Introducing SINFONIA: Symplectic, slimplectic and Magnusian (Neural) Flows for Orbital Numerical Integration and Acceleration

arXiv:2609.03329 · gr-qc, astro-ph.HE, astro-ph.IM, cs.LG, physics.comp-ph · Submitted 2026-09-03 · Read on arXiv

gr-qc, astro-ph.HE, astro-ph.IM, cs.LG, physics.comp-ph

Submitted: 2026-09-03

Updated: 2026-09-03

Comments: 21 pages, 1 table, 5 figures. Comments welcomed

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Benchmark — 13× in this paper · explained in 2 episodes
• Accuracy — 12× in this paper · explained in 1 episode
• Adam — 5× in this paper · explained in 2 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• Benchmarking — 2× in this paper · explained in 3 episodes
• Degeneracy — 2× in this paper · explained in 3 episodes
• Distillation — 2× in this paper · explained in 2 episodes
• Magnus Expansion — 2× in this paper · explained in 4 episodes
• Core — 1× in this paper · explained in 2 episodes
• Failure Modes — 1× in this paper · explained in 3 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Initial Data — 1× in this paper · explained in 2 episodes
• Physical Constraints — 1× in this paper · explained in 7 episodes

Sources

• The Magnusian generator for dissipative systems and application to leading 2.5PN radiation-reaction dynamics
• Message Passing Neural PDE Solvers
• Symplectic Neural Flows for Modeling and Discovery
• LISA Definition Study Report
• Lagrangian Neural Networks
• Fourier Neural Operators Explained: A Practical Perspective
• Learning Hamiltonian flows from numerical integrators and examples
• The principle of stationary nonconservative action for classical mechanics and field theories
• Fourier Neural Operator for Parametric Partial Differential Equations
• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• Autoregressive rollout error in latent-space reduced-order models of bluff-body wakes is accumulated phase drift
• Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately
• CoSynFlow: Conformal Symplectic Neural Flows for Cross-System Prediction of Dissipative Hamiltonian Dynamics

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