Parameter Identification for Tidal Constituents Using Automatic Differentiation

It is important to compute exact value of the gradient in the inverse problem. In case that the problem is given, the minimization of function is usually used to obtain the gradient. Thus, the analytical calculation of variation of functional should be introduced. But the variation is difficult to formulate and programming. Therefore, there is a method of computation to pursue the variation of functional, Automatic Differentiation (AD). The AD is implemented with C++ programs using operator overloading technique. The partial derivatives are computed according to the differentiation rule of a composite function whenever basic operations are performed. In this study, AD is applied to the parameter identification problems. AD is used in order to calculate the partial derivatives of the performance function. The algorithm of computing the gradient using AD is much simpler than any other method, for example, the adjoint equation method of the Language multiplier, etc. AD is proposed as a new approach to the sensitivity analysis of the inverse problems. This research presents a method of analysis and numerical simulation to apply the parameter identification problem included in the inverse problems using Automatic Differentiation