Solving Hamiltonian systems based on a data-driven deep learning algorithm

Hamiltonian systems have important properties like preservation of symplectic structure and conservation of energy. Traditional numerical iteration methods generally violate these properties. In this paper, we propose solving separable Hamiltonian systems based on a data-driven deep learning algorithm, which is computationally efficient and scalable. The proposed algorithm is both symplectic and energy-conserving. Additionally, it efficiently works with few data points and the obtained solution is continuous. The algorithm consists of three main steps which are (i) obtaining data points from a symplectic solver, (ii) data augmentation part and (iii) providing energy conservation. We evaluated the algorithm on simple harmonic oscillator, nonlinear oscillator and Lotka-Voltera. In conclusion, we have shown that the proposed algorithm works smoothly no matter which solver chosen on all examples.