While these techniques are widely used and understood, they work primarily with a model of the abstract sound produced by an instrument or object, not a model of the instrument or object itself. A more recent approach is physical modeling- based audio synthesis, where the audio waveforms are generated using detailed numerical simulation of physical objects or instruments.

via Realtime GPU Audio – ACM Queue.

There are various approaches to physical modeling sound synthesis. One such approach, studied extensively by Stefan Bilbao,¹ uses the finite difference approximation to simulate the vibrations of plates and membranes. The finite difference simulation produces realistic and dynamic sounds (examples can be found at http://unixlab.sfsu.edu/~whsu/FDGPU). Realtime finite difference-based simulations of large models are typically too computationally-intensive to run on CPUs. In our work, we have implemented finite difference simulations in realtime on GPUs.