Abstract

Uncertainty Quantification lies at the interface of applied mathematics, probability, computation and applied sciences, and has been called ``the end-to-end study of the reliability of scientific inferences.’’ It is the understanding of how information (or uncertainty) propagates through systems to produce information (or uncertainty) about output quantities of interest (e.g. structural failure risks or financial portfolio returns), and corresponding inverse problems. In many real-world applications, this information propagation spans multiple components or scales and is probabilistic in nature, but is complicated by non-negligible uncertainty about which probability distributions and models are the ``correct’’ ones. In the Optimal UQ (OUQ) framework, these problems are formalized as optimization problems over infinite-dimensional feasible sets of probability measures and transfer functions.