Extra seminar Computational Mathematics - Dr. J. Köllermeier University of Leuven

Title: Hierarchical moment models for self-learning simulations in fluid dynamics

Abstract:

Applications of artificial intelligence are characterized by a large variety of separate models for specific tasks. The same holds true for multi-scale fluid models, e.g., in atmospheric re-entry flows and geophysical flows. This model variety poses significant difficulties for the generalization towards multi-purpose models as the differences between models lead to problems both for the mathematical analysis and for the numerical computation. We thus need to rethink mathematical modelling for future numerical simulations.

In this talk, I will introduce hierarchical moment models as a flexible way to derive hierarchies of models in fluid dynamics and other applications. The general derivation procedure results in structural similarities of the models, which facilitate physical insight, model adaptivity, and the development of suitable numerical methods. Based on rarefied gases and shallow flows, I will exemplify the hierarchical moment approach and highlight runtime and accuracy improvements with respect to existing models using numerical results.

In the end, I will outline how these hierarchical moment models can be used adaptively as self-learning models with the help of control or data-driven approaches.