Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data
This work addresses the challenge of modeling physical systems from data for researchers in computational physics and applied mathematics, though it appears incremental as it builds on existing Hamiltonian reconstruction techniques.
The authors tackled the problem of reconstructing unknown Hamiltonian systems from trajectory data by developing a structure-preserving numerical method that directly approximates the Hamiltonian to enforce conservation, demonstrating its effectiveness through numerical examples.
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.