What's a word for knowing something from experience?

I'm trying to figure out a word that describes subconsciously knowing something from experience. My initial attempt was "instinct", but that has more gifted and primal connotations.

The use case I had in mind was as follows:

"If we assume that the model is applicable, it tells us what we've ________ known for a while [...]"

Update:

The word that fits best for my use case seems to be intuitively.

Another good one was empirically, but it tends to imply there were some experiments carried out to glean the knowledge, which wasn't the case.

How about conditioned?

OD:

condition: train or accustom to behave in a certain way or to accept certain circumstances: ‘our minds are heavily conditioned and circumscribed by habit’ [with object and infinitive] ‘they are beliefs which he has been conditioned to accept’ ‘social conditioning’

More example sentences

‘We have become conditioned into being, behaving, reacting to any situation in a certain way, and we perpetuate this conditioning by the way we think.’

‘They are beliefs which he has been conditioned to accept.’

Conditioned fits the sense of knowing something but without being conscious of it.

Update: Based on your edits to the question, how about intuitive?

OD:

intuitive: using or based on what one feels to be true even without conscious reasoning; instinctive

Your example:

"If we assume that the model is applicable, it tells us what we've known intuitively for a while [...]"

One develops intuition based on experience. For example, chemists often speak of chemical intuition when speculating on the outcome of chemical reactions.

As per the example sentence, practically/empirically fits here.

"If we assume that the model is applicable, it tells us what we've practically/empirically known for a while [...]"

TFD:

practically adv

2. in actuality rather than in theory: what can we do practically to help?.

Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

ODO:

empirically ADVERB

By means of observation or experience rather than theory or pure logic.

‘But let me say loud and clear that this idea is theoretical and to my knowledge has not been studied empirically.’

Noun: know-how ('now,haw)

The (technical) knowledge and skill required to do something

• knowledge

Derived forms: know-hows

Type of: ability, power

-- WordWebOnline