- Advantages: If you know the mathematical model of the process that produced your data, you can (likely) estimate the parameters of the process with reasonable accuracy, giving you insight into the process. It is a parametric regression.
- Disadvantages: You have to have a reasonably representative model of your system to start with, and a reasonably accurate initial estimate of your parameter set (at least with respect to orders-of-magnitude) in order to get a reasonable fit.
- Advantages: You do not need to have a model of your system for the net to provide a reasonable approximation of your data.
- Disadvantages: Since it is a non-parametric ‘black box’, you learn nothing about the dynamics of your system.