When it comes to neural amp modelling, they pretty much all do the same thing: estimate the amp's input/output behaviour by sending a known test signal through the input and recording the response at the output. The model is then trained to reproduce that relationship. Depending on the system, the test signal may contain sweeps, noise-like signals, impulses, etc.

Back in the olden days, you'd emulate guitar cabinets using multiband EQs and filters, either analog or digital, sculpting the frequency response until it sounded close enough to the real deal. Then people started measuring the cabinet's actual response directly: send a known signal through it, record the result, and derive an impulse response. That IR could then be used with convolution to reproduce the cabinet's filtering accurately. Neural networks came later, mainly to model the nonlinear behaviour of amps and pedals.

That's basically the 15+ year progress we've had in the guitar world.