The paper introduces SINFONIA, a family of neural-flow architectures designed to learn finite-time evolution maps for orbital dynamics while preserving key physical structures. Three variants—symplectic/slimplectic, Taylor-anchored, and Magnusian—are applied to a 2.5PN neutron-star inspiral, demonstrating that long-term accuracy depends on a single secular channel tied to energy–angular-momentum balance rather than pointwise errors. These learned maps achieve accurate phase evolution over up to $10^{5}$ orbital periods at lower computational cost than traditional integrators, and can also be used to infer unmodeled forces from accumulated phase data.
arXiv:2607. 23501v1 Announce Type: new Abstract: Locating periodic solutions of chaotic dynamical systems normally requires an initial guess close enough to the target orbit for numerical continuation or gradient-based search to converge.
By Nikolaos Kollias, Nikolaos Matzakos
The paper introduces Riemannian Neural Hamiltonian Flows, a generative model that extends Hamiltonian normalizing flows to Riemannian manifolds by combining a fixed kinetic energy, a learned scalar potential, and a geodesic leapfrog integrator. It provides an analysis showing how the learned Hamiltonian can be interpreted through an implicit profile and a matched potential, with special cases such as isotropic Gaussian and local harmonic analysis around modes. Experiments on Euclidean, hyperbolic, and spherical spaces demonstrate competitive sample quality and computational efficiency compared to a Riemannian continuous normalizing flow, while confirming the interpretability of the learned potential.
By Vincent Souveton
arXiv:2607. 03339v1 Announce Type: new Abstract: Learning dissipative dynamics from discrete observations is essential for reliable long-horizon prediction and physically meaningful parameter identification.
By Jiale Gong (School of Mathematics), Pengzhan Jin (National Engineering Laboratory for Big Data Analysis and Applications, Peking University, Beijing, China), Dongyang Kuang (School of Mathematics), Lu Li (School of Mathematics), Yifa Tang (State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China)
arXiv:2608. 10235v1 Announce Type: new Abstract: Hamiltonian Neural Networks (HNNs) parameterize conservative dynamics through a learned scalar Hamiltonian, providing an architectural prior that is absent from generic vector-field neural networks.
By Lenick Kemunto Nyabuto, Yae Ulrich Gaba, Birahim Tewe
arXiv:2510. 01788v2 Announce Type: replace Abstract: This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes.
By Cl\'ementine Court\`es (IRMA, MACARON), Emmanuel Franck (MACARON), Michael Kraus (IPP), Laurent Navoret (IRMA, MACARON), L\'eopold Tr\'emant (LML)