The problem is this. We have a set of ODEs that include two or three parameters which determine the solutions one can obtain with NDSolve. The ODEs do not have analytical solutions. The question is, if one has a set of data which is in principle described by the solutions of the equations for some choice of values for the parameters, how can one make, for example a least squared distances fit of the solutions to the data and find the parameter values that produce the best fitting solutions to the data? Is it clear what my question is? NDSolve returns an interpolating function, I do not know how to use such object to optimize my parameters (as far as I know, the dependence on the parameter is just not there). Do we need to write our own numerical ODE solving procedure? Apologies if the question is not totally clear, I can try to make my question clearer. Thank you.



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