Is it possible to find potential generic functions or algorithm that maps a set of numbers (x) to another (y)?

OK i have two large sets of numbers that the one is computed from the other but I don't know how. Is there a methodology, a field in mathematics that deals with this problem in some generic way? Is there software that finds possible functions that match the numbers? I need exact functions not statistically probable ones. There may be multiple functions that govern the relationship between the data any one that derives exactly the second from the first set will do although the least complex one would be preferable.