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Abstract Numerical relativity (NR) simulations of binary black hole (BBH) systems provide the most accurate gravitational wave predictions, but at a high computational cost—especially when the black holes have nearly extremal spins (i.e. spins near the theoretical upper limit) or very unequal masses. Recently, the technique of reduced order modeling has enabled the construction of ‘surrogate models’ trained on an existing set of NR waveforms. Surrogate models enable the rapid computation of the gravitational waves emitted by BBHs. Typically these models are used for interpolation to compute gravitational waveforms for BBHs with mass ratios and spins within the bounds of the training set. Because simulations with nearly extremal spins are so technically challenging, surrogate models almost always rely on training sets with only moderate spins. In this paper, we explore how well surrogate models can extrapolate to nearly extremal spins when the training set only includes moderate spins. For simplicity, we focus on one-dimensional surrogate models trained on NR simulations of BBHs with equal masses and equal, aligned spins. We assess the performance of the surrogate models at higher spin magnitudes by calculating the mismatches between extrapolated surrogate model waveforms and NR waveforms, by calculating the differences between extrapolated and NR measurements of the remnant black-hole mass, and by testing how the surrogate model improves as the training set extends to higher spins. We find that while extrapolation in this one-dimensional case is viable for current detector sensitivities, surrogate models for next-generation detectors should use training sets that extend to nearly extremal spins.
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Sequence modeling of higher-order wave modes of binary black hole mergers
Higher-order gravitational wave modes from quasi-circular, spinning, non-precessing binary black hole mergers encode key information about these systems' nonlinear dynamics. We model these waveforms using transformer architectures, targeting the evolution from late inspiral through ringdown. Our data is derived from the \texttt{NRHybSur3dq8} surrogate model, which includes spherical harmonic modes up to ℓ≤4 (excluding (4,0), (4,±1) and including (5,5) modes). These waveforms span mass ratios q≤8, spin components sz1,2∈[−0.8,0.8], and inclination angles θ∈[0,π]. The model processes input data over the time interval t∈[−5000M,−100M) and generates predictions for the plus and cross polarizations, (h+,h×), over the interval t∈[−100M,130M]. Utilizing 16 NVIDIA A100 GPUs on the Delta supercomputer, we trained the transformer model in 15 hours on over 14 million samples. The model's performance was evaluated on a test dataset of 840,000 samples, achieving mean and median overlap scores of 0.996 and 0.997, respectively, relative to the surrogate-based ground truth signals. We further benchmark the model on numerical relativity waveforms from the SXS catalog, finding that it generalizes well to out-of-distribution systems, capable of reproducing the dynamics of systems with mass ratios up to q=15 and spin magnitudes up to 0.998, with a median overlap of 0.969 across 521 NR waveforms and up to 0.998 in face-on/off configurations. These results demonstrate that transformer-based models can capture the nonlinear dynamics of binary black hole mergers with high accuracy, even outside the surrogate training domain, enabling fast sequence modeling of higher-order wave modes.
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- Award ID(s):
- 2209892
- PAR ID:
- 10617110
- Publisher / Repository:
- ArXiv
- Date Published:
- Format(s):
- Medium: X
- Institution:
- ArXiv
- Sponsoring Org:
- National Science Foundation
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