8 citations · 23 across the 18 of their papers we have counts for
4 papers · 2 filters
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…