I'm not sure what you mean by "fuzzy"? Different people mean different things by this word. Do you mean something to do with probabilities?
As regards AI, a standard start point is the excellent introductory text book by S Russell and P Norvig. called "Artificial Intelligence: A Modern Approach" -- Prentice Hall.
Sadly, there are no short cuts to understanding...
It is a bit unclear what you mean, but AI is a research field with a lot of different technologies and topics.
But if I understand you properly, you look for a possibility to find a proper initial vector for solfing you differential equation? Did you try to model your observed system with artificial neural networks (ANN) or with recurrent ANN?