Trajectory prediction based on conditional Hamiltonian generative network for incomplete observation image sequences

The combination of Hamiltonian formalism and neural networks is playing an important role in dealing with chaotic systems. Aiming at the problem of motion control under the condition of unknown physical quantity and incomplete observation set, a trajectory prediction model based on conditional Hamiltonian generating network (CHGN) for incomplete observation image sequences is proposed. CHGN is composed of Conditional AutoEncoder (CVAE), Hamiltonian neural network (HNN) and Velocity–Verlet integrator. CVAE encoder converts the short-term continuous observation image sequence into target motion state features represented by generalized coordinates and generalized momentum, and generates the trajectory prediction image at the specified time. HNN is used to learn potential Hamiltonian physical quantities, so as to understand more chaotic system dynamics information to realize state cognition. Velocity–Verlet integrator predicts the motion state at any moment according to the Hamiltonian learned by HNN at the current moment. The motion state and the specified time are used as the input of CVAE decoder to generate the target prediction image from the potential motion space. Experimental results show that CHGN can accurately predict target trajectories over a long period of time based on incomplete short-term image sequences, and has better performance with minimum mean square error(MSE) on three physical system datasets than existing deep learning methods.