In this talk, we introduce machine learning methods that exploit the underlying physical models of power systems to achieve an up to 100x speedup in power system dynamic security assessment. We propose neural network training procedures that make use of the wide range of mathematical models describing power system behavior, both steady-state and dynamics, and integrate those inside the neural network training process. Physics-informed neural networks require substantially less input data for training, while achieving high accuracy. Methods such as the ones we discuss in this talk unlock the potential of neural networks to perform power system tasks at extremely fast computing times. This allows to efficiently handle the increasing uncertainty in power system operation by assessing large number of possible scenarios in a fraction of the time.