PLS-Based Multivariate Metamodeling of Dynamic Systems

  • Harald Martens
  • Kristin Tøndel
  • Valeriya Tafintseva
  • Achim Kohler
  • Erik Plahte
  • Jon Olav Vik
  • Arne B. Gjuvsland
  • Stig W. Omholt
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 56)

Abstract

In this paper, we discuss the use of bi-linear methods for assessing temporal dynamics, in particular with regard to the understanding of complex biological processes. We show how the dynamics in multivariate time series measurements can be summarized efficiently by principal component analysis. Then we demonstrate how the development and use of complex, high-dimensional nonlinear differential equation models can be facilitated by multivariate metamodeling using nonlinear pls-based subspace data modeling. Different types of metamodels are outlined and illustrated. Finally, we discuss some cognitive topics characterizing different modeling cultures. In particular, we tabulate various metaphors deemed relevant for how the time domain is envisioned.

Key words

Metamodeling Complex systems Differential equations Time domain metaphors Nonlinear dynamics Multivariate subspace modeling Pls regression Chemometrics 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Harald Martens
    • 1
    • 2
  • Kristin Tøndel
    • 1
  • Valeriya Tafintseva
    • 1
  • Achim Kohler
    • 3
  • Erik Plahte
    • 1
  • Jon Olav Vik
    • 1
  • Arne B. Gjuvsland
    • 1
  • Stig W. Omholt
    • 1
  1. 1.IMT (CIGENE)Norwegian University of Life SciencesÅsNorway
  2. 2.Nofima ÅsÅsNorway
  3. 3.Centre for Integrative GeneticsNorwegian University of Life SciencesÅsNorway

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