Learn English – What’s the difference between “knowledge of sth” and “perception of sth “

I don't think they're synonymous, no; one suggests a more complete level of penetration than the other. Judging by the definitions, I'd guess that you'd penetrate through, but you'd compentrate throughout.

I initially wondered if compenetrate is a word used in a specialized field (perhaps something scientific, e.g., to describe how an electrical field might compenetrate throughout a substance), so I did a search on Google books.

What I found was rather instructive. First, the word is indeed rather rare (only 75,000 hits, versus more than 12 million for penetrate). More significantly, it appears to be a word used almost exclusively in the realm of philosophy – a great preponderance of the cited references were scholarly works in philosophy or religion, such as:

It has no foregone character or status; it lacks anything of the ready-made; it is a process where personal activities and unpersonal events compenetrate, reshape each other, endowing the past with a new meaning... (H.M Kallen & S. Hook, American Philosophy Today and Tomorrow, 1935)

Faith and reason compenetrate to produce a distinct consciousness, a consciousness with identifiable cognitive dimensions or facets. I have tried to identify three such dimensions, overlapping as they are, as protective (or corrective), dispositive, and directive. (S. E. Lammers & A. Verhey, On Moral Medicine: Theological Perspectives in Medical Ethics, 1998)

As I perused through the results, a few quotes kept appearing over and over again, such as:

"All felt times coexist and overlap or compenetrate each other."

This quote, along with some others that were oft-repeated, was attributed to turn-of-the-century philosopher William James. I saw the word appear in so many references to his writings that I began to wonder if he coined the term, but the OED refuted that theory:

compenetrate trans. To penetrate in every part, pervade, permeate.

1686 R. Boyle Free Enq. Notion Nature 359 A Philosophizer may justly ask, How a Corporeal Being can so pervade, and, as it were, com-penetrate the Universe, as to be intimately present with all its Minute Parts.
1836 F. Mahony in Fraser's Mag. XIV. 91 Animal matter‥impregnated, or, to use the school term, ‘compenetrated,’ by a spiritual essence.
1855 N. Wiseman Fabiola 73 The world‥felt itself surrounded, filled, compenetrated by a mysterious system.

My spellchecker doesn't like the word. There's probably very little need to use the term, outside of esoteric philosophical writings discussing various levels of consciousness and subconsciousness, parallel universes, and the like. I can think of very few everyday uses for the word, although I suppose it might be apt if you were trying to describe the compenetrating Vulcan mind meld that Mr. Spock gave to Dr. McCoy.

These are complements of sense verbs (the first case discussed in this answer) and have a number of peculiarities. Of particular interest is the fact that the non-volitional sense verbs can take all four varieties of complement. Which includes gerund and infinitive complements, like these.

The difference between infinitive and gerund complements, "roughly speaking", according to McCawley, is that gerunds correspond to events, while infinitives correspond to situation types. There is minimal or no difference between the meanings of

• He saw me talking to her.
• He saw me talk to her.

because of facts about vision and conversation, and the usages of complements.

• He saw me talking to her means he witnessed my conversational activity with her.
• He saw me talk to her means he knows that I talked to her because he witnessed the event.

In other words, if he saw one, he saw the other. This is not necessarily true for all predicates;
i.e, He saw me running the marathon does not necessarily mean He saw me run the marathon.