MUQ: The MIT Uncertainty Quantification Library

Forward and Backward Uncertainty Quantification in Optimization

This contribution gathers some of the ingredients presented during the Iranian Operational Research community gathering in Babolsar in 2019.It is a collection of several previous publications on how to set up an uncertainty quantification (UQ) cascade with ingredients of growing computational complexity for both forward and reverse uncertainty propagation.

Monotonicity - preserving uncertainty quantification

The need for accurate resolution of shock waves in Computational Fluid Dynamics (CFD) is a major driver in the development of robust numerical methods for approximating discontinuities. The Local Extremum Diminishing (LED) robustness concept has, for example, been introduced into the Finite Volume Method (FVM) for preventing overshoots at discontinuities (Jameson 1993). However, LED schemes hav...

Optimal Uncertainty Quantification

We propose a rigorous framework for uncertainty quantification (UQ) in which the UQ objectives and its assumptions/information set are brought to the forefront. This framework, which we call optimal uncertainty quantification (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as v...

Introduction to Uncertainty Quantification

Convex Optimal Uncertainty Quantification

Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an OUQ problem can be reformulated as a finite-dimensional convex optimization problem, for which efficient numerical solutions can be obtained. The sufficient ...