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)
The paper introduces a world model that learns to predict the evolution of physical systems while respecting key physical principles. By hard‑coding a general structure—generating dynamics from the gradient of a learned energy via a fixed reversible operator and imposing constraints on energy, dissipation, and interventions—the model achieves second‑law compatible dissipation, accurate responses to parameter changes, long‑term stability, and robustness to disturbances. Experiments on an electromagnetic cavity, a particle‑in‑cell grid, and shallow‑water fluid demonstrate that the model can recover accurate constitutive functions, distinguish conserving from dissipating regimes, and transfer learned physics to unseen conditions, outperforming unconstrained models.
By Yufeng Wang, Parivesh Priye, Lu Wei, Haibin Ling
arXiv:2606. 27029v2 Announce Type: replace Abstract: Hamiltonian Neural Networks (HNNs) integrate physical priors into neural models by learning a system's Hamiltonian, improving generalization and sample efficiency.
By Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta, Melvin Leok, Georgios Korpas
arXiv:2609.24737v1 Announce Type: new
Abstract: We introduce Ananke, a representation-learning framework that scaffolds latent representations onto a structured product-torus prior, and its flagship...
By Zhongping Ji
arXiv:2606. 27029v1 Announce Type: new Abstract: Hamiltonian Neural Networks (HNNs) integrate physical priors into neural models by learning a system's Hamiltonian, improving generalization and sample efficiency.
By Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta, Melvin Leok, Georgios Korpas
We introduce Ananke, a representation-learning framework that scaffolds latent representations onto a structured product-torus prior, and its flagship visual backbone realization, Contractive Torus At...
The paper demonstrates that learned simulators can fail in two distinct ways when conditions change: long‑horizon drift due to accumulated errors and incorrect responses to interventions on physical parameters. By adding a symplectic integrator to preserve conservative dynamics, rollouts remain stable for up to 100× the training horizon, while encoding physical coupling via explicit linear factorization allows the model to generalize to unseen signs of that coupling. The study shows that stability and counterfactual generalization arise from separate structural choices, enabling designers to impose each property independently.
By Yufeng Wang, Parivesh Priye, Lu Wei, Haibin Ling