Uncertainty Quantification

Schematic of the Yearly Assessment Cycle, showing how QMU drives and coordinates the experimental, computational and modeling efforts. (click to enlarge)

The formulation of rigorous and affective uncertainty quantification (UQ) methodology is a grand challenge of our time. Such UQ analysis is an integral and indispensable part of Predictive Science. The certification of complex engineering systems is sometimes described in terms of quantification of margins and uncertainties (QMU). Compelling as this picture is, the challenge of rendering it in rigorous and precise mathematical terms—and of developing a set of computational tools enabling its efficient implementation—is quite considerable. By rigorous UQ we specifically mean a set of mathematically provable inequalities that provide rigorous upper bounds for the probability of failure of the system. While verification and validation (V&V) and UQ have been the subject of extensive research in recent years, a rigorous mathematical and computational framework of the type just described does not appear to had been devised to date.

A central focus of the Caltech Center is the development of UQ methodology that rigorously bounds uncertainties in performance measures in a computationally tractable manner. This objective is the main intellectual driver of the center that shapes its remaining thrusts, including physics modeling, the development of numerical capability and the computational and experimental campaigns. The theoretical foundation underlying the proposed approach to UQ, based on the use of so-called concentration-of-measure (CoM) inequalities, has been recently developed at Caltech. The degree of mathematical rigor and the extent of integration between experiment, simulation and uncertainty quantification contemplated in this approach are unprecedented and are expected to lead to significant advances in the field, both in theory and in praxis.