Introducing SINFONIA: Symplectic, slimplectic and Magnusian (Neural) Flows for Orbital Numerical Integration and Acceleration
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 102--105 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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BibTeX
@misc{silva2026introducing,
title = {{Introducing SINFONIA: Symplectic, slimplectic and Magnusian (Neural) Flows for Orbital Numerical Integration and Acceleration}},
author = {Lidia J. Gomes Da Silva},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03329},
eprint = {2609.03329},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03329},
}
RIS
TY - UNPB
TI - Introducing SINFONIA: Symplectic, slimplectic and Magnusian (Neural) Flows for Orbital Numerical Integration and Acceleration
AU - Lidia J. Gomes Da Silva
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03329
UR - https://arxiv.org/abs/2609.03329
AB - 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.
ER -