What's Next? Predicting Hamiltonian Dynamics from Discrete Observations of a Vector Field
This work addresses a domain-specific problem in physics and machine learning for predicting Hamiltonian systems, but it is incremental as it builds on existing methods without introducing a new paradigm.
The paper tackles the problem of predicting Hamiltonian dynamics from discrete vector field observations, comparing methods that are either informed or uninformed of the Hamiltonian property, and finds that incorporating this information improves effectiveness with varying efficiency trade-offs across systems.
We present several methods for predicting the dynamics of Hamiltonian systems from discrete observations of their vector field. Each method is either informed or uninformed of the Hamiltonian property. We empirically and comparatively evaluate the methods and observe that information that the system is Hamiltonian can be effectively informed, and that different methods strike different trade-offs between efficiency and effectiveness for different dynamical systems.