Learning higher order PN dynamics from Numerical Relativity using DHNNs

Analytical approximations to General Relativity—such as the post-Newtonian (PN), post-Minkowskian, and black hole perturbation theory frameworks—model the dynamics and gravitational radiation of black hole binaries under limiting assumptions that are valid only at specific phases. The Effective One Body (EOB) formalism unifies these approaches to provide a self-consistent description of the entire binary evolution. However, accurate waveform modeling within the EOB framework still relies on phenomenological calibrations to Numerical Relativity (NR) simulations. These calibrations typically introduce effective, next-to-known-order PN coefficients determined by fitting to NR waveform catalogs. While this strategy yields sufficient accuracy for current gravitational-wave data analysis, it does not resolve the underlying source of discrepancies: the lack of higher-order PN terms and an analytic model for the transition between late inspiral and merger dynamics.

In this study, we leverage recent advances in Dissipative Hamiltonian Neural Networks to infer the functional form of residual corrections to the EOB Hamiltonian beyond a known PN order. Starting from a 3PN-accurate EOB model, we train the Schwarzschild-like potentials to reproduce the 4+PN corrections and validate the results against the analytically known 4PN EOB model. Our results demonstrate the potential of machine learning–augmented Hamiltonian frameworks to systematically recover missing physical information and improve analytical waveform models for gravitational-wave astrophysics.