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13:30   Zuiderduinzaal: Keynote: Mishra Siddhartha, ETH Zurich, Switzerland 13:30 45 mins Statistical solutions and uncertainty quantification for hyperbolic systems of conservation laws Mishra Siddhartha Abstract: Hyperbolic systems of conservation laws arise in a wide variety of problems in physics and engineering. Uncertainty quantification (UQ) is essential for these models on account of measurement errors for inputs and possible chaotic dynamics of the system. However, efficient UQ is very challenging due to the low regularity of underlying solutions due to shocks and turbulence as well as the need for possibly high dimensional description of the probability space. We present the recently proposed concept of statistical solutions as a suitable UQ framework for these PDEs. Statistical solutions are time-parameterized probability measures on integrable functions and we present a convergent Monte Carlo algorithm for computing them. Moreover, we will present several alternatives to accelerate the baseline Monte Carlo method. These include Multi-level Monte Carlo (MLMC), Quasi-Monte Carlo (QMC) and machine learning algorithms and we evaluate their applicability in this context.