You can improve attributes permenantly with Cr rituals but can you also do it via rigourous training?
As we do in non-mythic Europe...
i.e you spend a season undergoing rigourous athletic regime & eat high meat foods and manage to improve strength by one. Maybe helped by a ReMe spell that forces you to push your limits.
The mindset of the system is that your stats aren't changeable, except through aging. So your score in each characteristic represents the pinacle you can attain.
They are modified lower while you are young, reach to maximum when you reach maturity, then decline are you become old. Training has nothing to do with it.
The game does have a system for gaining Virtues during play, and Improved Characteristics is a Virtue. Imagine a Mystery Initiation something like this:
The Initiate spends a season in a focused regimen of physical activity (+1), sacrifices considerable wealth to buy specialized food from throughout Europe (+1), and the Mystagogue serves as a personal trainer every day for the entire season (+3). A sympathetic bonus of +3 is assigned for the appropriateness of the physical training regimen to gaining Improved Characteristics, which must be spent on Strength or Stamina.
A Mystagogue with Pre +2, the appropriate Lore skill of 5, and Improved Characteristics would be able to initiate this “Mystery”.
Now, there’s no such Mystery. But if you rename the Mystagogue to “Personal Trainer” and allow the use of, say, Athletics for the relevant Lore, you have an Ars Magica mechanic that does what you want it to do.
That or the intense training gives them decrepitude points. Which a young man looking to get buff doesn't worry about because it will be years before they affect his aging rolls.
I suppose training to improve physical stats could also take the form of walking from the rhine to Jerusalem on a pilgrimage to gain Improved Characteristics virtue.
Otherwise wouldn't you just train Athletics? For physcial feats I'd consider rolling stat+Athltics to do stuff, and the ability training represents getting in shape.
You can train Athletics to succeed at physical feats and you can train Single Weapon to do more damage, but only Strength allows you to carry more Load. A wizard with a Strength of 0 or less carrying nothing but a staff has an encumbrance penalty.