用于旋进双黑洞波形的快速可微分神经网络代理模型

中文摘要 AI 辅助

引力波参数估计每个事件需要数百万次波形评估，这一成本限制了实时推断和种群研究。我们提出一种用于旋进数值相对论模型NRSur{}的快速、完全可微分的神经网络代理模型，覆盖其全部内禀参数空间λ=(q, χ₁, χ₂)以及参考轨道频率ω₀。该代理模型并非预测固定取向的单一偏振，而是预测惯性系球谐模式h_{ℓm}（ℓ≤4），因此可通过一次网络评估结合解析的可微分模式到应变投影，从任意取向（ι,φ,ψ）重建两种偏振h₊、hₓ。在6×10⁵个波形上训练后，对于q∈[1,4]、|χ₁,₂|≤0.8的情况，它的固定取向匹配度均值为0.975（中位数0.988），取向平均匹配度均值为0.940（中位数0.975），同时保持整体应变振幅符合物理规律（中位数比值0.98）。它在单个GPU上生成单个波形耗时12毫秒，批量生成速度约为每秒3.5×10⁴个。由于模式到应变投影是解析的，该代理模型对内禀和外禀参数均可微分，可生成完整的13维费舍尔矩阵（已通过有限差分验证），支持基于梯度的（HMC/NUTS）参数估计。

英文摘要

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 \NRSur{}, spanning its full intrinsic parameter space $λ=(q,\,\boldsymbolχ_1,\,\boldsymbolχ_2)$ together with the reference orbital frequency $ω_0$. Rather than a single polarization at a fixed orientation, the surrogate predicts the \emph{inertial-frame spherical-harmonic modes} $h_{\ell m}$ ($\ell\leq 4$), so that both polarizations $h_+,h_\times$ at an arbitrary orientation $(ι,φ,ψ)$ 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 $q\in[1,4]$, $|\boldsymbolχ_{1,2}|\leq 0.8$, while keeping the overall strain amplitude physical (median ratio $0.98$). It generates a waveform in $\SI{12}{ms}$ (single) and ${\sim}3.5\times10^4$ 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.

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8 pages, 4 figures