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Blind model reduction for high-dimensional time-dependent data

Please always quote using this URN:urn:nbn:de:0296-matheon-3145
  • We consider the problem of automatically extracting simplified models out of complex high--dimensional and t ime--dependent data. The simplified model is given by a linear Langevin equation with time--varying coeffici ents. The reduced model may still be high--dimensional, but it is physically intuitive and much easier to in terpret than the original data. In particular we can distinguish whether dynamical effects are influenced b y friction, noise, or deterministic motion. The parameters for the reduced model are obtained by a robust an d efficient numerical predictor--corrector scheme which relies on analytical solutions to a maximum-likeliho od problem provided the time steps between successive observations are not too large. If the data set is ver y heterogeneous the time series is better described not by a single model, but by a collection of reduced mo dels. This scenario is accounted for by embedding the parameter estimation procedure into the framework of h idden Markov models, i.e., we decompose the data into several subsets, each of which gives rise to an approp riate linear Langevin model. The switching between the local model is done by a Markov jump process. The opt imal decomposition into submodels can then be regarded as one global Langevin model with piecewise constant coefficients. We illustrate the performance of the algorithm by means of several examples. Especially we foc us on the numerical error as a function of the time step of the observation sequence.

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Metadaten
Author:Illia Horenko, Carsten Hartmann
URN:urn:nbn:de:0296-matheon-3145
Referee:Christof Schütte
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2006/01/06
Release Date:2005/12/20
Institute:Freie Universität Berlin
Zuse Institute Berlin (ZIB)
Preprint Number:334
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