Dear Taiwo,

Here are links and attached files in subject, ihope that information can be help you in research.

- Fitting a Model to Data - Data Science for Business [Book]

https://www.safaribooksonline.com/library/view/data.../ch04.htm

- Model Fitting

courses.washington.edu/matlab1/ModelFitting.html

- Modeling Data and Curve Fitting — Non-Linear Least-Squares ...

https://lmfit.github.io/lmfit-py/model.html

Best regards

This is a typical inverse problem and can be solved by any nonlinear programming problem solver, for example IpOpt (open source software; use Google).  Do you have ODEs with parameters which have to be fitted to real data? In this case you made need a modelling tool like Ample (there is a book on how to use it) which allows you to describe your problem easily and provides your NLP solver (IpOpt) with exact gardients.

Yes, you are right. However, optimization and parameter fitting are both inverse problems. You most probably will be able to solve both problems with the software I mentioned, eventually even simultaneously, if this makes sense.

The question is how to treat the different objective functions: either first the parameter fit, which may bring your model close to reality, and then the optimization or both together. Then you will run into a Pareto optimization problem. Here one can, for example, multiply the objective functions by different weighting parameters and add them. So you steer into a compromize between data fitting and optimization. I would prefer the first approach.

Best regards and much success,

Hans Josef Pesch

Thanks all. Your responses are very valuable. I am getting things clearly now. No more confusion.