Learning Binary Black Hole Orbital Dynamics with Neural Ordinary Differential Equations (Neural ODEs)

Neural ordinary differential equations (neural ODEs) provide a machine learning framework for modeling dynamical systems, where the time evolution is described by a combination of known physics and data-driven components. Rather than learning the full dynamics from scratch, one can embed the established lower-order terms of the governing equations and use neural networks to represent unknown or higher-order corrections. This hybrid approach is particularly valuable in gravitational-wave astronomy, where accurate modeling of binary black hole dynamics underpins the waveform templates used by detectors such as the Laser Interferometer Gravitational-Wave Observatory (LIGO). In order to infer the properties of binary black hole systems from the observed signals, it is necessary to have a comprehensive template bank which spans the parameter space. However, creating one fully accurate template can take weeks on a supercomputer. By using neural networks to learn portions of the underlying equations of motion for binary black hole systems, we aim to accelerate and refine the template creation process. We present a proof of concept of a set of trained neural networks which accurately replicate Keplerian orbital dynamics consisting of a conservative Keplerian Hamiltonian with an additional Post-Newtonian energy loss term due to gravitational wave radiation. Application of the approach to a Keplerian system with additional environmental effects is also discussed. Finally, we will consider application of the framework to the Effective One-Body (EOB) formalism used to describe the evolution of binary black hole systems.