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Parameter estimation with a novel gradient-based optimization method for biological lattice-gas cellular automaton models

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Abstract

Lattice-gas cellular automata (LGCAs) can serve as stochastic mathematical models for collective behavior (e.g. pattern formation) emerging in populations of interacting cells. In this paper, a two-phase optimization algorithm for global parameter estimation in LGCA models is presented. In the first phase, local minima are identified through gradient-based optimization. Algorithmic differentiation is adopted to calculate the necessary gradient information. In the second phase, for global optimization of the parameter set, a multi-level single-linkage method is used. As an example, the parameter estimation algorithm is applied to a LGCA model for early in vitro angiogenic pattern formation.

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Authors and Affiliations

  1. Department for Innovative Methods of Computing, Center for Information Services and High Performance Computing, Technische Universität Dresden, Nöthnitzer Strasse 46, 01062, Dresden, Germany

    Carsten Mente, Lutz Brusch & Andreas Deutsch

  2. Institute of Pathology, Universitätsklinikum Carl Gustav Carus, Technische Universität Dresden, Schubertstrasse 15, 01307, Dresden, Germany

    Ina Prade & Georg Breier

Authors
  1. Carsten Mente
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  2. Ina Prade
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  3. Lutz Brusch
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  4. Georg Breier
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  5. Andreas Deutsch
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Correspondence to Andreas Deutsch.

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Mente, C., Prade, I., Brusch, L. et al. Parameter estimation with a novel gradient-based optimization method for biological lattice-gas cellular automaton models. J. Math. Biol. 63, 173–200 (2011). https://doi.org/10.1007/s00285-010-0366-4

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  • DOI: https://doi.org/10.1007/s00285-010-0366-4

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