A former colleague did his PHD in particle physics with a novel technique (matrix element method). I can't really explain it, but it is extremely CPU intensive. That working group did it on CERN's resources, and they had to borrow quotas from a bunch of other people. For fun they calculated how much it would have cost on AWS and came up with something ridiculous like 3 million euros.
(The expensive part of these experiments is simulating billions of collisions and how the thousands of outgoing particles propagate though a detector the size of a small building. Simulating a single event takes around a minute on a modern CPU, and the experiments will simulate billions of events in a few months. If AWS is charging 5 cents a minute it works out to tens of millions easy.)