Gravity-Informed Neural Networks for Post-Newtonian Binary Dynamics
Abstract
We introduce a gravity-informed neural-network (GravINNs) framework for learning post-Newtonian binary orbital dynamics. The method incorporates the equations of motion directly into the training phase and is developed at three complementary levels. First, we construct single-orbit surrogates for conservative post-Newtonian dynamics and assess their accuracy across different orbital configurations. We then extend the approach to a parametric model spanning a four-dimensional parameter space defined by the initial separation, radial and tangential momenta, and symmetric mass ratio, allowing a single trained network to represent entire families of orbits and replace repeated numerical integrations. Finally, we consider dissipative dynamics by including the leading radiation-reaction contribution at $2.5$PN order. In this regime, the network reproduces the orbital evolution and the associated secular energy loss, starting from a conservative 2PN warm start and without using dissipative reference trajectories in the training. These results show that physics-informed neural-networks (PINNs) can provide accurate and flexible representations of both conservative and dissipative post-Newtonian dynamics. The complete implementation and the models used in this work are publicly available through the \texttt{GravINNs} repository.
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BibTeX
@misc{barbagallo2026gravityinformed,
title = {{Gravity-Informed Neural Networks for Post-Newtonian Binary Dynamics}},
author = {Gabriele Barbagallo and Javier Matulich},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.25222},
eprint = {2609.25222},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25222},
}
RIS
TY - UNPB
TI - Gravity-Informed Neural Networks for Post-Newtonian Binary Dynamics
AU - Gabriele Barbagallo
AU - Javier Matulich
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2609.25222
UR - https://arxiv.org/abs/2609.25222
AB - We introduce a gravity-informed neural-network (GravINNs) framework for learning post-Newtonian binary orbital dynamics. The method incorporates the equations of motion directly into the training phase and is developed at three complementary levels. First, we construct single-orbit surrogates for conservative post-Newtonian dynamics and assess their accuracy across different orbital configurations. We then extend the approach to a parametric model spanning a four-dimensional parameter space defined by the initial separation, radial and tangential momenta, and symmetric mass ratio, allowing a single trained network to represent entire families of orbits and replace repeated numerical integrations. Finally, we consider dissipative dynamics by including the leading radiation-reaction contribution at $2.5$PN order. In this regime, the network reproduces the orbital evolution and the associated secular energy loss, starting from a conservative 2PN warm start and without using dissipative reference trajectories in the training. These results show that physics-informed neural-networks (PINNs) can provide accurate and flexible representations of both conservative and dissipative post-Newtonian dynamics. The complete implementation and the models used in this work are publicly available through the \texttt{GravINNs} repository.
ER -