I would say it's essentially equivalent, especially if you choose a neural network architecture with a very low-dimensional layer in the middle with only a handful of variables.
Then the first half of the network (before the low-dimensional layer) will learn how to "encode" the state of the system in the video in as few variables as possible, such as the orientations and angular momenta of the double pendulum. This is equivalent to what humans do when we look at a messy physical system like the Solar System and model it with a few quantitative parameters.
The bottleneck layer will represent the handful of state variables, and then finally the other half of the network will learn the mathematical function that predicts the system's evolution. This is equivalent to what humans do when we work out physical laws and equations of motion.
Then the first half of the network (before the low-dimensional layer) will learn how to "encode" the state of the system in the video in as few variables as possible, such as the orientations and angular momenta of the double pendulum. This is equivalent to what humans do when we look at a messy physical system like the Solar System and model it with a few quantitative parameters.
The bottleneck layer will represent the handful of state variables, and then finally the other half of the network will learn the mathematical function that predicts the system's evolution. This is equivalent to what humans do when we work out physical laws and equations of motion.