I have a set of input-output data and I would like to derive a mathematical model from that data. I want to know which approach would be better. Should I use NN or should I go for curve fitting? What are the advantages of one over the other?
It depends on the data and wether you need to interpret your mapping function.
If yes, use polynomial curve fitting or similar interpretable methods. Otherwise you can use neural networks or ensemble classifiers like xgboost regressor.
Arseniy, what do you mean by interpreting? Can you please elaborate ? I have already used a polynomial curve fitting once to map my data set but I want to know if NN holds any advantage over it.
Ramkrushna, you mean to say that NN should be used for complicated cases involving large data sets with very little correlation ?? Can you please elaborate your answer a bit ? Also can you answer the why?
Neural networks can work better as well, but if you have a small dataset then curve fitting will give good enough results compared to NN, trading off the complexity of the NN and the time it will take to learn.