no code implementations • 26 Mar 2024 • Jan Heiland, Yongho Kim, Steffen W. R. Werner
Polytopic autoencoders provide low-dimensional parametrizations of states in a polytope.
no code implementations • 19 Jan 2024 • Jan Heiland, Yongho Kim
With the advancement of neural networks, there has been a notable increase, both in terms of quantity and variety, in research publications concerning the application of autoencoders to reduced-order models.
no code implementations • 1 Jun 2023 • Jingjing Zhang, Jan Heiland, Peter Benner, Xin Du
We show that our FDSC scheme is capable to approximate the solid in-band performance while maintaining acceptable out-of-band performance with regard to global time horizons as well as localized time horizons.
no code implementations • 2 Feb 2023 • Yongho Kim, Jan Heiland
Simulations of large-scale dynamical systems require expensive computations.
1 code implementation • 13 Oct 2020 • Peter Benner, Pawan Goyal, Jan Heiland, Igor Pontes Duff
To that end, we utilize the intrinsic structure of the Navier-Stokes equations for incompressible flows and show that learning dynamics of the velocity and pressure can be decoupled, thus leading to an efficient operator inference approach for learning the underlying dynamics of incompressible flows.
no code implementations • 20 Nov 2018 • Maximilian Behr, Peter Benner, Jan Heiland
The differential Sylvester equation and its symmetric version, the differential Lyapunov equation, appear in different fields of applied mathematics like control theory, system theory, and model order reduction.
Numerical Analysis 15A24, 65F60, 65L05