Vertical integration is a promising solution to further increase the performance of future ICs, but such 3D ICs present complex thermal issues that cannot be solved by conventional cooling techniques. Interlayer liquid cooling has been proposed to extract the heat accumulated within the chip. However, the development of liquid-cooled 3D ICs strongly relies on the availability of accurate and fast thermal models. In this work, we present a novel thermal model for 3D ICs with interlayer liquid cooling that exploits the neural network theory. Neural Networks can be trained to mimic with high accuracy the thermal behaviour of 3D ICs and their implementation can efficiently exploit the massive computational power of modern parallel architectures such as graphic processing units. We have designed an ad-hoc Neural Network model based on pertinent physical considerations of how heat propagates in 3D IC architectures, as well as exploring the most optimal configuration of the model to improve the simulation speed without undermining accuracy. We have assessed the accuracy and run-time speed-ups of the proposed model against a 3D IC simulator based on compact model. We show that the proposed thermal simulator achieves speed-ups up to 106x for 3D ICs with liquid cooling while preserving the maximum absolute error lower than 1.0 degrees C.