Julius Smith wrote pretty comprehensive textbook on the subject of building physical models of musical instruments, available online. Here, for example, is a chapter on modeling bowed string sounds: https://ccrma.stanford.edu/~jos/pasp/Bowed_Strings.html
From the article:
> As a demonstration, the researchers applied the computational violin to play two short excerpts: one from “Bach’s Fugue in G Minor,” and another from “Daisy Bell” — a nod to the first song that was ever produced by a computer-synthesized voice.
Ouch: this is completely inaccurate. Physical modeling has its roots in the 80s and Stefan Bilbao has been doing FDM based methods for over 20 years. I think he discusses fem in numerical sound sysnthesis
"Show HN: Anyma V, a hybrid physical modelling virtual instrument" 01-aug-2024 https://news.ycombinator.com/item?id=41132104 29 comments
"Show HN: I built a synthesizer based on 3D physics" 02-may-2025 https://news.ycombinator.com/item?id=43873074 123 comments
https://github.com/Qzping/ELGAR
It's just fun to see solutions to problems you didn't even know to exist.
> Violin bowing, the researchers say, is a much more complicated interaction to model.
I have no doubt there's been analytical/semi-analytical models around for decades. I mean a program that can take an arbitrary geometry or class thereof with specific materials and simulate the high frequency vibrations and model interactions with the body with high fidelity (not through ad-hoc models) is probably still out of scope of real time simulation.
My point is really that there's often families of models that deal with one thing, from semi-analytical first coded in Fortran in the 80s that can run in milliseconds but is only valid in certain configurations with a low degree of accuracy, to "first principles" simulations that may well require a supercomputer to produce results to a useful degree of accuracy (and not in real time). So, just because you see someone claim they can "simulate X", and then another makes the same claim 40 years later, that doesn't mean they're doing the same thing.
For instance, aeronautics has XFOIL. It's a semi-analytical model first devised in the 80s that computes aeronautics coefficients for a certain class of airfoils (NACA). My understanding is it's a very clever, and industrially significant, piece of code, but ultimately it works in a narrow regime with some heavy simplifications. You can now get results from this in real time on a webpage. A proper CFD calculation to a NACA wing will take in the order of minutes to hours on a workstation (depending on requested precision and settings, e.g. speed of air), and while closer to first principles, it's still using physical simplifications (RANS). So yeah, although nominally people have been "simulating airfoils" for 40 years, the techniques have refined considerably, and will continue to do so (practical LES and, someday, DNS). It might be another century that people are still "simulating airfoils" in ever more accurate (nailing down within the constraints), high fidelity (lifting constraints) and generic ways.
Back to instruments, this is a difficult coupled problem, in fairly high frequencies (high frequencies = more expensive), with possible fluid-structure interactions, not to mention the geometries are fairly complex (to even get a workable mesh to begin with). My uneducated guess is we're still at either semi-analytical, or at the "considerably simplified first principles" stage for this type of problems. Just like DNS, I'm sure you could "just resolve the scales and run it through a simulation with a really tiny time step", and this is liable to be similarly expensive as DNS (million dollar single simulation). Additionally, they have to deal with the human ear, which is perhaps more unforgiving than an error plot on drag or lift. So I wouldn't dismiss news of instrument simulation as stale just because someone made something that produced similar artifacts in the past, as the methods will continue to evolve considerably.
It's much more difficult to use, though - you have to control lots of aspects of the simulation (using automation in DAW or MIDI controllers) to make it sound actually realistic.
OK I guess it seems like this is more of a tool for luthiers than for composers or music producers.
I currently use a raspberry pi with Pianoteq as sound output for my digital piano. It got a reluctant stamp of approval from my pianist son, although of course he prefers the physical response of even a poor acoustic piano.
90s physical modelling was a very simplified modular kind of modelling. Instead of analogue oscillators and filters you had "string" models, "pipe" models, various resonators, and so on.
The models were interesting, but still quite crude and basic.
This project is the most physical kind of physical modelling. It's an unsimplified brute-force model of the entire instrument body and string system, in full.
It doesn't try to "model a resonator", it models blocks of wood with various holes, and calculates how they distort and radiate as sound passes through them.
It's ridiculously expensive computationally, but it's also the only way to get all of the nuances of the sound.
I expect they're already working on a stick-slip model for bowing.
Theoretically you could use the same technique to model a piano or guitar, and you would get something indistinguishable from a real instrument.
You'd likely need a supercomputer to run the model in anything approaching real time.
But the advantage is that once you've got it you can do insane things like replace the strings with wood instead of metal, or use different metals, or "build" nonphysical pianos that are fifty feet long and have linear overtones all the way down to the bass.
I can tell the difference between Pianoteq and a real piano, but I can't in general tell the difference between Pianoteq and a recording of a piano. Maybe there's some insane level of hi-fi gear which would let me, idk? But in general, when it's good enough for Steinway, Petrof and my conservatory student son to give their stamp of approval, I think it's good enough for me as well :) quite a few of those insane things you mention you can already do with pianoteq's physical model (i.e. emulating a 20m grand), and I suspect they keep a few knobs to themselves to sell virtual instruments.