pith. sign in

arxiv: 2606.11959 · v1 · pith:VSXRLDPOnew · submitted 2026-06-10 · 🌌 astro-ph.HE · astro-ph.GA

Identifiability of g mode Resonances in Eccentric Binary Neutron Stars with Multidetector Observations

Mengfei Sun , Jie Wu , Qianning Hu , Jin Li , Nan Yang , Xianghe Ma , Borui Wang , Minghui Zhang
show 1 more author
Yuanhong Zhong
This is my paper

Pith reviewed 2026-06-27 08:51 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.GA
keywords g-mode resonanceseccentric binary neutron starsdeep learningmatched filteringEinstein TelescopeCosmic Explorertidal effectsphase morphology
0
0 comments X

The pith

Deep learning classifiers identify weak g-mode resonant phase shifts in eccentric binary neutron star signals from third-generation detectors, outperforming matched filtering.

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

The paper tests whether the subtle phase signature from g-mode resonances in eccentric binary neutron stars can be distinguished in noisy time-domain strain data expected from future detectors. It constructs a four-class dataset of point-particle, adiabatic-tide, resonant g-mode, and pure-noise waveforms in an eccentric harmonic framework and trains neural classifiers on Einstein Telescope and Cosmic Explorer data. The models reach accuracies of 0.655, 0.815, and 0.897 for ET, CE, and combined observations, exceeding the matched-filtering accuracies of 0.514, 0.677, and 0.689 on identical samples. This advantage arises because the resonant correction appears as a weak local phase morphology difference on top of the adiabatic tidal background that the network can learn directly from the full strain segment. Joint third-generation observations therefore improve the chance of extracting internal-structure information beyond bulk tidal deformability.

Core claim

The resonant correction manifests as a weak phase morphology difference superimposed on the adiabatic tidal background that neural classifiers can learn from the complete time-domain strain segment, whereas matched filtering, which responds only to overall similarity, performs worse. On the simulated four-class dataset the deep-learning accuracies are 0.655 (ET), 0.815 (CE), and 0.897 (ET+CE), compared with 0.514, 0.677, and 0.689 for matched filtering; joint observations therefore improve identifiability of the weak internal-mode phase information.

What carries the argument

A four-class dataset built in an eccentric harmonic framework, with deep-learning classifiers trained on time-domain strain segments from ET and CE detectors to distinguish resonant g-mode phase morphology from adiabatic tides and noise.

Load-bearing premise

The resonant correction appears as a weak phase morphology difference on the adiabatic tidal background that a neural network can learn from the full strain segment while matched filtering cannot.

What would settle it

If classification accuracy on resonant g-mode samples remains statistically indistinguishable from accuracy on adiabatic-tide-only samples when the same networks are retrained and tested on independent realizations of ET/CE noise, the claim that the phase signature is learnable would be falsified.

Figures

Figures reproduced from arXiv: 2606.11959 by Borui Wang, Jie Wu, Jin Li, Mengfei Sun, Minghui Zhang, Nan Yang, Qianning Hu, Xianghe Ma, Yuanhong Zhong.

Figure 1
Figure 1. Figure 1: FIG. 1: BNS redshift distribution. The histogram [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Time domain reference waveforms for the same [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Normalized frequency domain residuals under [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Data generation pipeline. The procedure starts from physical parameters, source geometry, and distance [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Network architecture used in this work. Panel (a) shows the single detector version, whose backbone [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Overall performance for ET, CE, and ET+CE [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Confusion matrices for ET, CE, and ET+CE configurations. The top row shows the deep learning [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Average ROC curves and overall separability [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: ROC curves and class wise separability for the four classes. [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: AT+ [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
read the original abstract

$g$ mode resonances in eccentric binary neutron star systems are potential probes of internal stratification, superfluidity, composition gradients, and the equation of state. Although such weak dynamical tidal signatures are unlikely to be resolved with current detector sensitivities, third generation observations may make them accessible, in which case identifying the weak resonant phase shift would provide information beyond the bulk adiabatic tidal deformability. We build a four class dataset in an eccentric harmonic framework, containing point particle, adiabatic tide, resonant $g$ mode, and pure noise samples, and use Einstein Telescope (ET) and Cosmic Explorer (CE) detector data to test whether this weak resonant phase signature can be identified from noisy time domain strain. The ET, CE, and ET+CE deep learning models reach accuracies of $0.655$, $0.815$, and $0.897$, respectively. On the same simulated samples, the matched filtering method reaches lower accuracies of $0.514$, $0.677$, and $0.689$. This result arises from the fact that the resonant correction manifests as a weak phase morphology difference superimposed on the adiabatic tidal background, whereas matched filtering is sensitive only to the overall similarity. Hence, in the presence of weak phase differences, the neural classifier employed in deep learning is better able to learn these local phase and morphology features from the complete time domain strain segment. The results indicate that joint third generation observations improve the identifiability of weak internal mode phase information.

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

1 major / 1 minor

Summary. The manuscript constructs a four-class dataset of simulated eccentric binary neutron star waveforms (point-particle, adiabatic tide, resonant g-mode, pure noise) and trains deep learning classifiers on Einstein Telescope (ET), Cosmic Explorer (CE), and combined ET+CE time-domain strain data. It reports overall accuracies of 0.655 (ET), 0.815 (CE), and 0.897 (ET+CE) for the neural networks versus 0.514, 0.677, and 0.689 for matched filtering on the same samples, attributing the improvement to the networks' ability to learn weak resonant phase morphology differences superimposed on the adiabatic tidal background.

Significance. If the performance gap is shown to arise specifically from the resonant versus adiabatic distinction rather than easier class separations, the result would indicate that deep learning can extract subtle dynamical tidal phase information inaccessible to matched filtering in third-generation detector data, offering a route to probe neutron-star internal stratification and equation of state via g-mode resonances.

major comments (1)
  1. [Abstract and dataset/results description] The reported overall accuracies do not establish that the networks are learning the weak resonant phase morphology rather than coarser distinctions. The four-class dataset explicitly includes pure noise and point-particle samples that differ strongly in amplitude or signal presence; without per-class precision/recall, confusion matrices, or metrics isolating the adiabatic-tide versus resonant-g-mode contrast, the headline numbers (abstract) cannot support the claim that the resonant correction is identifiable while remaining invisible to matched filtering.
minor comments (1)
  1. [Methods] Training details, hyperparameter choices, cross-validation procedure, and error bars on the quoted accuracies are not mentioned in the abstract and should be supplied in the methods section for reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting this important point regarding the interpretation of the reported accuracies. We address the comment below and will revise the manuscript to incorporate the requested metrics.

read point-by-point responses

  1. Referee: The reported overall accuracies do not establish that the networks are learning the weak resonant phase morphology rather than coarser distinctions. The four-class dataset explicitly includes pure noise and point-particle samples that differ strongly in amplitude or signal presence; without per-class precision/recall, confusion matrices, or metrics isolating the adiabatic-tide versus resonant-g-mode contrast, the headline numbers (abstract) cannot support the claim that the resonant correction is identifiable while remaining invisible to matched filtering.

    Authors: We agree that overall accuracy on the four-class problem does not by itself isolate performance on the adiabatic-tide versus resonant-g-mode distinction. The matched-filtering baseline was evaluated on exactly the same samples and yields lower accuracy, which is consistent with the networks extracting additional phase-morphology information, but this remains an indirect argument. To directly resolve the concern we will add, in the revised manuscript, full confusion matrices for the ET, CE and ET+CE classifiers together with per-class precision, recall and F1 scores. These will be presented both for the full four-class task and for the two-class sub-problem of adiabatic tide versus resonant g-mode, allowing readers to assess whether the performance gain is driven by the subtle resonant signature. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical accuracies from independent simulations

full rationale

The paper constructs a four-class simulated dataset (point-particle, adiabatic tide, resonant g-mode, noise) and reports classification accuracies from trained neural networks versus matched filtering on the same samples. No equations, parameters, or derivations reduce the reported accuracies (0.655/0.815/0.897) to quantities defined inside the paper by construction. The central claim rests on numerical experiments whose inputs (waveform generation, noise realization, network training) are external to the output metrics. No self-citations, ansatzes, or uniqueness theorems are invoked as load-bearing steps. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract supplies no explicit free parameters, axioms, or invented entities; the work rests on standard assumptions of numerical relativity waveform generation and detector noise modeling that are not detailed here.

pith-pipeline@v0.9.1-grok · 5827 in / 1163 out tokens · 15496 ms · 2026-06-27T08:51:55.225782+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

61 extracted references · 3 canonical work pages · 3 internal anchors

  1. [1]

    For the first ordergmode con- sidered here, we denote the corresponding coupling by Λg, whose typical scale can lie between 10 −2 and 1. In the simulations below, we focus on a weak coupling por- tion of this range, taking Λg from 0.03 to 0.30 to examine how the resonant phase amplitude affects identification performance [25]. The external tidal tensor is...

  2. [2]

    In the simulations, the correspondingF I +, F I ×, andS n,I(f) enter the detector projection and col- ored noise generation

    and the CE next generation ground based detector design [41]. In the simulations, the correspondingF I +, F I ×, andS n,I(f) enter the detector projection and col- ored noise generation. B. Noise modeling and strain construction For each detector, a colored Gaussian noise realization nI(t) is generated with PyCBC from the one sided de- tector power spectr...

    2048

  3. [3]

    LIGO Scientific Collaboration and Virgo Collaboration, Gw170817: Observation of gravitational waves from a bi- nary neutron star inspiral, Physical Review Letters119, 161101 (2017), arXiv:1710.05832 [gr-qc]

    Pith/arXiv arXiv 2017

  4. [4]

    LIGO Scientific Collaboration and Virgo Collaboration, GW170817: Measurements of neutron star radii and equation of state, Physical Review Letters121, 161101 (2018)

    2018

  5. [5]

    S. De, D. Finstad, J. M. Lattimer, D. A. Brown, E. Berger, and C. M. Biwer, Tidal deformabilities and radii of neutron stars from the observation of GW170817, Physical Review Letters121, 091102 (2018)

    2018

  6. [6]

    Annala, T

    E. Annala, T. Gorda, A. Kurkela, and A. Vuori- nen, Gravitational-wave constraints on the neutron-star- matter equation of state, Physical Review Letters120, 172703 (2018)

    2018

  7. [7]

    LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration, Gwtc-3: Compact bi- nary coalescences observed by ligo and virgo during the second part of the third observing run, arXiv preprint arXiv:2111.03606 10.48550/arXiv.2111.03606 (2021), arXiv:2111.03606 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2111.03606 2021

  8. [8]

    Annala, T

    E. Annala, T. Gorda, E. Katerini, A. Kurkela, J. N¨ attil¨ a, V. Paschalidis, and A. Vuorinen, Multimessenger con- straints for ultradense matter, Physical Review X12, 011058 (2022)

    2022

  9. [9]

    Hinderer, Tidal love numbers of neutron stars, The Astrophysical Journal677, 1216 (2008)

    T. Hinderer, Tidal love numbers of neutron stars, The Astrophysical Journal677, 1216 (2008)

    2008

  10. [10]

    Damour and A

    T. Damour and A. Nagar, Relativistic tidal properties of neutron stars, Physical Review D80, 084035 (2009)

    2009

  11. [11]

    Hinderer, B

    T. Hinderer, B. D. Lackey, R. N. Lang, and J. S. Read, Tidal deformability of neutron stars with realistic equa- tions of state and their gravitational wave signatures in binary inspiral, Physical Review D81, 123016 (2010)

    2010

  12. [12]

    Yagi and N

    K. Yagi and N. Yunes, I-Love-Q: Unexpected universal relations for neutron stars and quark stars, Science341, 365 (2013)

    2013

  13. [13]

    Hinderer, A

    T. Hinderer, A. Taracchini, F. Foucart, A. Buonanno, J. Steinhoff, M. Duez, L. E. Kidder, H. P. Pfeiffer, M. A. Scheel, B. Szilagyi, K. Hotokezaka, K. Kyutoku, M. Shibata, and C. W. Carpenter, Effects of neutron- star dynamic tides on gravitational waveforms within the effective-one-body approach, Physical Review Letters 116, 181101 (2016)

    2016

  14. [14]

    Steinhoff, T

    J. Steinhoff, T. Hinderer, A. Buonanno, and A. Tarac- chini, Dynamical tides in general relativity: Effective action and effective-one-body hamiltonian, Physical Re- view D94, 104028 (2016)

    2016

  15. [15]

    Pratten, P

    G. Pratten, P. Schmidt, and N. Williams, Impact of dy- namical tides on the reconstruction of the neutron star equation of state, Physical Review Letters129, 081102 (2022)

    2022

  16. [16]

    E. M. Kantor and M. E. Gusakov, Composition temperature-dependent g modes in superfluid neutron stars, Monthly Notices of the Royal Astronomical Soci- ety: Letters442, L90 (2014)

    2014

  17. [17]

    Passamonti, N

    A. Passamonti, N. Andersson, and W. C. G. Ho, Buoy- ancy and g-modes in young superfluid neutron stars, Monthly Notices of the Royal Astronomical Society455, 1489 (2016)

    2016

  18. [18]

    Constantinou, S

    C. Constantinou, S. Han, P. Jaikumar, and M. Prakash, g-modes of neutron stars with hadron-to-quark crossover transitions, Physical Review D104, 123032 (2021)

    2021

  19. [19]

    Jaikumar, A

    P. Jaikumar, A. Semposki, M. Prakash, and C. Con- stantinou, g-mode oscillations in hybrid stars: A tale of two sounds, Physical Review D103, 123009 (2021)

    2021

  20. [20]

    A. R. Counsell, F. Gittins, N. Andersson, and I. Tews, Interface modes in inspiralling neutron stars: A gravitational-wave probe of first-order phase transitions, Physical Review Letters135, 081402 (2025)

    2025

  21. [21]

    Passamonti, N

    A. Passamonti, N. Andersson, and P. Pnigouras, Dy- namical tides in neutron stars: The impact of the crust, Monthly Notices of the Royal Astronomical Society504, 1273 (2021), arXiv:2012.09637 [astro-ph.HE]

    arXiv 2021

  22. [22]

    Lai, Resonant oscillations and tidal heating in coalesc- ing binary neutron stars, Monthly Notices of the Royal Astronomical Society270, 611 (1994)

    D. Lai, Resonant oscillations and tidal heating in coalesc- ing binary neutron stars, Monthly Notices of the Royal Astronomical Society270, 611 (1994)

    1994

  23. [23]

    Reisenegger and P

    A. Reisenegger and P. Goldreich, Excitation of neutron star normal modes during binary inspiral, The Astro- physical Journal426, 688 (1994)

    1994

  24. [24]

    K. D. Kokkotas and G. Sch¨ afer, Tidal and tidal-resonant effects in coalescing binaries, Monthly Notices of the Royal Astronomical Society275, 301 (1995)

    1995

  25. [25]

    Vick and D

    M. Vick and D. Lai, Tidal effects in eccentric coalescing neutron star binaries, Physical Review D100, 063001 (2019)

    2019

  26. [26]

    Tak´ atsy, L

    J. Tak´ atsy, L. Zwick, P. Saini, and J. Samsing, Orbital eccentricity can make neutron star g-mode resonances ob- servable with current gravitational-wave detectors, arXiv e-prints , arXiv:2402.15111 (2024), arXiv:2402.15111 [gr- qc]

    arXiv 2024

  27. [27]

    Tak´ atsy, L

    J. Tak´ atsy, L. Zwick, P. Saini, and J. Samsing, Or- bital eccentricity can make neutron star g-mode reso- nances observable with current gravitational-wave detec- tors, Phys. Rev. D113, 103047 (2026), arXiv:2602.15111 [astro-ph.HE]

    arXiv 2026

  28. [28]

    P. C. Peters and J. Mathews, Gravitational radiation from point masses in a keplerian orbit, Physical Review 131, 435 (1963)

    1963

  29. [29]

    P. C. Peters, Gravitational radiation and the motion of two point masses, Physical Review136, B1224 (1964)

    1964

  30. [30]

    R. Gold, S. Bernuzzi, M. Thierfelder, B. Br¨ ugmann, and F. Pretorius, Eccentric binary neutron star mergers, Physical Review D86, 121501 (2012)

    2012

  31. [31]

    W. E. East, F. Pretorius, and B. C. Stephens, Dynamical capture binary neutron star mergers, The Astrophysical Journal Letters760, L4 (2012)

    2012

  32. [32]

    Paschalidis, W

    V. Paschalidis, W. E. East, F. Pretorius, and S. L. Shapiro, One-arm spiral instability in hypermassive neu- tron stars formed by dynamical-capture binary neutron star mergers, Physical Review D92, 121502 (2015)

    2015

  33. [33]

    A. H. Nitz, A. Lenon, and D. A. Brown, Search for eccen- tric binary neutron star mergers in the first and second observing runs of advanced ligo, The Astrophysical Jour- nal890, 1 (2020), arXiv:1912.05464 [astro-ph.HE]

    arXiv 2020

  34. [34]

    A. K. Lenon, A. H. Nitz, and D. A. Brown, Measuring the eccentricity of gw170817 and gw190425, Monthly No- tices of the Royal Astronomical Society497, 1966 (2020), arXiv:2005.14146 [astro-ph.HE]

    arXiv 1966

  35. [35]

    A. K. Lenon, D. A. Brown, and A. H. Nitz, Eccentric bi- nary neutron star search prospects for Cosmic Explorer, 15 Physical Review D104, 063011 (2021)

    2021

  36. [36]

    Dutta Roy and P

    P. Dutta Roy and P. Saini, Impact of unmodeled eccen- tricity on the tidal deformability measurement and impli- cations for gravitational wave physics inference, Physical Review D110, 024002 (2024)

    2024

  37. [37]

    Kacanja, K

    K. Kacanja, K. Soni, and A. H. Nitz, Eccentricity signa- tures in ligo-virgo-kagra’s bns and nsbh binaries, arXiv e-prints , arXiv:2508.00179 (2025), arXiv:2508.00179 [gr- qc]

    arXiv 2025

  38. [38]

    Punturo, M

    M. Punturo, M. Abernathy, F. Acernese, B. Allen,et al., The einstein telescope: A third-generation gravitational wave observatory, Classical and Quantum Gravity27, 194002 (2010)

    2010

  39. [39]

    S. Hild, M. Abernathy, F. Acernese, P. Amaro-Seoane, et al., Sensitivity studies for third-generation gravita- tional wave observatories, Classical and Quantum Grav- ity28, 094013 (2011)

    2011

  40. [40]

    Science Case for the Einstein Telescope

    M. Maggiore, C. van den Broeck, N. Bartolo, E. Bel- gacem, D. Bertacca,et al., Science case for the einstein telescope, arXiv preprint arXiv:1912.02622 10.48550/arXiv.1912.02622 (2019), arXiv:1912.02622 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1912.02622 1912

  41. [41]

    Reitzeet al., Cosmic explorer: The u.s

    D. Reitzeet al., Cosmic explorer: The u.s. contribu- tion to gravitational-wave astronomy beyond ligo, Bul- letin of the American Astronomical Society51, 35 (2019), arXiv:1907.04833 [astro-ph.IM]

    Pith/arXiv arXiv 2019

  42. [42]

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

    M. Evans, R. X. Adhikari, C. Afle, S. Ballmer,et al., A horizon study for cosmic explorer: Science, observato- ries, and community, arXiv preprint arXiv:2109.09882 10.48550/arXiv.2109.09882 (2021), arXiv:2109.09882 [astro-ph.IM]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2109.09882 2021

  43. [43]

    E. D. Hall, Cosmic explorer: A next-generation ground- based gravitational-wave observatory, Galaxies10, 90 (2022)

    2022

  44. [44]

    Allen, W

    B. Allen, W. G. Anderson, P. R. Brady, D. A. Brown, and J. D. E. Creighton, FINDCHIRP: An algorithm for detection of gravitational waves from inspiraling compact binaries, Physical Review D85, 122006 (2012)

    2012

  45. [45]

    Veitch, V

    J. Veitch, V. Raymond, B. Farr, W. Farr, P. Graff, S. Vitale, B. Aylott, K. Blackburn, N. Christensen, M. Coughlin, W. Del Pozzo, F. Feroz, J. Gair, C.- J. Haster, V. Kalogera, T. Littenberg, I. Mandel, R. O’Shaughnessy, M. Pitkin, C. Rodriguez, C. R¨ over, T. Sidery, R. Smith, M. Van Der Sluys, A. Vecchio, W. Vousden, and L. Wade, Parameter estimation fo...

    2015

  46. [46]

    Ashton, M

    G. Ashton, M. H¨ ubner, P. D. Lasky, C. Talbot, K. Ack- ley, S. Biscoveanu, Q. Chu, A. Divakarla, P. J. Easter, B. Goncharov, F. Hernandez Vivanco, J. Harms, M. E. Lower, G. D. Meadors, D. Melchor, E. Payne, M. D. Pitkin, J. Powell, N. Sarin, R. J. E. Smith, and E. Thrane, Bilby: A user-friendly bayesian inference li- brary for gravitational-wave astronom...

    2019

  47. [47]

    George and E

    D. George and E. A. Huerta, Deep learning for real-time gravitational wave detection and parameter estimation: Results with advanced ligo data, Physics Letters B778, 64 (2018), arXiv:1711.03121 [gr-qc]

    Pith/arXiv arXiv 2018

  48. [48]

    M. Sun, J. Li, S. Cao, and X. Liu, Deep learning forecasts of cosmic acceleration parameters from DECi-hertz inter- ferometer gravitational-wave observatory, Astronomy & Astrophysics682, A177 (2024)

    2024

  49. [49]

    Gabbard, M

    H. Gabbard, M. Williams, F. Hayes, and C. Messen- ger, Matching matched filtering with deep networks for gravitational-wave astronomy, Physical Review Letters 120, 141103 (2018)

    2018

  50. [50]

    M. Sun, J. Wu, J. Li, B. McCane, N. Yang, X. Ma, B. Wang, and M. Zhang, Conditional autoencoder for generating binary neutron star waveforms with tidal and precession effects, Physical Review D112, 084016 (2025)

    2025

  51. [51]

    Cuoco, J

    E. Cuoco, J. Powell, M. Cavagli` a, K. Ackley,et al., En- hancing gravitational-wave science with machine learn- ing, Machine Learning: Science and Technology2, 011002 (2020)

    2020

  52. [52]

    Sun and J

    M. Sun and J. Li, Parameter estimation for intermediate- mass binary black holes through gravitational waves ob- served by DECIGO, arXiv e-prints , arXiv:2312.07834 (2023), arXiv:2312.07834 [gr-qc]

    arXiv 2023

  53. [53]

    A. J. K. Chua and M. Vallisneri, Learning bayesian pos- teriors with neural networks for gravitational-wave infer- ence, Physical Review Letters124, 041102 (2020)

    2020

  54. [54]

    M. Sun, J. Wu, Q. Hu, J. Li, N. Yang, X. Ma, B. Wang, M. Zhang, and Y. Zhong, Detection of multi- band lensed gravitational waves from dark matter ha- los with deep learning, Physical Review D113, 103004 (2026), arXiv:2511.09107 [astro-ph.IM]

    Pith/arXiv arXiv 2026

  55. [55]

    M. Dax, S. R. Green, J. Gair, J. H. Macke, A. Buonanno, and B. Sch¨ olkopf, Real-time gravitational wave science with neural posterior estimation, Physical Review Letters 127, 241103 (2021)

    2021

  56. [56]

    A. Nitz, I. Harry, D. Brown, C. M. Biwer, J. Willis, T. D. Canton, C. Capano, T. Dent, L. Pekowsky, G. S. C. Davies, S. De, M. Cabero, S. Wu, A. R. Williamson, B. Machenschalk, D. Macleod, F. Pannarale, P. Kumar, S. Reyes, dfinstad, S. Kumar, M. T´ apai, L. Singer, P. Ku- mar, veronica villa, maxtrevor, B. U. V. Gadre, S. Khan, S. Fairhurst, and A. Tolley...

    2024

  57. [57]

    W. Zhao, C. Van Den Broeck, D. Baskaran, and T. G. F. Li, Determination of dark energy by the Einstein Tele- scope: Comparing with CMB, BAO, and SNIa observa- tions, Physical Review D83, 023005 (2011)

    2011

  58. [58]

    Schneider, V

    R. Schneider, V. Ferrari, S. Matarrese, and S. F. Porte- gies Zwart, Low-frequency gravitational waves from cos- mological compact binaries, Monthly Notices of the Royal Astronomical Society324, 797 (2001)

    2001

  59. [59]

    Cutler and D

    C. Cutler and D. E. Holz, Ultrahigh precision cosmology from gravitational waves, Physical Review D80, 104009 (2009)

    2009

  60. [60]

    Cai and T

    R.-G. Cai and T. Yang, Estimating cosmological param- eters by the simulated data of gravitational waves from the Einstein Telescope, Physical Review D95, 044024 (2017)

    2017

  61. [61]

    Albanesi, R

    S. Albanesi, R. Gamba, S. Bernuzzi, J. Fontbut´ e, A. Gon- zalez, and A. Nagar, Effective-one-body modeling for generic compact binaries with arbitrary orbits, Physical Review D112, L121503 (2025)

    2025