New ideas in optimal adaptivity: Time-dependent problems and Neural networksHausdorff Colloquium

by Michael Feischl (TU Wien)

Wednesday Jun 10, 2026, 3:00 PM → 4:30 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Abstract:

The classical theory of adaptive finite element methods is tailored to stationary PDEs. Recent developments made it possible to prove optimality results also for 

simple time-dependent PDEs like the heat equation, and also non-linear ODEs. These methods and ideas can be used to design and train neural networks, that have an almost optimal

number of parameters to reach a certain approximation error. The talk will give an overview over the approach, present key steps in the proofs, and show numerical examples.

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