Simulating an acoustic piano sound without using samples is not so easy.
Doing it with samples on the Axoloti wouldn't work too well (it isn't the best solution for big long samples).
You could always try and get close using FM and subtractive synthesis, maybe wavetable too, but it won't sound very realistic and may be quite limited in polyphony.
Electric piano's are easier.
If only someone like Pianoteq open-sources how they manage to synthesize real piano's so well, we could hope to have nice piano's everywhere.
I was thinking about doing a piano these last days, as I was seriously thinking about launching a General Midi collaboration job. So I started looking into it.
I did find this video, but it says nothing about how he supposedly created the sound (apart from having to sample his synth sound to get real polyphony).
I think there are a couple of Nord Modular piano patches, but I've never heard them, so I can't talk about them.
So it's a good question, and a no real answer from me, sorry