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A method for solution of the multi-objective inverse problems under uncertainty

  • Molecular Biophysics
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Abstract

We describe a method to solve multi-objective inverse problems under uncertainty. The method was tested on non-linear models of dynamic series and population dynamics, as well as on the spatiotemporal model of gene expression in terms of non-linear differential equations. We consider how to identify model parameters when experimental data contain additive noise and measurements are performed in discrete time points. We formulate the multi-objective problem of optimization under uncertainty. In addition to a criterion of least squares difference we applied a criterion which is based on the integral of trajectories of the system spatiotemporal dynamics, as well as a heuristic criterion CHAOS based on the decision tree method. The optimization problem is formulated using a fuzzy statement and is constrained by penalty functions based on the normalized membership functions of a fuzzy set of model solutions. This allows us to reconstruct the expression pattern of hairy gene in Drosophila even-skipped mutants that is in good agreement with experimental data. The reproducibility of obtained results is confirmed by solution of inverse problems using different global optimization methods with heuristic strategies.

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Authors and Affiliations

  1. Center for Perspective Research, St.Petersburg State Polytechnical University, St.Petersburg, 195251, Russia

    A. S. Pisarev & M. G. Samsonova

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  1. A. S. Pisarev
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  2. M. G. Samsonova
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Correspondence to A. S. Pisarev.

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Original Russian Text © A.S. Pisarev, M.G. Samsonova, 2013, published in Biofizika, 2013, Vol. 58, No. 2, pp. 221–232.

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Pisarev, A.S., Samsonova, M.G. A method for solution of the multi-objective inverse problems under uncertainty. BIOPHYSICS 58, 157–166 (2013). https://doi.org/10.1134/S0006350913020139

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