model's predictions and associated experiments as well as the robustness of this agreement given imperfections in both the model's mathematical representation of reality as well as its input parameter values.