3 citations · 6 across the 15 of their papers we have counts for
7 papers · 1 filter
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…
Parametric model reduction of mean-field and stochastic systems via higher-order action matching
Jules Berman, Tobias Blickhan, Benjamin Peherstorfer
The aim of this work is to learn models of population dynamics of physical systems that feature stochastic and mean-field effects and that depend on physics parameters. The learned…
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…
Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equations
Huan Zhang, Yifan Chen, Eric Vanden-Eijnden +1
Sequential-in-time methods solve a sequence of training problems to fit nonlinear parametrizations such as neural networks to approximate solution trajectories of partial different…
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…
CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equations
Jules Berman, Benjamin Peherstorfer
This work introduces reduced models based on Continuous Low Rank Adaptation (CoLoRA) that pre-train neural networks for a given partial differential equation and then continuously…