Generative AI for Numerical Simulation and Inverse Problems: from Theory to TechnologyHausdorff Colloquium
by
Endenicher Allee 60/1-016 - Lipschitzsaal
Mathezentrum
Abstract:
We discuss applications of generative machine learning in numerical simulation both from the theoretical and numerical level. When it comes to learning on data generated by deterministic systems like turbulent flow, several amendments to statistical learning theory have to be taken care of. In particular, we have to replace the standard assumption of independent and identically distributed data with ergodicity assumptions for dynamical systems. We show that this is possible, including derivation of convergence rates. Loosely based on this conceptual basis, we present numerical studies on turbulent flow starting from state snapshots going over to dynamics learned by world models. We furthermore discuss the solution to inverse problems based on recent diagonal flow matching models and how to combine this with generative simulations into interactive and explainable generative design systems.
Website of the Hausdorff Colloquium
Herbert Koch, Johannes Alt, Jürgen Dölz