  The simulation of power system dynamics poses a computationally expensive
task. Considering the growing uncertainty of generation and demand patterns,
thousands of scenarios need to be continuously assessed to ensure the safety of
power systems. Physics-Informed Neural Networks (PINNs) have recently emerged
as a promising solution for drastically accelerating computations of non-linear
dynamical systems. This work investigates the applicability of these methods
for power system dynamics, focusing on the dynamic response to load
disturbances. Comparing the prediction of PINNs to the solution of conventional
solvers, we find that PINNs can be 10 to 1000 times faster than conventional
solvers. At the same time, we find them to be sufficiently accurate and
numerically stable even for large time steps. To facilitate a deeper
understanding, this paper also present a new regularisation of Neural Network
(NN) training by introducing a gradient-based term in the loss function. The
resulting NNs, which we call dtNNs, help us deliver a comprehensive analysis
about the strengths and weaknesses of the NN based approaches, how
incorporating knowledge of the underlying physics affects NN performance, and
how this compares with conventional solvers for power system dynamics.
