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Optimal estimation of parameters of dynamical systems by neural network collocation method. (English) Zbl 1196.93078
Summary: We propose a new method to estimate parameters of a dynamical system from observation data on the basis of a neural network collocation method. We construct an object function consisting of squared residuals of dynamical model equations at collocation points and squared deviations of the observations from their corresponding computed values. The neural network is then trained by optimizing the object function.The proposed method is demonstrated by performing several numerical experiments for the optimal estimates of parameters for two different nonlinear systems. Firstly, we consider the weakly and highly nonlinear cases of the Lorenz model and apply the method to estimate the optimum values of parameters for the two cases under various conditions. Then we apply it to estimate the parameters of one-dimensional oscillator with nonlinear damping and restoring terms representing the nonlinear ship roll motion under various conditions. Satisfactory results have been obtained for both the problems.

MSC:
93E10 Estimation and detection in stochastic control theory
37N35 Dynamical systems in control
92B20 Neural networks for/in biological studies, artificial life and related topics
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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