First-principle simulations are at the heart of the high-energy physics research program. They link the vast data output of multi-purpose detectors with fundamental theory predictions and interpretation. In the coming LHC runs, these simulations will face unprecedented precision requirements to match the experimental accuracy. New ideas and tools based on neural networks have been developed at the interface of particle physics and machine learning. They can improve the speed and precision of forward simulations and handle the complexity of collision data. Such networks can be employed within established simulation tools or as part of a new framework. Since neural networks can be inverted, they open new avenues in LHC analyses.