In classical mechanics, $F=ma$ tells us how to evolve a system at time $t=t_0$ to $t=t_0+dt$.

In quantum mechanics, the Schrodinger equation gives us a similar recipe.

These equations are, in a certain sense, completely deterministic. Is it possible that nature only appears to be deterministic because the only language we know how to express physics is math (particularly equations), which (not to offend statisticians) seems to be particularly apt at describing deterministic systems?

In other words, are there possible time-evolution laws that are both non-deterministic and falsifiable?

If not, is determinism not falsifiable?