hamiltonian-neural-networks

The paper presents a controlled matched-integrator evaluation of Hamiltonian Neural Networks against a parameter-matched baseline on pendulum and Kepler dynamics, showing significant reductions in energy drift and trajectory error. It also examines the behavior of Störmer–Verlet-style rollouts with learned non-separable Hamiltonians.

Introduces Quantum Port-Hamiltonian Neural Networks (Q-pHNNs) that learn classical dynamics while preserving conservation and dissipation properties using quantum circuits with measurement-induced nonlinearity. Experiments show low energy drift and accurate damping coefficient identification.

The paper identifies failure modes in Hamiltonian Generative Networks (HGN) that prevent temporal generalization to different step sizes in non-conservative environments, and proposes targeted fixes for stable dynamics prediction at variable temporal resolutions.

A blog post explaining Hamiltonian Neural Networks through differential geometry, using a simple mass-spring system to demonstrate how imposing conservation laws via network architecture can lead to more efficient learning. The author builds up mathematical tools like symplectic manifolds and Poisson brackets from basic calculus.