UQ Principes de la Quantification et de la Propagation des Incertitudes

The presentation underscored the importance of UQ in the context of High Performance Computing (HPC), Reduced Order Modelling (ROM), and other advanced computational techniques. Pasquet emphasized the need for good deterministic analysis, optimization, and the handling of complexities in simulations, particularly in CPU-intensive scenarios like the 136 simulations of USBO transient requiring a High Performance Cluster. The "Curse of Dimensionality" was highlighted in relation to mesh refinement and sampling in 3D spaces, demonstrating the challenges in achieving accurate simulations. He discussed UQ as a science of quantifying and reducing uncertainties in applications through statistical estimation, modelization, and propagation, stressing the importance of assumptions like Gaussian processes, uniform distributions, and linearity in simulations. Monte-Carlo simulations and Latin Hypercube Sampling (LHS) were compared, showcasing their effectiveness and limitations in sampling parameters and achieving convergence in simulations. Pasquet also introduced semi-analytical methods like FORM and SORM, which use standard normal distribution approximations for failure probability calculation. Permutation-Box or Random sets methods were discussed as efficient alternatives for handling uncertainties in simulations with fewer operations compared to Monte-Carlo simulations. These methods focus on calculating probabilities and sets for independent parameters. Sensitivity analysis, another critical aspect of UQ, was covered, demonstrating its utility in determining the most impactful variables in a simulation. Pasquet concluded by recommending strategies to reduce uncertainties, such as expert opinions, measurements, interval analysis, and model reduction techniques.