AI forecasting of higher-order wave modes of spinning binary black hole mergers

Abstract

We present a physics-inspired transformer model that predicts the non-linear dynamics of higher-order wave modes emitted by quasi-circular, spinning, non-precessing binary black hole mergers. The model forecasts the waveform evolution from the pre-merger phase through the ringdown, starting with an input time-series spanning $ t \in [-5000\textrm{M}, -100\textrm{M}) $. The merger event, defined as the peak amplitude of waveforms that include the $l = |m| = 2$ modes, occurs at $ t = 0\textrm{M} $. The transformer then generates predictions over the time range $ t \in [-100\textrm{M}, 130\textrm{M}] $. We produced training, evaluation and test sets using the NRHybSur3dq8 model, considering a signal manifold defined by mass ratios $ q \in [1, 8] $; spin components $ s^z_{\{1,2\}} \in [-0.8, 0.8] $; modes up to $l \leq 4$, including the $(5,5)$ mode but excluding the $(4,0)$ and $(4,1)$ modes; and inclination angles $\theta \in [0, \pi]$. We trained the model on 14,440,761 waveforms, completing the training in 15 hours using 16 NVIDIA A100 GPUs in the Delta supercomputer. We used 4 H100 GPUs in the DeltaAI supercomputer to compute, within 7 hours, the overlap between ground truth and predicted waveforms using a test set of 840,000 waveforms, finding that the mean and median overlaps over the test set are 0.996 and 0.997, respectively. Additionally, we conducted interpretability studies to elucidate the waveform features utilized by our transformer model to produce accurate predictions. The scientific software used for this work is released with this manuscript.