11 Interfakultäre Einrichtungen

Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/12

Browse

Author: search.filters.author.Unger, BenjaminSubject: search.filters.subject.510

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    ItemOpen Access
    Identification of linear time-invariant systems with dynamic mode decomposition
    (2022) Heiland, Jan; Unger, Benjamin
    Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant under linear transformations in the image of the data matrix. If, in addition, the data are constructed from a linear time-invariant system, then we prove that DMD can recover the original dynamics under mild conditions. If the linear dynamics are discretized with the Runge–Kutta method, then we further classify the error of the DMD approximation and detail that for one-stage Runge–Kutta methods; even the continuous dynamics can be recovered with DMD. A numerical example illustrates the theoretical findings.
  • Thumbnail Image
    ItemOpen Access
    Efficient wildland fire simulation via nonlinear model order reduction
    (2021) Black, Felix; Schulze, Philipp; Unger, Benjamin
    We propose a new hyper-reduction method for a recently introduced nonlinear model reduction framework based on dynamically transformed basis functions and especially well-suited for transport-dominated systems. Furthermore, we discuss applying this new method to a wildland fire model whose dynamics feature traveling combustion waves and local ignition and is thus challenging for classical model reduction schemes based on linear subspaces. The new hyper-reduction framework allows us to construct parameter-dependent reduced-order models (ROMs) with efficient offline/online decomposition. The numerical experiments demonstrate that the ROMs obtained by the novel method outperform those obtained by a classical approach using the proper orthogonal decomposition and the discrete empirical interpolation method in terms of run time and accuracy.