I wrote my masters thesis on this exact topic. First, to slightly correct an assumption in the question: If you look just at the Fall of '67, the US was struggling, both branches trading in a nearly 1:1 ratio. (source is the primary documents of the Red Baron Reports, but acig.org has correct stats listed for every air-to-air engagement that resulted in a kill).

Responding to this, the Navy and Air Force both pursued major technological changes/improvements to their missiles and aircraft. The NAvy also created Top Gun. The NAvy's ratio did not increase to anywhere near 13:1 after 1970, in fact, there were not even that many engagements, if I remember correctly. Air-to-air combat was rare, especially for the navy, who generally operated much further south. The Navy's kill ratio after '70 was slightly under 4:1.

Getting to the point of your question though, part of the reason that they Navy had so many fewer engagements with MiGs was because, yes, the North Vietnamese WERE aware that the Navy was becoming much more adept at dogfighting. Were they aware of Top Gun? Probably not -- Top Gun was a very "fringe" thing that the NAvy brass considered an experiment and didn't take too seriously at first (read Robert Wilcox's "Scream of Eagles" for the details). But, the North Vietnamese definitely knew that the Navy was getting better. According to the memoir of Randy Cunningham, "Fox Two," there was a rumor that North Vietnamese pilots put signs up in their airfields that read, "Don't shoot gray Phantoms!" Gray signifying Navy craft.

So yes, the North Vietnamese were aware of the increase, and started backing off of Navy patrolled areas. But I would doubt that they knew anything specific about Top Gun.

Hopefully that helps.

To anyone interested in answering this question, don't make the same mistake as the deleted comments. This is the question at hand:

TOPGUN resulted in the US Navy kill:death ratio in Vietnam increasing from 3.7:1 (1965-1967) to 13:1 (after 1970).

To what did the Soviet and North Vietnamese airforces attribute this marked increase?

Were they (The Soviet Union and North Vietnam) aware of the program?

Follow up question: if the increase can't be attributed to TOPGUN, are there other possibilities? Have there been any papers published on this increase in kill:death ratio?

What was TOPGUN, other than a movie?