@inproceedings{bibcite_131,
  author = {Yaojun Li and Yulong Yang and Christine Alen-Blanchette},
  title = {Frequency-Structured Hamiltonian Neural Network for Multi-Timescale Dynamics},
  abstract = {<p>Hamiltonian Neural Networks and related structure-preserving dynamics models encode conservation laws, but their scalar Hamiltonian parameterizations inherit the spectral bias of deep networks, limiting their ability to learn stiff multi-timescale systems with coupled fast and slow dynamics. We introduce the Frequency-Structured Hamiltonian Neural Network (FS-HNN), which decomposes the system Hamiltonian into learned components trained on frequency-filtered views of observed trajectories, then recombines them into a single scalar Hamiltonian so that the learned ODE dynamics remain Hamiltonian by construction. For PDEs with unknown or problem-dependent structure, FS-HNN represents Hamiltonians as neural functionals, learns the action of the dynamics operator, and uses projection to enforce conservative structure when appropriate. Across ODE and PDE benchmarks, including the Fermi--Pasta--Ulam--Tsingou chain, shallow water equations, and incompressible Taylor--Green vortex, FS-HNN achieves improved long-horizon rollout accuracy and more accurate energy behavior than existing structure-preserving baselines.</p>},
  year = {2026},
  journal = {Conference on Neural Information Processing Systems (NeurIPS)},
}