IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v166y2019icp76-92.html
   My bibliography  Save this article

Model order reduction for random nonlinear dynamical systems and low-dimensional representations for their quantities of interest

Author

Listed:
  • Pulch, Roland

Abstract

We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The state or inner variables as well as a quantity of interest are expanded into series with orthogonal basis functions like the polynomial chaos expansions, for example. On the one hand, the stochastic Galerkin method yields a large coupled dynamical system. On the other hand, a stochastic collocation method, which uses a quadrature rule or a sampling scheme, can be written in the form of a large weakly coupled dynamical system. We apply projection-based methods of nonlinear model order reduction to the large systems. A reduced-order model implies a low-dimensional representation of the quantity of interest. We focus on model order reduction by proper orthogonal decomposition. The error of a best approximation located in a low-dimensional subspace is analysed. We illustrate results of numerical computations for test examples.

Suggested Citation

  • Pulch, Roland, 2019. "Model order reduction for random nonlinear dynamical systems and low-dimensional representations for their quantities of interest," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 76-92.
  • Handle: RePEc:eee:matcom:v:166:y:2019:i:c:p:76-92
    DOI: 10.1016/j.matcom.2019.01.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475419301442
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2019.01.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Pulch, Roland, 2018. "Model order reduction and low-dimensional representations for random linear dynamical systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 1-20.
    2. Pulch, Roland & ter Maten, E. Jan W. & Augustin, Florian, 2015. "Sensitivity analysis and model order reduction for random linear dynamical systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 111(C), pages 80-95.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li, Yanpeng & Jiang, Yaolin & Yang, Ping, 2021. "Time domain model order reduction of discrete-time bilinear systems with Charlier polynomials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 905-920.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pulch, Roland, 2024. "Stochastic Galerkin method and port-Hamiltonian form for linear dynamical systems of second order," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 187-197.
    2. Pulch, Roland, 2018. "Model order reduction and low-dimensional representations for random linear dynamical systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 1-20.
    3. Delagnes, T. & Henneron, T. & Clenet, S. & Fratila, M. & Ducreux, J.P., 2023. "Comparison of reduced basis construction methods for Model Order Reduction, with application to non-linear low frequency electromagnetics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 470-488.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:166:y:2019:i:c:p:76-92. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.