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    Higher-multipole spin-aligned eccentric gravitational waveform generation via Fourier neural networks

    Ruijun Shi1,2,3, Zun Wang1,2, Xiaolin Liu4, Tianyu Zhao5, Zhixiang Ren6, and Zhoujian Cao1,2,7,*

    • *Contact author: zjcao@amt.ac.cn

    Phys. Rev. D 112, 084025 – Published 9 October, 2025

    DOI: https://doi.org/10.1103/hzsq-5v2n

    Abstract

    We present a new data-driven waveform model for spin-aligned, eccentric binary black hole waveforms, constructed using a Fourier analysis network (FAN) architecture. Compared to conventional multilayer perceptron (MLP) architecture, the FAN architecture achieves 2.55× higher accuracy under the same parameter budget and reduces training time by 7%. Its trigonometric activation functions embed Fourier features into the network, mitigating MLPs’ spectral bias and enabling more accurate modeling of oscillatory waveform structures. Our model supports mass ratios q<8, eccentricities e<0.5, aligned spins |χ1,2|<0.99, and relativistic anamaly ζ∈[0,2π], covering {(ℓ,m)=(2,2),(2,1),(3,3),(3,2),(4,4),(4,3)} spin-weighted spherical harmonic modes. For (2,2)-mode, the median mismatch of our model is 1e-3 under advanced Laser Interferometer Gravitational Wave Observatory sensitivity, and the generation speed is ∼5  ms, which is 50× faster than seobnrv5ehm. In the low-mismatch region (e<0.42, q<6.5, ζ∈[0,2π], and |χ1,2|<0.8), the maximum mismatch for the (2,2) mode is below 1.3%. Compared to existing eccentric surrogate or data-driven waveform models, it achieves broader parameter coverage while maintaining a comparable level of accuracy (mismatch ∼10−3). These results demonstrate that the proposed FAN-based model offers a reliable and efficient framework for eccentric waveform modeling, with the potential to accelerate gravitational wave data analysis.

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