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In this work, we focus on reduced order modeling (ROM) techniques forhyperbolic conservation laws with application in uncertainty quantification(UQ) and in conjunction with the well-known Monte Carlo sampling method.Because we are interested in model order reduction (MOR) techniques forunsteady non-linear hyperbolic systems of conservation laws, which involvemoving waves and discontinuities, we explore the parameter-time framework andin the same time we deal with nonlinearities using a POD-EIM-Greedy algorithm\cite{Drohmann2012}. We provide under some hypothesis an error indicator, whichis also an error upper bound for the difference between the high fidelitysolution and the reduced one.

Model order reduction for parametrized nonlinear hyperbolic problems as an application to Uncertainty Quantification