8 papers
Two-Parameter Flows for Learning Population Dynamics of Physical Systems
Paul Schwerdtner, Tobias Blickhan, Benjamin Peherstorfer
This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory informat…
Randomized time stepping of nonlinearly parametrized solutions of evolution problems
Yijun Dong, Paul Schwerdtner, Benjamin Peherstorfer
The Dirac-Frenkel variational principle is a widely used building block for using nonlinear parametrizations in the context of model reduction and numerically solving partial diffe…
Hankel Singular Value Regularization for Highly Compressible State Space Models
Paul Schwerdtner, Jules Berman, Benjamin Peherstorfer
Deep neural networks using state space models as layers are well suited for long-range sequence tasks but can be challenging to compress after training. We use that regularizing th…
Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reduction
Paul Schwerdtner, Prakash Mohan, Julie Bessac +2
Quadratic manifolds for nonintrusive reduced modeling are typically trained to minimize the reconstruction error on snapshot data, which means that the error of models fitted to th…
Energy matching in reduced passive and port-Hamiltonian systems
Tobias Holicki, Jonas Nicodemus, Paul Schwerdtner +1
It is well known that any port-Hamiltonian (pH) system is passive, and conversely, any minimal and stable passive system has a pH representation. Nevertheless, this equivalence is…
Nonlinear model reduction with Neural Galerkin schemes on quadratic manifolds
Philipp Weder, Paul Schwerdtner, Benjamin Peherstorfer
Leveraging nonlinear parametrizations for model reduction can overcome the Kolmogorov barrier that affects transport-dominated problems. In this work, we build on the reduced dynam…