Devising protein structure prediction methods comes to mind. The problem is, there's only finite training/evaluation data; I have no idea how one would avoid hideous overfitting if performing an infinite number of trials. This is probably a problem with any machine-learning type problem.

I don't know if there are existing molecular dynamics sims that would give good answers given enough cycles (fivemack?); if so then one could generate one's own training data (and get structures for all known sequences while we're at it).