[论文解读] Rapid inference of gravitational-wave signals in the time domain using a heterodyned likelihood

Neha Sharma, A. Vijaykumar+1 more|arXiv (Cornell University)|Jan 16, 2026

Pulsars and Gravitational Waves Research被引用 0

一句话总结

引入时域异频似然极大地提升对长伽马射线信号的贝叶斯参数估计速度，通过对波形模态进行下采样并使用预计算的摘要数据，在后验分布上几乎无差别的前提下实现数量级的加速。

ABSTRACT

Parameter estimation of gravitational wave signals is computationally intensive and typically requires millions of likelihood evaluations to construct posterior probability distributions. This computational cost increases significantly in the time domain, which requires non-diagonal covariance matrices to compute the likelihood. Consequently, parameter estimation of long-duration gravitational wave signals, such as binary neutron star mergers, becomes computationally infeasible in time domain. In this work, we detail a framework for the heterodyned likelihood that enables rapid inference in the time domain. Our method is applicable to signals with arbitrary mode content, and leverages the smoothness of the ratio of complex-valued waveform modes, approximating the ratio as a linear function within appropriately chosen time bins. This allows downsampling of the waveform modes and a reformulation of the likelihood, such that it depends only on the bin edges. We demonstrate that this likelihood recovers posteriors that are indistinguishable from those obtained using the standard likelihood in the time domain. We also observe dramatic improvement in speed - for a 128 seconds-long gravitational wave signal, our method is at least $\sim 400$ times faster than the standard time-domain analysis, reducing the wall clock time to just a few hours. We also demonstrate the reliability and unbiasedness of the likelihood using percentile-percentile tests for binary black hole and binary neutron star injections. We use the Gohberg-Semencul representation of the inverse of Toeplitz covariance matrix to accelerate matrix-vector products, which has potential applications even in non heterodyned time-domain inference.

研究动机与目标

• 在时域GW分析中因计算成本高而需要快速参数估计的动机。
• 开发一个异频似然框架，在时间区间内对波形模比进行线性近似（异频）。
• 制定摘要数据和分箱策略，以在保持精度的同时加速似然估计。
• 通过对BBH和BNS情景的注入与pp测试，展示准确性与速度提升。

提出的方法

• 将似然表示为复数波形多极h^{3lm}与基准波形h^{3lm}_o之比，并在时间分箱内对这些比值进行线性近似（异频）。
• 通过仅在分界边界处计算波形模并需要时通过插值重构完整波形来实现下采样。
• 预先计算依赖于基准模、探测器噪声和数据的摘要数据，以避免采样过程中的大矩阵乘法。
• 使用比值r^{3lm}和摘要数据来表示对数似然，避免每次迭代的矩阵求逆和乘积。
• 采用自适应时间分箱方案，在向 inspiral 方向扩展分箱，在靠近 merger 时扩大或缩小分箱，以在精度和速度之间取得平衡。

实验结果

研究问题

• RQ1 异频时域似然是否能够再现与完整时域似然相同的后验分布？
• RQ2 对于不同持续时间的GW信号，时域异频能带来怎样的可观测加速？
• RQ3 在尽量减少计算量的同时，如何选择时间分箱以保持在 merger 附近的精度？
• RQ4 该方法是否能扩展到次主模态和前旋转波形？
• RQ5 pp 测试在 BBH 和 BNS 注入下如何验证方法的无偏性？

主要发现

Duration of GW signal [s]	Number of bins	Summary data computation time [s]	Heterodyned Likelihood [ms]	Full Likelihood [ms]	Speedup factors	Number of bins (Frequency Domain)	Heterodyned Likelihood [ms]	Full Likelihood [ms]	(Frequency domain speedup)
2	191	8.6989	2.290	42.9296	120	119	1.445	4.596
4	193	53.9353	2.418	89.97518	121	121	1.724	8.662
8	302	116.1305	3.860	216.558	121	121	1.812	14.14
16	382	561.3549	6.378	791.557	124.10740	121	1.801	27.35
32	476	967.96419	8.580	884.42	103.07940	121	1.848	51.18
64	483	4103.1448	9.140	4163.54	455.5295	121	1.817	105.3
128	486	20012.4119	9.191	3129.884	340.5379	121	1.849	209.6

• 在测试的注入中，来自异频时域似然的后验分布与完整似然的后验分布无可辨别差异。
• 对于2秒信号，异频使似然评估比完整时域方法快约19倍。
• 对于16秒和128秒信号，单次似然评估分别约为~6.4 ms和~9.2 ms，带来约124x和约340x的加速。
• 加速随信号持续时间增加而放大，使原本需要数周到数月才能完成的分析在数小时内完成。
• 分箱策略（自适应、以 inspiral 为优先、靠 merger 时更关注近 merger 的分箱）在大幅减少波形评估次数的同时保持了精度。
• 针对 BBH 和 BNS 注入的 p-p 测试显示无偏后验，验证了方法的可靠性。