A Simultaneous Approach for Parameter Estimation of a System of Ordinary Differential Equations, Using Artificial Neural Network Approximation

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• 作者：Vivek Dua ; Pinky Dua
• 刊名：Industrial & Engineering Chemistry Research
• 出版年：2012
• 出版时间：February 1, 2012
• 年：2012
• 卷：51
• 期：4
• 页码：1809-1814
• 全文大小：792K
• 年卷期：v.51,no.4(February 1, 2012)
• ISSN：1520-5045

文摘

Parameter estimation for system of ordinary differential equations (ODEs) is formulated as a nonlinear programming (NLP) problem. The objective function of the NLP consists of two terms, which are simultaneously minimized. The first term is the summed square of the difference between the ODE model predictions and experimental data. The solution of the ODE model is postulated as an artificial neural network (ANN) model given by time points as the inputs and the state variables as the outputs. The outputs of the ANN model can be analytically differentiated with respect to the input, providing the differential terms of the ODE model. The summed square of the difference between these differential terms and the right-hand side of the ODE model represents the second term in the objective function of the NLP problem.