Hi Aliyeh, the validation of a mathematical model (given by a set of ODEs or PDEs,etc..) by comparison between experimental data and numerical simulations is a priori independent from any optimization criterion. In which way is your mathematical programming problem related to the model itself?

The validation of the model is carried out by the experimentation and comparison of the experimental results with those calculated by the model. If you have a sufficiently precise simulation procedure the experimentation could be carried out using the simulation procedure. Another thing is the validation of the optimality of the solution(s) found. This last one could by done by the generation of a great quantity of random numbers, corresponding to the decision variables values and the verification that none of them is better than the optimal(s) one by the optimization criteria selected.

I agree with the views of the colleagues. In addition, the coefficient of determination and the mean absolute error are usually important measures for the appropriateness, or not, of the model.

Regards