A fast, differentiable neural-network surrogate for precessing binary black-hole waveforms

Gravitational-wave parameter estimation requires millions of waveform evaluations per event, a cost that constrains real-time inference and population studies. We present a fast, fully differentiable neural-network surrogate for the precessing numerical-relativity model, spanning its full intrinsic parameter space lambda=(q,, 1,, 2) together with the reference orbital frequency omega 0. Rather than a single polarization at a fixed orientation, the surrogate predicts the inertial-frame spherical-harmonic modes h m (at most 4), so that both polarizations h+,h times at an arbitrary orientation (iota, phi, psi) are reconstructed from one network evaluation through an analytic, differentiable mode-to-strain projection. Trained on 6 times10 5 waveforms, it attains a fixed-orientation match of mean 0.975 (median 0.988) and an orientation-averaged match of mean 0.940 (median 0.975) for q in[1,4], 1,2 at most 0.8, while keeping the overall strain amplitude physical (median ratio 0.98). It generates a waveform in ms (single) and about 3.5 times10 4 per second in batches on a single GPU. Because the mode-to-strain projection is analytic, the surrogate is differentiable in both intrinsic and extrinsic parameters, yielding a full 13-dimensional Fisher matrix (validated against finite differences) and gradient-based (HMC/NUTS) parameter estimation.