8 citations · 23 across the 18 of their papers we have counts for
20 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…
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…
Empirical sparse regression on quadratic manifolds
Paul Schwerdtner, Serkan Gugercin, Benjamin Peherstorfer
Approximating field variables and data vectors from sparse samples is a key challenge in computational science. Widely used methods such as gappy proper orthogonal decomposition an…
Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction
Paul Schwerdtner, Prakash Mohan, Aleksandra Pachalieva +3
This work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in-situ analysis of numerical simulation data on the Petab…
Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction
Paul Schwerdtner, Benjamin Peherstorfer
Dimensionality reduction on quadratic manifolds augments linear approximations with quadratic correction terms. Previous works rely on linear approximations given by projections on…
Nonlinear embeddings for conserving Hamiltonians and other quantities with Neural Galerkin schemes
Paul Schwerdtner, Philipp Schulze, Jules Berman +1
This work focuses on the conservation of quantities such as Hamiltonians, mass, and momentum when solution fields of partial differential equations are approximated with nonlinear…
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…
Fixed-Order H-Infinity Controller Design for Port-Hamiltonian Systems
Paul Schwerdtner, Matthias Voigt
We present a new fixed-order H-infinity controller design method for potentially large-scale port-Hamiltonian (pH) plants. Our method computes controllers that are also pH (and thu…
Structured Optimization-Based Model Order Reduction for Parametric Systems
Paul Schwerdtner, Manuel Schaller
We develop an optimization-based algorithm for parametric model order reduction (PMOR) of linear time-invariant dynamical systems. Our method aims at minimizing the $\mathcal{H}_\i…
Structure-Preserving Model Order Reduction for Index Two Port-Hamiltonian Descriptor Systems
Tim Moser, Paul Schwerdtner, Volker Mehrmann +1
We present a new optimization-based structure-preserving model order reduction (MOR) method for port-Hamiltonian descriptor systems (pH-DAEs) with differentiation index two. Our me…
Structure-Preserving Model Order Reduction for Index One Port-Hamiltonian Descriptor Systems
Paul Schwerdtner, Tim Moser, Volker Mehrmann +1
We develop optimization-based structure-preserving model order reduction (MOR) methods for port-Hamiltonian (pH) descriptor systems of differentiation index one. Descriptor systems…
Adaptive Sampling for Structure Preserving Model Order Reduction of Port-Hamiltonian Systems
Paul Schwerdtner, Matthias Voigt
We present an adaptive sampling strategy for the optimization-based structure preserving model order reduction (MOR) algorithm developed in [Schwerdtner, P. and Voigt, M. (2020). S…
Port-Hamiltonian System Identification from Noisy Frequency Response Data
Paul Schwerdtner
We present a new method for the identification of linear time-invariant passive systems from noisy frequency response data. In particular, we propose to fit a parametrized port-Ham…
Risk Assessment for Machine Learning Models
Paul Schwerdtner, Florens Greßner, Nikhil Kapoor +5
In this paper we propose a framework for assessing the risk associated with deploying a machine learning model in a specified environment. For that we carry over the risk definitio…
SOBMOR: Structured Optimization-Based Model Order Reduction
Paul Schwerdtner, Matthias Voigt
Model order reduction (MOR) methods that are designed to preserve structural features of a given full order model (FOM) often suffer from a lower accuracy when compared to their no…
Structure-Preserving Model Reduction for Dissipative Mechanical Systems
Rebekka S. Beddig, Peter Benner, Ines Dorschky +4
Suppressing vibrations in mechanical systems, usually described by second-order dynamical models, is a challenging task in mechanical engineering in terms of computational resource…
Large-Scale Computation of -Norms by a Greedy Subspace Method
Nicat Aliyev, Peter Benner, Emre Mengi +2
We are concerned with the computation of the -norm for an -function of the form , where the middle factor is t…