title: [A method for solution of the multi-objective inverse problems under uncertainty].
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.
authors.forename: A S
authors.initials: AS
authors.lastname: Pisarev
authors.forename: M G
authors.initials: MG
authors.lastname: Samsonova
mesh_terms: D000465:Algorithms; D000818:Animals; D019521:Body Patterning / Q000235:genetics; D004330:Drosophila; D015870:Gene Expression; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D035501:Uncertainty