Validation of Physical Models in the Presence of Uncertainty

Over the last century, the field of computational modeling has grown tremendously, from virtually non-existent to pervasive. During this time, simultaneous advances in simulation algorithms and computer hardware have enabled the development and application of increasingly complicated and detailed models to represent evermore complex physical phenomena. These advances are revolutionizing the ways in which models are used in the design and analysis of complex systems, enabling simulation results to be used in support of critical design and operational decisions [25, 1]. With continued advances in models, algorithms, and hardware, numerical simulations will only become more critical in modern science and engineering. Given the importance of computational modeling, it is increasingly important to assess the reliability, in light of the purpose of a given simulation, of the models that form the basis of computational simulations. This reliability assessment is the domain of validation. While the concept of model validation is not new, it has recently received renewed attention due to the rapid growth in the use of models as a basis for making decisions [3, 5, 29]. This article provides an overview of the state-of-the-art in validation of physical models in the presence of uncertainty. In science and engineering, the word validation is often used to refer to simple comparisons between model outputs and experimental data such as plotting the model results and data on the same axes to allow visual assessment of agreement or lack thereof. While comparisons between model and data are at the core of any validation procedure, there are a number of problems with such naive comparisons.