  We present a numerical approach for approximating unknown Hamiltonian systems
using observation data. A distinct feature of the proposed method is that it is
structure-preserving, in the sense that it enforces conservation of the
reconstructed Hamiltonian. This is achieved by directly approximating the
underlying unknown Hamiltonian, rather than the right-hand-side of the
governing equations. We present the technical details of the proposed algorithm
and its error estimate in a special case, along with a practical de-noising
procedure to cope with noisy data. A set of numerical examples are then
presented to demonstrate the structure-preserving property and effectiveness of
the algorithm.
