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arxiv: 2505.20996 · v3 · submitted 2025-05-27 · 🌀 gr-qc · astro-ph.CO· astro-ph.IM· hep-ph· hep-th

Parameter inference of millilensed gravitational waves using neural spline flows

Zheng Qin , Tian-Yang Sun , Bo-Yuan Li , Jing-Fei Zhang , Xiao Guo , Xin Zhang This is my paper

Pith reviewed 2026-05-19 13:17 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COastro-ph.IMhep-phhep-th
keywords millilensed gravitational wavesneural spline flowsparameter inferencegravitational lensingBayesian inferencenormalizing flowsfast parameter estimation
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The pith

Neural spline flows infer millilensed gravitational wave parameters with traditional accuracy but in seconds instead of days.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper explores the application of neural spline flows to perform posterior inference on the parameters of millilensed gravitational waves. These events involve additional lens parameters that make conventional Bayesian sampling computationally expensive, often requiring days per event. By training a neural network on simulated data, the authors achieve inference times averaging 0.8 seconds while maintaining comparable accuracy for most parameters. The network also shows good generalization to the spin parameters of the gravitational wave sources.

Core claim

A neural spline flow network can be trained to approximate the posterior distributions over eleven lens and source parameters from millilensed gravitational wave waveforms, yielding results similar in accuracy to traditional methods such as Bilby with dynesty sampling but with a reduction in inference time from about three days to 0.8 seconds on average.

What carries the argument

Neural spline flows used as a fast approximator to the posterior probability distribution over the combined source and lens parameters.

If this is right

  • Parameter estimation for lensed events becomes feasible at scale for future gravitational wave catalogs.
  • Low-latency searches for millilensed signals can be implemented in real-time analysis pipelines.
  • The demonstrated generalization to spin parameters suggests the approach can handle variations in source properties without additional training.
  • Similar techniques could be adapted for other waveform modifications that add parameters to the inference problem.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the method holds for real data, it could enable statistical analyses of lens populations from gravitational wave observations.
  • Extensions to strong lensing or other exotic propagation effects might benefit from the same speed advantage.
  • Hybrid systems that use fast neural approximations for initial estimates and traditional methods for refinement could optimize both speed and precision.

Load-bearing premise

The simulated training waveforms and lens models are sufficiently representative of real millilensed events that the learned posterior approximation remains accurate when applied to actual detector data containing noise and unmodeled effects.

What would settle it

A direct comparison on injected millilensed signals with known parameters shows the NSF posteriors differing substantially in location or width from those recovered by exact sampling methods on the same data.

Figures

Figures reproduced from arXiv: 2505.20996 by Bo-Yuan Li, Jing-Fei Zhang, Tian-Yang Sun, Xiao Guo, Xin Zhang, Zheng Qin.

Figure 1
Figure 1. Figure 1: FIG. 1: A classical gravitational lensing system composed of a GWs source on the source plane, a lens on the lens plane, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Workflow of the NSF network. The input is the GW [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Changes in loss values on the training set and valida [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Cumulative distribution of the quantiles where the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Marginal one-dimensional and two-dimensional posterior distribution plots for the same event without spin, inferred [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The KS test evaluating the performance of the NSF [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

When gravitational waves (GWs) propagate near massive objects, they undergo gravitational lensing that imprints lens model dependent modulations on the waveform. This effect provides a powerful tool for cosmological and astrophysical studies. Due to the added parameters of lenses and the uncertainty of lens models, parameter inference for lensed GW events using traditional methods is extremely time-consuming, thus requiring more efficient parameter inference methods. In this work, we explore the use of neural spline flows (NSFs) for posterior inference of millilensed GWs, and successfully apply NSFs to the inference of 11-dimensional lens parameters. Our results demonstrate that compared with traditional methods like Bilby dynesty that rely on Bayesian inference, the NSF network we built not only achieves inference accuracy comparable to traditional methods for most parameters, but also can reduce the inference time from approximately 3 days to 0.8 s on average. Additionally, the network exhibits strong generalization for the spin parameters of GW sources. It is anticipated to become a powerful tool for future low-latency searches for lensed GW signals.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a neural spline flow (NSF) approach for posterior inference on an 11-dimensional parameter space describing millilensed gravitational-wave signals. It reports that the trained NSF recovers posteriors with accuracy comparable to Bilby/dynesty nested sampling on simulated data while reducing inference time from approximately three days to 0.8 s on average, with notably good generalization on spin parameters, and positions the method as enabling low-latency searches for lensed events.

Significance. If the reported accuracy and generalization hold under realistic conditions, the work would provide a valuable computational tool for the expected increase in lensed-GW detections with future detectors. The demonstrated speedup addresses a genuine bottleneck in high-dimensional lensing analyses and could support both archival studies and real-time follow-up, extending the utility of machine-learning density estimators in gravitational-wave astronomy.

major comments (2)
  1. [Abstract and results section] Abstract and results section: the claim that the NSF 'achieves inference accuracy comparable to traditional methods' is stated without quantitative metrics (e.g., median fractional errors, coverage probabilities, or Jensen-Shannon divergences between NSF and dynesty posteriors), error bars on the comparisons, or explicit description of the training/validation/test splits. This information is load-bearing for the central accuracy claim.
  2. [Results and discussion sections] Results and discussion sections: all reported benchmarks use simulated waveforms with chosen lens models and idealized noise realizations. No injection campaign into real LIGO/Virgo strain data, no tests with non-Gaussian glitches, and no analysis of any candidate event are described. Because the headline utility for 'future low-latency searches' requires the learned 11-dimensional posterior to remain accurate on actual detector data, this omission is a load-bearing limitation.
minor comments (2)
  1. [Figures] Figure captions and axis labels could more explicitly state the number of test injections and the precise definition of 'accuracy' used in each panel.
  2. [Methods] The NSF architecture hyperparameters (number of layers, spline knots, etc.) are listed as free parameters but their specific values and sensitivity study are not tabulated.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments. We address each major comment below, indicating where revisions have been made to the manuscript.

read point-by-point responses

  1. Referee: [Abstract and results section] Abstract and results section: the claim that the NSF 'achieves inference accuracy comparable to traditional methods' is stated without quantitative metrics (e.g., median fractional errors, coverage probabilities, or Jensen-Shannon divergences between NSF and dynesty posteriors), error bars on the comparisons, or explicit description of the training/validation/test splits. This information is load-bearing for the central accuracy claim.

    Authors: We agree that the accuracy claim would be strengthened by explicit quantitative metrics. In the revised manuscript we have added median fractional errors, coverage probabilities, and Jensen-Shannon divergences between the NSF and dynesty posteriors for the principal parameters, together with error bars on the relevant comparison figures. We have also inserted a clear description of the training/validation/test data splits, including sample sizes and partitioning procedure. revision: yes

  2. Referee: [Results and discussion sections] Results and discussion sections: all reported benchmarks use simulated waveforms with chosen lens models and idealized noise realizations. No injection campaign into real LIGO/Virgo strain data, no tests with non-Gaussian glitches, and no analysis of any candidate event are described. Because the headline utility for 'future low-latency searches' requires the learned 11-dimensional posterior to remain accurate on actual detector data, this omission is a load-bearing limitation.

    Authors: We accept that the current validation is limited to simulated data and that this restricts immediate claims about performance on real detector output. The revised discussion section now explicitly states this scope limitation, notes the idealized noise assumptions, and outlines planned future work on real-strain injections and glitch robustness. We have also moderated the language concerning low-latency applicability to reflect the simulation-based nature of the present results. revision: partial

Circularity Check

0 steps flagged

No circularity: NSF trained on external simulations and benchmarked against independent dynesty sampler

full rationale

The paper trains a neural spline flow on simulated millilensed GW waveforms (with chosen lens models) and reports posterior accuracy comparable to Bilby/dynesty plus a large speed-up. No load-bearing step reduces by construction to a fitted quantity defined inside the paper, nor does any uniqueness theorem or ansatz rest on self-citation. The central claims rest on an external sampler comparison and simulation-to-simulation tests, making the derivation self-contained against independent benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions of general relativity for lensing, the validity of the chosen lens model family, and the representativeness of the simulated training set. No new physical entities are introduced.

free parameters (1)
  • NSF architecture hyperparameters
    Number of layers, spline knots, and hidden units chosen during network design and training.
axioms (1)
  • domain assumption Gravitational lensing of GWs follows the standard thin-lens approximation in GR
    Invoked when generating training waveforms and defining the 11 lens parameters.

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Reference graph

Works this paper leans on

105 extracted references · 105 canonical work pages · cited by 1 Pith paper · 25 internal anchors

  1. [1]

    B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Aber- nathy, and others., Phys. Rev. Lett. 116, 221101 (2016), 1602.03841

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  2. [2]

    B. P. Abbott, B. P. Abbott, LIGO Scientific, and Virgo Collaboration, Phys. Rev. Lett. 121, 129902 (2018)

    work page 2018

  3. [3]

    B. P. Abbott, R. Abbott, T. D. Abbott, S. Abraham, F. Acernese, and others., Phys. Rev. D 100, 104036 (2019), 1903.04467

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  4. [4]

    B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, and others., Phys. Rev. Lett. 123, 011102 (2019), 1811.00364

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  5. [5]

    Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog

    R. Abbott, T. D. Abbott, S. Abraham, F. Acernese, K. Ackley, and others., Phys. Rev. D 103, 122002 (2021), 2010.14529

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  6. [6]

    Tests of General Relativity with GWTC-3

    The LIGO Scientific Collaboration, the Virgo Collabo- ration, the KAGRA Collaboration, R. Abbott, H. Abe, Acernese, and others., arXiv e-prints arXiv:2112.06861 (2021), 2112.06861

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  7. [7]

    Abbottet al.(LIGO Scientific, Virgo, KAGRA), Astrophys

    R. Abbott, H. Abe, F. Acernese, K. Ackley, and others., Astrophys. J. 949, 76 (2023), 2111.03604

    work page arXiv 2023

  8. [8]

    Barausse, E

    E. Barausse, E. Berti, T. Hertog, and others., General Relativity and Gravitation 52, 81 (2020), 2001.09793

    work page arXiv 2020

  9. [9]

    Ruan, Z.-K

    W.-H. Ruan, Z.-K. Guo, R.-G. Cai, and Y.-Z. Zhang, International Journal of Modern Physics A 35, 2050075 (2020)

    work page 2020

  10. [10]

    J. Luo, H. An, L. Bian, R.-G. Cai, Z. Cao, W. Han, J. He, M. A. Hendry, B. Hu, Y.-M. Hu, et al., arXiv e-prints arXiv:2502.20138 (2025), 2502.20138

    work page arXiv 2025

  11. [11]

    Science Case for the Einstein Telescope

    M. Maggiore, C. Van Den Broeck, N. Bartolo, E. Bel- gacem, D. Bertacca, M. A. Bizouard, M. Branchesi, S. Clesse, S. Foffa, J. Garc´ ıa-Bellido, et al., J. Cosmol. Astropart. P. 2020, 050 (2020), 1912.02622

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  12. [12]

    A Horizon Study for Cosmic Explorer: Science, Observatories, and Community

    M. Evans, R. X. Adhikari, C. Afle, S. W. Ballmer, S. Biscoveanu, S. Borhanian, D. A. Brown, Y. Chen, R. Eisenstein, A. Gruson, et al., arXiv e-prints arXiv:2109.09882 (2021), 2109.09882

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  13. [13]

    On the waveforms of gravitationally lensed gravitational waves

    L. Dai and T. Venumadhav, arXiv e-prints arXiv:1702.04724 (2017), 1702.04724

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  14. [14]

    Detecting Lensing-Induced Diffraction in Astrophysical Gravitational Waves

    L. Dai, S.-S. Li, B. Zackay, S. Mao, and Y. Lu, Phys. Rev. D 98, 104029 (2018), 1810.00003

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  15. [15]

    H. G. Choi, C. Park, and S. Jung, Phys. Rev. D 104, 063001 (2021)

    work page 2021

  16. [16]

    Guo and Y

    X. Guo and Y. Lu, Phys. Rev. D 106, 023018 (2022), 2207.00325

    work page arXiv 2022

  17. [17]

    K.-H. Lai, O. A. Hannuksela, A. Herrera-Mart´ ın, J. M. Diego, T. Broadhurst, and T. G. F. Li, Phys. Rev. D 98, 083005 (2018), 1801.07840

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  18. [18]

    J. Gais, K. K. Y. Ng, E. Seo, K. W. K. Wong, and T. G. F. Li, Astrophys. J. Lett. 932, L4 (2022), 2201.01817

    work page arXiv 2022

  19. [19]

    A. K. Meena, Mon. Not. R. Astron. Soc. 532, 3568 (2024), 2305.02880

    work page arXiv 2024

  20. [20]

    Wave diffraction by a cosmic string

    I. Fern´ andez-N´ u˜ nez and O. Bulashenko, Physics Letters A 380, 2897 (2016), 1605.03176

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  21. [21]

    Emergence of Fresnel diffraction zones in gravitational lensing by a cosmic string

    I. Fern´ andez-N´ u˜ nez and O. Bulashenko, Physics Letters A 381, 1764 (2017), 1612.07218

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  22. [22]

    B. Liu, Z. Li, and Z.-H. Zhu, Mon. Not. R. Astron. Soc. 487, 1980 (2019), 1904.11751

    work page internal anchor Pith review Pith/arXiv arXiv 1980

  23. [23]

    Gravitational-Wave Fringes at LIGO: Detecting Compact Dark Matter by Gravitational Lensing

    S. Jung and C. S. Shin, Phys. Rev. Lett. 122, 041103 (2019), 1712.01396

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  24. [24]

    Urrutia and V

    J. Urrutia and V. Vaskonen, Mon. Not. R. Astron. Soc. 509, 1358 (2022), 2109.03213

    work page arXiv 2022

  25. [25]

    J.-S. Wang, A. Herrera-Mart´ ın, and Y.-M. Hu, Phys. Rev. D 104, 083515 (2021), 2108.12394

    work page arXiv 2021

  26. [26]

    S. Cao, J. Qi, Z. Cao, M. Biesiada, W. Cheng, and Z.-H. Zhu, Astron. Astrophys. 659, L5 (2022), 2202.08714

    work page arXiv 2022

  27. [27]

    Fairbairn, J

    M. Fairbairn, J. Urrutia, and V. Vaskonen, J. Cosmol. Astropart. P. 2023, 007 (2023), 2210.13436

    work page arXiv 2023

  28. [28]

    C ¸ alı¸ skan, N

    M. C ¸ alı¸ skan, N. Anil Kumar, L. Ji, J. M. Ezquiaga, R. Cotesta, E. Berti, and M. Kamionkowski, Phys. Rev. D 108, 123543 (2023), 2307.06990

    work page arXiv 2023

  29. [29]

    Tambalo, M

    G. Tambalo, M. Zumalac´ arregui, L. Dai, and M. H.-Y. Cheung, Phys. Rev. D 108, 103529 (2023), 2212.11960

    work page arXiv 2023

  30. [30]

    M. H.-Y. Cheung, K. K. Y. Ng, M. Zumalac´ arregui, and E. Berti, Phys. Rev. D 109, 124020 (2024), 2403.13876

    work page arXiv 2024

  31. [31]

    S. Jana, S. J. Kapadia, T. Venumadhav, S. More, and P. Ajith, arXiv e-prints arXiv:2408.05290 (2024), 2408.05290

    work page arXiv 2024

  32. [32]

    S. Cao, J. Qi, Z. Cao, M. Biesiada, J. Li, Y. Pan, and Z.- H. Zhu, Scientific Reports 9, 11608 (2019), 1910.10365

    work page arXiv 2019

  33. [33]

    Liu, Z.-H

    X.-H. Liu, Z.-H. Li, J.-Z. Qi, and X. Zhang, Astrophys. J. 927, 28 (2022), 2109.02291. 10

    work page arXiv 2022

  34. [34]

    Goyal, A

    S. Goyal, A. Vijaykumar, J. M. Ezquiaga, and M. Zu- malac´ arregui, Phys. Rev. D 108, 024052 (2023), 2301.04826

    work page arXiv 2023

  35. [35]

    Huang, Y.-M

    S.-J. Huang, Y.-M. Hu, X. Chen, J.-d. Zhang, E.-K. Li, Z. Gao, and X.-y. Lin, J. Cosmol. Astropart. P. 2023, 003 (2023), 2304.10435

    work page arXiv 2023

  36. [36]

    G. P. Smith, T. Baker, S. Birrer, C. E. Collins, et al., Philosophical Transactions of the Royal Society of Lon- don Series A 383, 20240134 (2025), 2503.19973

    work page arXiv 2025

  37. [37]

    Abbott, T

    R. Abbott, T. D. Abbott, S. Abraham, F. Acernese, K. Ackley, and others., Astrophys. J. 923, 14 (2021), 2105.06384

    work page arXiv 2021

  38. [38]

    Abbottet al.(LIGO Scientific, KAGRA, VIRGO), Astrophys

    R. Abbott, H. Abe, F. Acernese, K. Ackley, S. Adhicary, and others., Astrophys. J. 970, 191 (2024), 2304.08393

    work page arXiv 2024

  39. [39]

    Janquart, M

    J. Janquart, M. Wright, S. Goyal, J. C. L. Chan, A. Ganguly, ´A. Garr´ on, D. Keitel, A. K. Y. Li, A. Liu, R. K. L. Lo, et al., Mon. Not. R. Astron. Soc. 526, 3832 (2023), 2306.03827

    work page arXiv 2023

  40. [40]

    Barsode, S

    A. Barsode, S. Goyal, and P. Ajith, Astrophys. J. 980, 258 (2025), 2412.01278

    work page arXiv 2025

  41. [41]

    Goyal, S

    S. Goyal, S. J. Kapadia, J.-R. Cudell, A. K. Y. Li, and J. C. L. Chan, Phys. Rev. D 109, 023028 (2024), 2306.04397

    work page arXiv 2024

  42. [42]

    Goyal, D

    S. Goyal, D. Harikrishnan, S. J. Kapadia, and P. Ajith, Phys. Rev. D 104, 124057 (2021), 2106.12466

    work page arXiv 2021

  43. [43]

    K. Kim, J. Lee, O. A. Hannuksela, and T. G. F. Li, Astrophys. J. 938, 157 (2022), 2206.08234

    work page arXiv 2022

  44. [44]

    M. B. Sch¨ afer, O. Zelenka, A. H. Nitz, H. Wang, S. Wu, Z.-K. Guo, Z. Cao, Z. Ren, P. Nousi, N. Stergioulas, et al., Phys. Rev. D 107, 023021 (2023), 2209.11146

    work page arXiv 2023

  45. [45]

    S.-S. Li, S. Mao, Y. Zhao, and Y. Lu, Mon. Not. R. Astron. Soc. 476, 2220 (2018), 1802.05089

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  46. [46]

    K. K. Y. Ng, K. W. K. Wong, T. Broadhurst, and T. G. F. Li, Phys. Rev. D 97, 023012 (2018), 1703.06319

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  47. [47]

    Y. Wang, R. K. L. Lo, A. K. Y. Li, and Y. Chen, Phys. Rev. D 103, 104055 (2021), 2101.08264

    work page arXiv 2021

  48. [48]

    F. Xu, J. M. Ezquiaga, and D. E. Holz, Astrophys. J. 929, 9 (2022), 2105.14390

    work page arXiv 2022

  49. [49]

    Brando, S

    G. Brando, S. Goyal, S. Savastano, H. Villarrubia-Rojo, and M. Zumalac´ arregui, Phys. Rev. D 111, 024068 (2025), 2407.04052

    work page arXiv 2025

  50. [50]

    A. K. Meena and J. S. Bagla, Mon. Not. R. Astron. Soc. 492, 1127 (2020), 1903.11809

    work page arXiv 2020

  51. [51]

    S. Ali, E. Stoikos, E. Meade, M. Kesden, and L. King, Phys. Rev. D 107, 103023 (2023), 2210.01873

    work page arXiv 2023

  52. [52]

    Wave Effects in Gravitational Lensing of Gravitational Waves from Chirping Binaries

    R. Takahashi and T. Nakamura, Astrophys. J. 595, 1039 (2003), astro-ph/0305055

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  53. [53]

    Strong lensing of gravitational waves as seen by LISA

    M. Sereno, A. Sesana, A. Bleuler, P. Jetzer, M. Volon- teri, and M. C. Begelman, Phys. Rev. Lett. 105, 251101 (2010), 1011.5238

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  54. [54]

    Bulashenko and H

    O. Bulashenko and H. Ubach, J. Cosmol. Astropart. P. 2022, 022 (2022), 2112.10773

    work page arXiv 2022

  55. [55]

    Gabbard, C

    H. Gabbard, C. Messenger, I. S. Heng, F. Tonolini, and R. Murray-Smith, Nature Physics 18, 112 (2022), 1909.06296

    work page arXiv 2022

  56. [56]

    S. R. Green and J. Gair, Mach. Learn. Sci. Tech. 2, 03LT01 (2021), 2008.03312

    work page arXiv 2021

  57. [57]

    S. R. Green, C. Simpson, and J. Gair, Phys. Rev. D 102, 104057 (2020), 2002.07656

    work page arXiv 2020

  58. [58]

    M. Dax, S. R. Green, J. Gair, J. H. Macke, A. Buo- nanno, and B. Sch¨ olkopf, Phys. Rev. Lett.127, 241103 (2021), 2106.12594

    work page arXiv 2021

  59. [59]

    H. Shen, E. A. Huerta, E. O’Shea, P. Kumar, and Z. Zhao, Machine Learning: Science and Technology 3, 015007 (2022), 1903.01998

    work page arXiv 2022

  60. [60]

    Whittaker, W

    T. Whittaker, W. E. East, S. R. Green, L. Lehner, and H. Yang, Phys. Rev. D 105, 124021 (2022), 2201.06461

    work page arXiv 2022

  61. [61]

    M. Dax, S. R. Green, J. Gair, M. P¨ urrer, J. Wildberger, J. H. Macke, A. Buonanno, and B. Sch¨ olkopf, Phys. Rev. Lett. 130, 171403 (2023), 2210.05686

    work page arXiv 2023

  62. [62]

    T. Zhao, R. Lyu, H. Wang, Z. Cao, and Z. Ren, Com- munications Physics 6, 212 (2023), 2207.07414

    work page arXiv 2023

  63. [63]

    T.-Y. Sun, Y. Shao, Y. Li, Y. Xu, and X. Zhang, arXiv e-prints arXiv:2407.14298 (2024), 2407.14298

    work page arXiv 2024

  64. [64]

    M. Du, B. Liang, H. Wang, P. Xu, Z. Luo, and Y. Wu, Science China Physics, Mechanics, and Astronomy 67, 230412 (2024), 2308.05510

    work page arXiv 2024

  65. [65]

    Sun, C.-Y

    T.-Y. Sun, C.-Y. Xiong, S.-J. Jin, Y.-X. Wang, J.-F. Zhang, and X. Zhang, Chinese Physics C 48, 045108 (2024), 2312.08122

    work page arXiv 2024

  66. [66]

    Leyde, S

    K. Leyde, S. R. Green, A. Toubiana, and J. Gair, Phys. Rev. D 109, 064056 (2024), 2311.12093

    work page arXiv 2024

  67. [67]

    M. Dax, S. R. Green, J. Gair, N. Gupte, M. P¨ urrer, V. Raymond, J. Wildberger, J. H. Macke, A. Buonanno, and B. Sch¨ olkopf, Nature (London) 639, 49 (2025), 2407.09602

    work page arXiv 2025

  68. [68]

    Xiong, T.-Y

    C.-Y. Xiong, T.-Y. Sun, J.-F. Zhang, and X. Zhang, Phys. Rev. D 111, 024019 (2025), 2405.09475

    work page arXiv 2025

  69. [69]

    R. B. Nerin, O. Bulashenko, O. G. Freitas, and J. A. Font, Phys. Rev. D 111, 084067 (2025), 2412.00566

    work page arXiv 2025

  70. [70]

    Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins

    P. Ajith, M. Hannam, S. Husa, Y. Chen, B. Br¨ ugmann, N. Dorband, D. M¨ uller, F. Ohme, D. Pollney, C. Reis- swig, et al., Phys. Rev. Lett. 106, 241101 (2011), 0909.2867

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  71. [71]

    T. A. Callister, S. J. Miller, K. Chatziioannou, and W. M. Farr, Astrophys. J. Lett. 937, L13 (2022), 2205.08574

    work page arXiv 2022

  72. [72]

    Biscoveanu, T

    S. Biscoveanu, T. A. Callister, C.-J. Haster, K. K. Y. Ng, S. Vitale, and W. M. Farr, Astrophys. J. Lett. 932, L19 (2022), 2204.01578

    work page arXiv 2022

  73. [73]

    Fishbach, C

    M. Fishbach, C. Kimball, and V. Kalogera, Astrophys. J. Lett. 935, L26 (2022), 2207.02924

    work page arXiv 2022

  74. [74]

    Roulet, H

    J. Roulet, H. S. Chia, S. Olsen, L. Dai, T. Venumad- hav, B. Zackay, and M. Zaldarriaga, Phys. Rev. D 104, 083010 (2021), 2105.10580

    work page arXiv 2021

  75. [75]

    Biscoveanu, M

    S. Biscoveanu, M. Isi, S. Vitale, and V. Varma, Phys. Rev. Lett. 126, 171103 (2021), 2007.09156

    work page arXiv 2021

  76. [76]

    H. Tong, S. Galaudage, and E. Thrane, Phys. Rev. D 106, 103019 (2022), 2209.02206

    work page arXiv 2022

  77. [77]

    Robust parameter estimation for compact binaries with ground-based gravitational-wave observations using the LALInference software library

    J. Veitch, V. Raymond, B. Farr, W. Farr, P. Graff, S. Vitale, B. Aylott, K. Blackburn, N. Christensen, M. Coughlin, et al., Phys. Rev. D 91, 042003 (2015), 1409.7215

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  78. [78]

    Searching for Gravitational Waves from Compact Binaries with Precessing Spins

    I. Harry, S. Privitera, A. Boh´ e, and A. Buonanno, Phys. Rev. D 94, 024012 (2016), 1603.02444

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  79. [79]

    R. Shi, Y. Zhou, T. Zhao, Z. Wang, Z. Ren, and Z. Cao, Phys. Rev. D 111, 044016 (2025), 2411.14893

    work page arXiv 2025

  80. [80]

    Wang, S.-J

    Y.-X. Wang, S.-J. Jin, T.-Y. Sun, J.-F. Zhang, and X. Zhang, Chinese Physics C 48, 125107 (2024), 2305.19003

    work page arXiv 2024

Showing first 80 references.