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Explore a comprehensive lecture on data-driven high fidelity Computational Fluid Dynamics (CFD) delivered by Andrea Beck at the Centre International de Rencontres Mathématiques in Marseille, France. Delve into advanced topics such as shock droplet interaction, icing, multiscale analysis, and high-order schemes. Examine the intricacies of Discontinuous Galerkin (DG) methods, including their derivation, nonlinear stability, and application to nonsmooth solutions. Investigate cutting-edge concepts in scientific machine learning and its controversial applications in CFD. Learn about dynamic load balancing, data tracking, and reproducible computational workflows. Gain insights into supervised learning, predictions in machine learning CFD, and data compression techniques. This lecture offers a deep dive into the intersection of advanced mathematics, computational methods, and machine learning in the field of fluid dynamics.