"Intuition" is defined as the ability to understand something instinctively, without the need for conscious reasoning.
Given that you are talking about scientific theories and principles, I don't think the "intuition" you refer to is a mere 'feeling' or devoid of "conscious reasoning". I think you are trying to describe an intuition based on experience. As such, there might be a better word or phrase than "intuition".
If you really want to use "intuition", it should really belong to someone, or a group of people. Intuition is something that people possess, not something that is documented, so you should state whose intuition it is, rather than say "the" intuition:
it is in agreement with our intuition that to fit a jump or a cusp we need fast oscillating terms.
Alternatively, if you agree that "intuition" might not be the most appropriate word, perhaps you could instead use "theory" or, even better "working theory". A working theory is based on known facts, not just guesswork or intuition. As a theory is normally documented, you can say "our theory" or "the theory" if you prefer, or if the theory is not yours.