[2604.00473] Phase space integrity in neural network models of Hamiltonian dynamics: A Lagrangian descriptor approach

Computer Science > Machine Learning arXiv:2604.00473 (cs) [Submitted on 1 Apr 2026] Title:Phase space integrity in neural network models of Hamiltonian dynamics: A Lagrangian descriptor approach Authors:Abrari Noor Hasmi, Haralampos Hatzikirou, Hadi Susanto View a PDF of the paper titled Phase space integrity in neural network models of Hamiltonian dynamics: A Lagrangian descriptor approach, by Abrari Noor Hasmi and 1 other authors View PDF HTML (experimental) Abstract:We propose Lagrangian Descriptors (LDs) as a diagnostic framework for evaluating neural network models of Hamiltonian systems beyond conventional trajectory-based metrics. Standard error measures quantify short-term predictive accuracy but provide little insight into global geometric structures such as orbits and separatrices. Existing evaluation tools in dissipative systems are inadequate for Hamiltonian dynamics due to fundamental differences in the systems. By constructing probability density functions weighted by LD values, we embed geometric information into a statistical framework suitable for information-theoretic comparison. We benchmark physically constrained architectures (SympNet, HénonNet, Generalized Hamiltonian Neural Networks) against data-driven Reservoir Computing across two canonical systems. For the Duffing oscillator, all models recover the homoclinic orbit geometry with modest data requirements, though their accuracy near critical structures varies. For the three-mode nonlinear Schröding...