Quantum tunnelling composites, or 'QTCs', are composites with an elastomeric polymer matrix and a metal particle filling (usually nickel). At rest, these metal particles do not touch each other and the polymer acts as an insulator. When the material is suitably deformed, however, the particles come together (without actually touching) and the quantum tunnelling effect is promoted, which causes the electrical resistance to fall drastically. This paper contains a detailed description of neural networks for a faster, simpler and more accurate modelling and simulation of QTC behaviour that is based on properly training these neural models with the help of data from characterization tests. Instead of using analytical equations that integrate different quantum and thermomechanical effects, neural networks are used here due to the notable nonlinearity of the aforementioned effects, which involve developing analytical models that are too complex to be of practical use. By conducting tests under different pressures and temperatures that encompass a wide range of operating conditions for these materials, different neural networks are trained and compared as the number of neurons is increased. The results of these tests have also enabled certain previously described phenomena to be simulated with more accuracy, especially those involving the response of QTCs to changes in pressure and temperature.