Comment by akoboldfrying

We don't ever actually know if any model is accurate -- that is, whether it actually models the underlying physical process. We just have a lot of models that have made predictions about the future that turned out to be more or less correct, much more often that you'd expect by chance, and so we develop trust in that correspondence with reality over time.

It's possible that our current climate models are wrong, by a little or a lot. It's also possible that General Relativity is wrong -- gravity might stop at this time tomorrow.

If you're interested, this issue is called the Problem of Induction in philosophy. (Confusingly, "induction" has a different meaning here than in mathematical induction.)