A process trains a neural network that digitally models an audio system. The process couples a test signal into an input of a reference audio system. The process further electronically collects an output of the reference audio system responsive to the test signal as captured information. Moreover, the process trains a neural network using at least some of the captured information such that the overall output of the neural network converges towards an output representative of the reference audio system. The process also outputs to a graphical user interface, a graphical representation associated with the trained neural network, the graphical representation visually displaying at least one virtual control. Here, upon coupling a musical instrument to the trained neural network, a digital signal representing a musical instrument signal from the musical instrument is processed through the trained neural network in the time domain with an algorithmic latency under 20 milliseconds.