8 citations · 23 across the 18 of their papers we have counts for
7 papers · 1 filter
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…
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…
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…