One example of "intuition" is Einstein's theory of relativity. It was theory, not proven until years later (parts of it are still being "proven").
There is a lot of creativity and intuition in persuing pure science. Theories are imagination, and then it takes imagination to test the theory.
The idea that things can be measured and that laws of nature are universal are assumptions based on "divine revealation".
The 12th century philosophers who began science assumed that the universe was logical because God was logical. Because God was logical, then man, using his logic, was doing the work of God when he explored the universe. So you could say that the entire field of science is based on a "divine revealation" that nature is not a mysterious god to be worshipped, but a creation of a logical creator. And science assumes there is a logical explanation behind nature, because the original philosophy behind science, i.e. Christianity, assumed a logical creator who created things logically.
Pattern recognition. It is one of the characteristics that evolved into most of the higher animals. Humans can take it to abstract levels.
However, pattern recognition fails as often as it succeeds. Even Einstein produced flawed theories that he later scrapped. The validation of such an extrapolation relies on physical observations. Until it is validated by the normal materialistic routes of knowledge, it is a guess, a speculation -- and reviewing the history of guesses -- usually flawed, incomplete, or just dead wrong.