Yes, you would. "Intuitively" here is a introductory phrase, specifically, an adverb.
Such introductory phrases or clauses, need to be set off with a comma. Examples include:
Barking insistently(introductory clause), the dog ran round the tree.
Unsteadily, he opened the box.
Edit: This site provides the rules:
Introductory clauses, phrases and words are:
Clauses, phrases or words that are not sentences.
Clauses, phrases or words that provide extra information.
The sentence makes sense with out the clause, phrase or words.
Clauses, phrases or extra words that come at the beginning of the sentence.
They are used as background information, extra information.
There can be more than one introductory clause, phrase or word in a sentences.
Commas are placed after the introductory clause, phase or words. If there is more than one introductory clause, phase or words a comma is placed after each introductory clause, phase or words.
Wow, that was a great movie.