Are there any rules that describes the ability to non-magically raise Characteristics due to physical training or XP?
No, not to my knowledge.
No. Heck no. The very closest you get is, perhaps, explaining why you have increased characteristics in character creation.....
Ok, just curious.
Just find it strange that if youu can raise most other things, then perhaps you might be able to raise characteristics in a book that I do not have.
I mean training a -1 Strength and/or -0 stamina for 2 or more seasons and dedicating your time to lift weights, swing a sword and climb trees/mountains as well as running should grant you a chance to raise them at least 1 step (maybe to a maxmum of +1)
What do you mean, when you say "you (sic) can raise most other things?"
The only other things that are raised in the game are Arts and Abilities.
The chief problem I see, is that being able to increase characteristics takes away from magic, in a game that is about magi. The other issue is if you did engage in some sort of comprehensive training program, how long should it take to progress, and why would it be limited to some sort of arbitrary maximum? If a character/player wants to increase their strength, I suggest some kind of story that leads them onto this path of increased strength, and perhaps it is bestowed by a faerie or creature from the magic realm. Still keeping it mythic, and it requires some effort and perhaps sacrifice on the part of the character.
The spells to increase attributes are high level rituals and therefore use a lot of vis. In my sagas I tend to leave these in the realm of the Mercere, but other magi could invent them from first principles of magic theory for themselves without repercussions. Since they are so high level, they will require a huge investment of a magus's time to get to a decent lab total, and then several seasons to invent the spell... And then when they cast it, there is the vis cost associated with it. Consider all that the magus has sacrificed to get to this point... True, they could sell their service in casting the spell, but unless they have virtues which reduce botch dice, and further practice the ritual to master it (more time sacrifice) it is an incredibly risky proposition...
What I mean is maybe not for magi but a comapnion or a grog, remember we play those as well 
I know, but the point still stands, at least the method your outlined takes away from magic in a game that is about magi. And it is why I recommended it be some sort of story. Maybe a demon sees the vanity of the person working out and tempts him to increase his strength? Maybe it's a Fae creature who will give him what he wants in return for a favor. There are times where arbitrary rules (and I like them, don't get me wrong) can get in the way of what could be some potentially interesting stories of how a grog got his impressive strength, and then brought ruin upon the covenant. Muhahahaha.
Oh, and let me add one other thing. If a character has a negative characteristic, it was a conscious choice to make it so. You get 7 points to make characteristics positive. They are never enough, but that's the case for every character. Now, sometimes a character can be poorly designed to do something, and it needs to be corrected. I don't take issue with corrections to make the characteristics fit the character concept. I do take issue with a character trying to end run around his own choices by trying to do a workout/training regimen.
The second paragraph under Characteristics in ArM5, page 18, covers the thinking, I believe. Characteristics are assumed to already be maximized in terms of the character's potential; to improve them further would require explanation of the person's core capability, and that normally means magic.
I think one key point is to remember that in the harsher climate of the 1200s, circumstances tended to require that a person always work towards their full capacity merely to survive. With comparatively primitive health care, often shaky nutrition, and the myriad of other issues, it was hard for even the most healthy and fit person to live past 30. Even having a "desk job" like being a scribe still meant you spent a good part of your day pumping your own water, dragging about your own firewood, etc. Certain a wealthy person would have servants to remove some of that load but I think the point still stands: life in such a world as Mythic Europe is so much more physical a thing that I'm really not sure how much more an exercise regime could really do for somebody unless something truly unusual has been going on, and I think that degree of suddenly unchained potential would, again, require magic.
Ok, thank you all. I got my answer 
That doesn't necessarily mean the discussion is over. 
Not at all, I just wanted to show gratitude that people answered my questions, but please continue to discuss
It isn't directly raising Characteristics as such, but there's always Virtue Initiation.
I can see scenarios where Great (Characteristic) or even Improved Characteristics might be gained for a direct increase, or Enduring Constitution or Reserves of Strength to raise certain conditional qualities. Keen Vision, Lightning Reflexes, Long Winded, Sharp Ears, and Tough are pretty good candidates to represent improvements in given traits.
While initiations are (I think) essentially mystical, new Virtues can be gained through pilgrimage. I can't remember whether there are any restrictions on the types of Virtue that can be gained, but The Church supplement is worth a look.
I think, with maybe the exception of Improved Characteristics, I'd be very open to characters initiating those Virtues to represent their growth.
If I were running the game, and a player companion wanted to increase his Strength, I'd ask him, "What Virtue are you prepared to give up, or additional Flaw are you prepared to accept, in exchange for Improved Characteristics?" And then, perhaps, a story can be made out of it.
As an example, lets say you've got a young man who is a recent University graduate, and he is eager to travel and see the world, but realizes swiftly that he is ill suited to such things, having Str -1 and Sta 0. Well, if he goes off on an adventure, and in the middle of that adventure he gets a Dagobah-style training montage in which he runs around the Alps with a dwarf on his back, we could give him Improved Characteristics, raise Str and Sta to +1 each, but because he's left his schoolboy days behind him, he loses his Book Learner Virtue.
It would totally be a House Rule, but it makes a good story, it lets the player do what he wants to do, and it's balanced mechanically. Your saga may vary.
No it isn't. It's a mystery cult initiation 
I knew you would say that. But rewrite the scenario without a cult, initiation or mystagogue, or rules for same, and I would still do it.
You're your own mystagogue, you've undergone an ordeal to sacrifice a virtue for the improved characteristics and you've sacrificed time at the same time. Just because there's no formal script written down doesn't change the fact it's an initiation. Technically, a pilgrimage is an initiation by the same ruleset, just that God is the mystagogue, so unless he decides you need to, there's no ordeal, just the sacrifice of time and the sacred site.
Well the way to get more than +7 points in attributes is... VIRTUES! So find a way to get more virtues. There is a pre-existing way to do this.
Adapt the rules for mystery cult initiations or pilgrimages!
Anyway you would first need to make a few changes to the initiations.
- The Gift does NOT help in anyway for non-magical virtues. I don't know who got the idea to allow the Gift to help you get Divine virtues, but that's stupid.
- Instead of Mystery Cult Lore change it to fit for general virtues. Athletics for physical characteristics, one of the academic abilities for most of that sort of virtue, affinity or puissant would require the ability itself.
- Particularly obvious things don't really need scripts. I.E. Exercise
- You are going to have to expand the options for script bonuses and remove one that don't make any damn sense.
Or you could go the pilgrimage route, the only change you'll need to make here is - Cut out anything that doesn't make sense. You are probably going to be left with seasons of effort and disease from overwork exercise for a physical virtue. Mental ones might make people jealous and cause conflict that way. Basically you want them to be a result of the characters efforts.
The other option is make them straight up learnable with xp. They cost 50xp per virtue point if you were wondering.
Summary of the methods and difficulty:
- Initiations are either really easy, or really hard depending on scripts and scores. At high end you can get a virtue a season. Or it might be nearly impossible.
- "Pilgrimages" take time no matter what, but its still doable. 6 or 10 seasons tops, depending on the virtue grade.
- Learning is even slower than the "pilgrimages" if you don't have a teacher, but it can be much faster with a really good one.
Anyway, I agree: People should be able to gain virtues. You should be able to learn things like how to write better. The fact that their isn't a quasi-unified system to do just that is a bit of an oversight in my mind.
You mean learning Supernatural Abilities (ArM5 p106), no?
- Learning Divine ones requires True Faith, which is believed to be the Divine version of The Gift.
- Learning Faerie ones requires enough Faerie Ranks, but Homunculus Wizard mentions a special Faerie version of The Gift.
- Learning Infernal ones requires but a touch of evil, but there's The False Gift.
Noble's Parma, but Faerie/Infernal allow to learn magical-aligned Abilities even if the reverse is not true.
I'm talking about the rules for mystery initiations. According to Hedge wizardry without the Gift you can 1) only initiate virtues you have and b) must always suffer an ordeal. Which IMO only makes sense for magical virtues. (And even then, I frown at it.)
Learning a supernatural ability doesn't actually get you the virtue. But yeah you are right about those ways to learn the various supernatural abilities.