Ok, so from what I understand, the key difference between reality and our simulations of chaotic systems, is that in our simulations, we need to use a discrete time step to do the calculations (over and over) to find future states.
Reality, on the other hand is continuous, so these models are only approximations that get more and more accurate as we decrease the time interval of the steps in the simulations. It’s impossible to exactly model these systems because we can’t use an infinitesimal interval in a simulation. The amount of steps we need to calculate grows towards infinity.
However we haven’t been able to confirm that time is actually continuous (www.clrn.org/is-time-discrete-or-continuous-data/). If time is not continuous, then it would be possible to use a discrete model to predict these chaotic systems arbitrarily far into the future in our universe.