[Learning Hamiltonian from Pixel Data] Can the embedding actually contains information about momentum?

[Young1906]

Hi, I have a question regarding the feasibility of learning canonical coordinates from a single image. In the paper, I understand that the CNN encoder maps pixel data to z, which contains information about the pendulum's position and momentum. However, I think z can't include any information about momentum since, given a position (same pixel data), the pendulum can have different velocities (given a different initial condition). I'm sorry if this is not a proper channel for querying. Thanks.