Determination of unknown parameters of mathematical model using the experimental design theory

The range of problems that can be solved with the help of mathematical modeling is constantly increasing, which creates new theoretical problems. One of them is connected with identification of unknown parameters of models. The problem of parameters determination belongs to the class of inverse problems. They are usually considered within the optimization theory. In the present paper, we propose a fundamentally new approach. The method is based on the theory of planning and processing of experiments developed by American scientists Box and Wilson. To evaluate the adequacy of model, a numerical criterion W is formulated depending only on the model parameters a1, a2,... ak. It is shown that the maximum adequacy is achieved for the minimum value of W. Therefore, solving the problem of calculating the parameters is reduced to determination of such values of a1, a2,... ak that provide the minimum value of the criteria W. This problem is solved by the steep ascent method due to Box and Wilson.