Learning Post-Newtonian Corrections from Numerical Relativity

Accurate modeling of gravitational waveforms from compact binary coalescences remains central to gravitational-wave (GW) astronomy. Post-Newtonian (PN) approximations capture the early inspiral dynamics analytically but break down near merger, while numerical relativity (NR) provides the accurate yet computationally expensive waveforms over limited parameter ranges. We develop a physics-informed neural network (PINN) framework that learns corrections mapping PN dynamics and waveforms to their NR counterparts. As a demonstration of the approach, we use the TaylorT4 PN model as the baseline, and train the network on a remarkably small dataset of only eight hybridized NR surrogate waveforms (NRHybSur3dq8) to learn higher-order corrections to the orbital dynamics and waveform modes for nonspinning noneccentric systems. Physically motivated loss terms enforce known limits and symmetries, such as vanishing corrections in the Newtonian limit and suppression of odd-$m$ modes in equal-mass systems, promoting consistent and reliable extrapolation beyond the training region. We simultaneously incorporate corrections that account for the different meaning of mass parameters in PN and NR descriptions. The learned corrections significantly reduce the phase and amplitude error through the inspiral up to about $200M$ before the merger. This approach provides a differentiable and computationally efficient bridge between PN and NR, offering a path toward waveform models that generalize more robustly beyond existing NR datasets.