Model reduction of port-Hamiltonian systems via neural networks

What the math gives to ML

The paper provides a directly transferable way to build neural dynamical systems whose learned vector field preserves port-Hamiltonian structure rather than merely fitting trajectories. The key asset is the factorization of the interconnection matrix as skew-symmetric and the dissipation matrix as positive semidefinite, which yields an energy balance and prevents the network from learning arbitrarily unstable dynamics. A practical adaptation is a latent neural ODE whose Hamiltonian, skew interconnection, and dissipation factors are all neural networks, allowing expressive state-dependent dynamics with a built-in Lyapunov-like energy law. This is most useful for long-horizon forecasting, system identification, differentiable simulators, and stable latent state-space models.