Parameter estimation with a novel gradient-based optimization method for biological lattice-gas cellular automaton models
- 260 Downloads
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.
KeywordsLattice-gas cellular automata Parameter estimation Algorithmic differentiation Angiogenic pattern formation
Mathematics Subject Classification (2000)92C15 92C50 65D25 49M37
Unable to display preview. Download preview PDF.
- Drasdo D, Kree R, McCaskill J (1995) A Monte Carlo approach to tissue cell populations. Phys Rev Lett E 52(6): 6635–6657Google Scholar
- Flouda, C, Pardalos, P (eds) (2000) Optimization in computational chemistry and molecular biology. Kluwer Academic Publishers, AmsterdamGoogle Scholar
- Hatzikirou H, Brusch L, Deutsch A (2010a) From cellular automaton rules to an effective macroscopic mean-field description. Acta Phys Pol B Proc Suppl 3: 399–416Google Scholar
- Meinhardt H (1982) Models of biological pattern formation. Academic Press, LondonGoogle Scholar
- Mitchell M, Crutchfield J, Das R (1996) Evolving cellular automata with genetic algorithms: a review of recent work. In: Goodman E (ed) Proceedings of the first international conference on evolutionary computation and its applications. Russian Academy of Sciences, MoscowGoogle Scholar
- Pepper M (2001) Extracellular proteolysis and angiogenesis. J Thromb Haemost 1(86): 346–355Google Scholar