In grad school, I had a tiny start-up with a classmate selling a virtual instrument doing just what you describe (for guitar sound synthesis). We had PDE models for the string, finger/string interaction, fret/string interactions etc. We would then discretize these PDEs to generate in real-time a synthetic "force" applied by the string on soundboard, and then convolve this in real-time with measured impulse responses of real acoustic guitar soundboards. Our website is still up (spicyguitar.com) and we give it for free now, but I don't know if it still works in recent DAWs.