Novel Mathematical and Computational Techniques for Robust Uncertainty Quantification.

摘要

Uncertainty quantification refers to a broad set of techniques for understanding the impact of uncertainties in complicated mechanical and physical systems. In this context 'uncertainty' can take on many meanings. Aleatoric uncertainty refers to inherent uncertainty due to stochastic or probabilistic variability. This type of uncertainty is irreducible in that there will always be positive variance since the underlying variables are truly random. Epistemic uncertainty refers to limited knowledge we may have about the model or system. This type of uncertainty is reducible in that if we have more information, e.g., take more measurements, then this type of uncertainty can be reduced. For many problems where uncertainty quantification is important, the acquisition of data is difficult or expensive. The epistemic uncertainty cannot be removed entirely, and so one needs modeling and computational techniques which can also accommodate this form of uncertainty.