What is the disadvantage of mathematical model since we use artificial intelligence to improve and replace it?
Mathematical models may be entirely appropriate for some situations and may not be appropriate at all in other cases. Generally a mathematical model represents a function, and has a transfer characteristic, input versus output, x versus y etc.. If the formula describes the system well, it is likely to work well. As the environment of the system changes, it may tend to not work so well. Adding the ability to respond to some conditions (if this or that) can improve the model, and you are on the way to an expert system. Also processing may involve several stages of mathematical formulae, corrections for conditions that become variables. I think a familiar version of AI is related to expert systems, which attempt to encapsulate the analytical knowledge of a person who is expert. This means they are able to adapt better to the environment of the system as it changes, more or less as we people do. In my view (thinking mainly of control systems) the expert system (which people often see as AI