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This research introduces SINFONIA, a suite of neural-flow architectures designed to solve long-duration gravitational-wave modeling by learning structure-preserving evolution maps. By leveraging symplectic, slimplectic, and Magnusian flows, the method prevents numerical phase drift over $10^2$–$10^5$ compositions while enabling physics inference for unmodeled forces. The work establishes a proof of concept for using differentiable, learned dynamics to accelerate orbital integration in high-energy astrophysics.
Introducing SINFONIA: Symplectic, slimplectic and Magnusian (Neural) Flows for Orbital Numerical Integration and Acceleration
arXiv:2609.03329v1 Announce Type: cross Abstract: Long-duration gravitational-wave modelling must resolve fast orbital motion together with slow dissipative evolution while preventing small numerical errors from accumulating into secular phase drift. Here we ask whether the finite-time evolution map itself can be learned as an explicit, differentiable, structure-preserving object and then repeatedly composed through a complete inspiral. We construct three neural-flow architectures: a symplectic and slimplectic flow on Galley's doubled phase space, [SINFONIA-J0]; a Taylor-anchored flow, [SINFONIA-J1]; and a Magnusian flow that learns the finite-time dissipative correction in the interaction picture, [SINFONIA-J2]. Applied to a 2.5PN neutron-star inspiral, all three expose the same controlling mechanism: long-time accuracy is governed not by pointwise map error alone, but by its signed projection onto a single secular channel fixed by energy--angular-momentum balance. Encoding this structure allows the learned maps to remain accurate through $10^{2}$--$10^{5}$ window compositions to coalescence at timesteps of a full orbital period and beyond, reaching chained phase errors orders of magnitude below a benchmark slimplectic integrator at lower cost. The same secular structure can also be exploited for physics inference: when the channel is left unconstrained, the accumulated phase retains enough information to recover an un-modelled dynamical-friction-like force, both parametrically and as a learned function of separation. Network-off controls isolate the contribution of learning from the analytic structure already built into each map. These results establish a proof of concept for structure-preserving learned evolution maps as tools for fast long-duration integration and physics inference in gravitational-wave source modelling.
Abstract:Long-duration gravitational-wave modelling must resolve fast orbital motion together with slow dissipative evolution while preventing small numerical errors from accumulating into secular phase drift. Here we ask whether the finite-time evolution map itself can be learned as an explicit, differentiable, structure-preserving object and then repeatedly composed through a complete inspiral. We construct three neural-flow architectures: a symplectic and slimplectic flow on Galley's doubled phase space, [SINFONIA-J0]; a Taylor-anchored flow, [SINFONIA-J1]; and a Magnusian flow that learns the finite-time dissipative correction in the interaction picture, [SINFONIA-J2]. Applied to a 2.5PN neutron-star inspiral, all three expose the same controlling mechanism: long-time accuracy is governed not by pointwise map error alone, but by its signed projection onto a single secular channel fixed by energy--angular-momentum balance. Encoding this structure allows the learned maps to remain accurate through $10^{2}$--$10^{5}$ window compositions to coalescence at timesteps of a full orbital period and beyond, reaching chained phase errors orders of magnitude below a benchmark slimplectic integrator at lower cost. The same secular structure can also be exploited for physics inference: when the channel is left unconstrained, the accumulated phase retains enough information to recover an un-modelled dynamical-friction-like force, both parametrically and as a learned function of separation. Network-off controls isolate the contribution of learning from the analytic structure already built into each map. These results establish a proof of concept for structure-preserving learned evolution maps as tools for fast long-duration integration and physics inference in gravitational-wave source modelling.
21 pages, 1 table, 5 figures. Comments welcomed
General Relativity and Quantum Cosmology (gr-qc); High Energy Astrophysical Phenomena (astro-ph.HE); Instrumentation and Methods for Astrophysics (astro-ph.IM); Machine Learning (cs.LG); Computational Physics (physics.comp-ph)
arXiv:2609.03329 [gr-qc]
(or arXiv:2609.03329v1 [gr-qc] for this version)
https://doi.org/10.48550/arXiv.2609.03329 arXiv-issued DOI via DataCite (pending registration)
From: Lidia J. Gomes Da Silva Miss [view email] [v1] Thu, 3 Sep 2026 03:31:07 UTC (1,342 KB)
Full text under the publisher's open licence · 305 words
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