An Incremental Approach to Dynamic Mode Decomposition for Time-Varying Systems with Applications to a Model for Erythropoiesis

Rohleff, Jan

An Incremental Approach to Dynamic Mode Decomposition for Time-Varying Systems with Applications to a Model for Erythropoiesis

Dateien

Rohleff_2-1oisnm3469emv6.pdfGröße: 3.11 MBDownloads: 437

Datum

2020

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Bachelorarbeit

Publikationsstatus

Published

Zusammenfassung

Dynamic Mode Decomposition (DMD) is a new popular, data driven technique to identify time invariant high dimensional dynamical systems by a reduced linearized model. Throughout this thesis, we will, first of all, introduce the standard DMD framework and the Dynamic Mode Decomposition with control (DMDc). Since many applications underly time-varying dynamics, we also will introduce DMD approaches to identify high dimensional systems underlying low dimensional time-varying dynamics. Here, we will come to an approach of block computation, and thereupon we will finally introduce the Online DMD. Considering the different approaches it will turn out, that there does not exist the perfect approach, instead it is depending on the given data. To analyze the different approaches of numerical performance, we will consider a model of Erythropoiesis. The model is a question of a hyperbolic partial differential equation. Therefore, we will also give a slight overview of numerical solving the resulting equation by introducing an upwind-finite-differences scheme.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Dynamic Mode Decomposition, DMD, Dynamic Mode Decomposition With Control, DMDc, Dynamical Systems, Time-Varying System, Upwind-Finite-Differences

Zitieren

ISO 690

ROHLEFF, Jan, 2020. An Incremental Approach to Dynamic Mode Decomposition for Time-Varying Systems with Applications to a Model for Erythropoiesis [Bachelor thesis]. Kontanz: Universität Konstanz

BibTex

@mastersthesis{Rohleff2020Incre-51127,
  year={2020},
  title={An Incremental Approach to Dynamic Mode Decomposition for Time-Varying Systems with Applications to a Model for Erythropoiesis},
  address={Kontanz},
  school={Universität Konstanz},
  author={Rohleff, Jan}
}

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Hochschulschriftenvermerk

Kontanz, Universität Konstanz, Bachelorarbeit, 2020

Universitätsbibliographie

Ja