There are theories in physics which detail the limits of what one can reasonably know about future measurements (e.g. quantum uncertainty principle, chaotic dynamics in classical physics), but there isn't a specific branch of physics dedicated to future knowledge.
In some ways, all of physics is a study about future knowledge. Given the present information of a system, and our theories describing how a system evolves in time, we can make reasonably good guesses about the future state of that system. Over time, physicists are also getting better at saying just how good those guesses can be.
Physics can't tell you very much about the future, though, because most systems (i.e. kittens) are much much too complicated to be described at the elementary level.