zbMATH — the first resource for mathematics

Parameter estimation in dynamical models. (English) Zbl 0992.76075
Chassignet, Eric P. (ed.) et al., Ocean modeling and parameterization. Proceedings of the NATO Advanced Study Institute held in Les Houches, France, January 20-30, 1998. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 516, 373-398 (1998).
Summary: We give a general introduction to the formulation and solution of the parameter estimation problem for dynamical models. A methodology is presented in which the dynamical model and its initial condition and poorly known parameters are all treated as weak constraints in a variational inverse formulation. The variational formulation penalizes deviations from the exact model equation and distances from the first guesses for the control variables. The minimum of the variational functional is an estimate which almost satisfies the model equations, and at the same time is “close” to the observations and the first guesses for the initial condition and parameters.
From this general weak constraint formulation it is easy to obtain Euler-Lagrange equations for suboptimal or less general strong constraint formulations. The basic method proposed here for estimating poorly known parameters defines a gradient descent iteration for parameters, while the remaining inverse problem (with parameters assumed given) is solved using the representer method. The method should be applicable to many problems as long as they are not too strongly nonlinear.
For the entire collection see [Zbl 0923.00026].

76M30 Variational methods applied to problems in fluid mechanics
86A05 Hydrology, hydrography, oceanography
93B30 System identification