You mean, do all the stuff you'd be doing for a physical model anyway. :sigh:
No, I'm only saying that what you'll be finding under the title "physical modelling" in the literature solves the wrong problem as far as the original poster's goal is concerned. A physical model of a single piano string or a flute is not a physical model of a piano. If that was the case, everybody would be using that model and it would sound like a real piano.
Since that's not the case, something is missing and that missing thing is not necessarily complex, but sure it is counter intuitive. (If it wasn't, somebody would come up with a theory and solve that problem). Since that did not happen, then we are sure it is counter intuitive and hard to measure, perhaps even hard to reproduce even when correctly simulated. Does the best piano recording sound exactly like the real thing? I guess that's not the case either.