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Life sciences · Preprint
arXiv · September 3, 2026
Raises a question worth testing. It does not answer one.
This preprint proposes three neural-flow architectures (SINFONIA-J0, J1, J2) designed to learn finite-time orbital evolution maps for gravitational-wave modelling while preserving symplectic structure. The authors demonstrate in a single 2.5PN neutron-star inspiral scenario that encoding secular energy–angular-momentum balance allows the learned maps to remain accurate through 10²–10⁵ window compositions with phase errors orders of magnitude below a slimplectic integrator benchmark. This is a proof-of-concept in silico result with no peer review, external validation, or application to real observational data.
Preprint. Numerical application to 2.5PN neutron-star binary inspiral; no observational or experimental population.. Intervention: Three neural-flow architectures (SINFONIA-J0, J1, J2) designed to learn finite-time orbital evolution maps with structure-preserving properties.. Compared with: Benchmark slimplectic integrator..
All three neural-flow architectures expose the same controlling mechanism: long-time accuracy governed by signed projection onto a single secular channel fixed by energy–angular-momentum balance. Learned maps remain accurate through 10²–10⁵ window compositions to coalescence at timesteps of a full orbital period and beyond. Chained phase errors reach orders of magnitude below a benchmark slimplectic integrator at lower computational cost.
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This is a proof-of-concept methodological study proposing neural-flow architectures for gravitational-wave modelling; it demonstrates feasibility in silico on a simplified system but does not validate clinical or observational outcomes and has not been peer reviewed.
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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.
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