I'm just curious whether in some future there will be a very bitcoin-specific method to predict, say, if you are going to have some zeros in the output or not. So you save some cycles and jump to next nonce. The algorithm can be probabilistic, of course. E.g. if we can figure out some patterns in the internal state during hash computation.
That's already being done. Bitcoin miners do not compute a complete SHA256 hash. There are several minor shortcuts already implemented in modern miners.