Hello!

Well Volterra series can be seen as a generalisation of convolution for non linear systems. In theory, you can model any non linear system with them. In practice it’s almost impossible to use because you need to calculate and process a lot of “kernels” to get an accurate emulation of any heavily non linear system, which generates more than 3 harmonics. That’s the reason you will never ever find any heavily non linear system simulation in a plug-in using only Volterra kernels.

The most well known is Acustica Audio Nebula, and even if its techonology can in theory model a lot of different things, even with time-varying behaviour, it can’t be used at all for stuff like guitar amplifiers, distortion pedals etc. I know also that some plug-ins and products use a simplification of the Volterra series called Hammerstein, with only the diagonal kernels, but it removes most of the interesting original stuff in the model and can also be used only for weakly non linear systems. There are also a couple of articles from Thomas Hélie for example where the Volterra kernels are calculated explicitely to model things like synths ladder filters up to the third harmonics…

But honestly, my advice here would be to forget about this approach and to use more efficient non linear systems modeling techniques instead…