Why nonlinear modelling and not some other form of mathematical modelling?

• It is not possible to use physical modelling in many situations.
• Even if it is possible, physical models usually compute the output slower than empirical or semi-empirical models.
• Development of physical models is time consuming. Nonlinear modelling tends to be expensive, but physical modelling usually costs even more.
• Physical models involve assumptions and simplifications.
  
  Thus empirical modelling is often a better alternative.
  
  
• Traditional empirical modelling is based on linear statistical techniques. Nothing in nature is absolutely linear. So it helps to take nonlinearities into account rather than ignore them. If the range of variables is small, linear techniques are sometimes sufficient.
• Proponents of linear techniques argue that one can include quadratic terms in linear regression to account for nonlinearities. This is usually not done, and even if it is done, it is not efficient. Just as nature is not linear, it is not very quadratic either. Nature does not follow the simplicities which we try to fit it in. New techniques of nonlinear modelling allow us to approximate nonlinearities without specifying in detail the nonlinearties to be accounted for. They allow for free form nonlinearities, unlike linear and nonlinear regression methods.