Pith. sign in

REVIEW 3 major objections 5 minor 83 references

Black Hole Spectroscopy with Conditional Variational Autoencoder

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A conditional variational autoencoder trained on simulated ringdown waveforms can produce posterior distributions for remnant mass, spin, mode amplitudes, phases, and braneworld tidal charge in seconds, matching time-domain Bayesian…

desk verdict A competent, clearly-scoped demonstration that a CVAE can reproduce Bayesian ringdown posteriors on simulated signals; the broader 'alternative to Bayesian inference' claim is only supported in-distribution. read the letter →

arxiv 2506.17618 v1 pith:4IADJFRK submitted 2025-06-21 gr-qc astro-ph.HE

Akash K Mishra This is my paper · ORCID
classification gr-qcastro-ph.HE
keywords gravitationalwavesblackholeringdownquasi-normalmodesconditionalvariationalautoencoderlikelihood-freeinferenceparameterestimationbraneworldtidalchargespectroscopy
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

A conditional variational autoencoder (CVAE), trained once on millions of simulated ringdown waveforms at current ground-based detector sensitivity, can replace the slow likelihood-based sampling normally used in black hole spectroscopy. The paper shows this for two waveform families: Kerr ringdowns with the fundamental quasi-normal mode plus one overtone, and braneworld ringdowns with an additional tidal-charge parameter. In both cases it reports that the network's posterior distributions for remnant mass, spin, mode amplitudes, and phases agree with time-domain Bayesian inference, and that probability-probability calibration is statistically consistent. If this holds, parameter estimation for a detected ringdown would take seconds rather than hours, making rapid and large-scale spectroscopy practical.

What carries the argument

The load-bearing object is the conditional variational autoencoder, a generative network with two encoders and one decoder. During training, one encoder maps the whitened ringdown time series into a Gaussian-mixture latent space while a second encoder maps the data together with the true parameters into a multivariate-normal latent space; the decoder then takes the data and a latent sample and outputs the parameters' mean and variance. Mass, spin, and amplitudes use truncated-Gaussian output distributions and phases use a circular distribution, so all samples stay in physical bounds. The loss is a reconstruction term plus a KL-divergence term with a beta schedule, and during inference the parameter-conditioned encoder is discarded. This machinery carries the argument by turning posterior sampling into a single forward pass through the decoder.

What would settle it

Run the trained network on a loud real ringdown event, or on simulated signals with unknown start time, variable sky location, or nonstationary noise, and compare its posteriors with time-domain Bayesian inference; the central claim fails if the PP calibration degrades or the posteriors shift beyond the scatter seen in the paper's injections.

Watch

Extended reading notes

Core claim

The central claim is that a CVAE can learn the posterior distribution over ringdown parameters directly from whitened strain data, without evaluating a likelihood, and with accuracy matching standard Bayesian analysis on test injections. The Kerr model has six inferred parameters: remnant mass, final spin, amplitudes of the fundamental mode and first overtone, and their phases. The braneworld model adds a seventh, the tidal charge, and the network still reproduces the Bayesian posteriors. The paper's quantitative evidence is side-by-side corner plots at signal-to-noise ratios from about 30 to 85 and PP-plot Kolmogorov-Smirnov p-values that indicate consistency with ideal calibration. It frames the result as a first demonstration that accelerated, likelihood-free inference can carry the extra parameters that make ringdown spectroscopy expensive.

Load-bearing premise

The result depends on the training distribution being representative of real data: ringdowns are assumed to be exactly the fundamental mode plus one overtone with a fixed start time, fixed sky location and angles, and stationary Gaussian noise of known covariance.

Editorial extensions

If this is right

  • A detected ringdown could be analyzed in seconds, allowing immediate spectral characterization after a candidate event is identified.
  • The same trained network can be applied across an entire catalog of events, making population-level Kerr tests computationally cheap.
  • Including an overtone and phases in the training set shows that the approach is not limited to the simplest single-mode ringdowns, extending earlier demonstrations.
  • Inference of the braneworld tidal charge alongside Kerr parameters indicates that additional theory parameters do not break the likelihood-free strategy, provided they are included in the training distribution.
  • PP-plot calibration means the network output can be treated as samples from a trustworthy posterior for credible-interval statements.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A decisive stress test the paper leaves for future work is varying the ringdown start time and sky location; because training fixes both, the network's timing and orientation invariance is unverified, and this should be checked before real-event use.
  • Since the decoder already outputs full distributions over seven parameters, the same architecture could be retargeted to test the Kerr no-hair theorem by placing independent parameters on the quasi-normal frequencies and checking consistency with a single mass and spin.
  • The network's speed suggests a natural use as a proposal or surrogate within hierarchical population analyses, although the paper does not demonstrate that application.
  • Applying the trained network to real detector noise, which is nonstationary and contains glitches, is the untested bridge between the paper's simulated calibration and observational black hole spectroscopy.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper presents a conditional variational autoencoder (CVAE) framework for fast posterior estimation of black-hole ringdown parameters from simulated gravitational-wave data. Two CVAE networks are trained: one for Kerr remnants, inferring final mass, spin, and the amplitudes and phases of the fundamental mode and first overtone; and one for braneworld black holes, adding the tidal charge parameter. The CVAE posteriors are compared with time-domain Bayesian inference (dynesty) on four Kerr and two braneworld injections across different SNRs, and calibration is assessed with PP plots over 256 test samples. The authors report that generating 20,000 posterior samples takes 4–5 seconds, versus hours for Bayesian inference, and conclude that the CVAE offers a computationally efficient alternative for black hole spectroscopy.

Significance. If the validation gap is addressed, the framework would enable rapid ringdown parameter estimation including modified-gravity parameters, which is relevant for real-time alerts and large-scale analyses. The extension to overtones and to a beyond-Kerr parameter (tidal charge) goes beyond the earlier CVAE ringdown study of Ref. [62]. The paper includes PP-plot calibration checks with KS p-values, explicit speed benchmarks, and a direct comparison with Bayesian inference, which are good practices. However, the validation is entirely in-distribution and the direct Bayesian comparison is limited to a handful of selected injections, so the practical significance for real gravitational-wave observations is not yet established.

major comments (3)
  1. [Section IV, Figs. 3 and 4] The direct quantitative comparison between CVAE and Bayesian posteriors is limited to four Kerr and two braneworld injections. The text claims "strong agreement" and "excellent agreement" based on these visual corner-plot comparisons, but this is insufficient to establish agreement across the prior. The authors should quantify the discrepancy (e.g., with Hellinger distance, Jensen-Shannon divergence, or a two-sample test) over a larger set of test samples, and show how the agreement depends on SNR and on the location in parameter space. This is load-bearing for the central claim that the CVAE reproduces the Bayesian posterior.
  2. [Section II and Section IV, Fig. 5] The PP-plot calibration test is performed on 256 test samples drawn from the same simulator used for training, with fixed sky location (α,δ)=(1.95,−1.22), fixed polarization/inclination/azimuth (ψ,ι,ϕ)=(0.82,π,0), fixed ringdown start time t0=0, a single known Gaussian noise covariance, and only the (2,2,0)+(2,2,1) mode superposition. This validates calibration only under the training distribution. Since the stated purpose (Abstract, Section V) is practical ringdown spectroscopy from real observations, the transfer to variable t0, sky location, nonstationary noise, and additional modes/physics is untested. The authors should either add experiments that vary these conditions or explicitly reframe the claim to an in-distribution approximation; as written, the conclusion that the CVAE is an "alternative to likelihood-based Bayesian inference" for real ringdown spectroscopy is not supported.
  3. [Section IV.B and Section V] The paper acknowledges that the CVAE performance degrades for low-SNR injections (SNR ≲ 20) and when multiple parameters lie near the prior edges, but it does not quantify these regimes or show where the network remains reliable. Because low-SNR events and parameters near prior boundaries are common in real observations, this limitation directly affects the practical claim. The authors should provide a quantitative reliability map (e.g., accuracy versus SNR and parameter location) or restrict the stated scope of the method accordingly.
minor comments (5)
  1. [Section IV.A, Fig. 5] The legend of the Kerr PP plot lists five parameters (Mf, A220, A221, φ220, φ221) while six KS p-values are reported; please clarify whether the spin χ is included and correct the legend or the p-value list.
  2. [Throughout (e.g., Section IV)] The text contains "Fig. Fig. 5" duplicated; this should be "Fig. 5". Also, some figure labels appear with Unicode artifacts (e.g., "uni00A0") in the source; the final PDF should be checked for clean rendering.
  3. [Section III, Eq. (III.1)] The β schedule is described only up to epoch 300; please specify whether β remains fixed at 1 for the rest of the 55,000-epoch training. Additionally, the paper mentions "optuna" for hyperparameter tuning but does not report the tuned values or the search objective; including these would improve reproducibility.
  4. [Section II] The prior ranges for amplitudes and the SNR cut at 15 are given, but the distribution of SNRs in the test dataset is not shown. A figure or table with the SNR distribution would help interpret the PP plots and the claims about SNR-dependent performance.
  5. [Section IV] The Bayesian comparison uses dynesty with 3000 live points, but the paper does not state the number of posterior samples used in the corner plots or report convergence diagnostics (e.g., log-evidence error). Reporting these would strengthen the comparison.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the CVAE posteriors are validated against Bayesian inference on the same forward model, and the cited braneworld QNM formulas are external inputs rather than outputs derived in this paper.

full rationale

The paper's derivation chain is: (i) define the ringdown waveform model (Eqs. II.1-II.2), (ii) simulate training data from that model with known parameters, (iii) train a CVAE to map whitened time series to posterior distributions over parameters, and (iv) compare those posteriors with time-domain Bayesian inference (dynesty) on the same model. None of these steps is self-referential: the CVAE is not defined in terms of the target parameters, the training loss (Eq. III.1) is a standard reconstruction-plus-KL objective, and the validation against Bayesian posteriors is an external benchmark. The waveform model itself uses QNM frequencies from Ref. [14] for Kerr and Refs. [29,33] for braneworld; these are model inputs, not claims the paper derives, and the braneworld QNM relations were published in prior peer-reviewed work and are externally falsifiable. The fact that some of these inputs are the author's own prior work does not make the CVAE result circular, because the paper's central claim is that the trained network reproduces the Bayesian posterior, which is independent of who computed the QNM fits. The PP plots (Fig. 5) and corner plots (Figs. 3-4) test this claim on held-out samples drawn from the same simulator; this is an internal consistency check of the amortized posterior, not a derivation of the parameters from the waveform model. No equation or fitted parameter is renamed as a prediction; no target result is assumed in the inputs. The in-distribution nature of the validation is a generalization concern rather than a circularity. Therefore no circular step can be exhibited, and the appropriate finding is no significant circularity (score 0).

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The CVAE does not introduce new physics. Its central assumption is that the simulated training distribution (waveform model, noise model, fixed extrinsic parameters) matches the conditions of interest. The free parameters are training choices and prior bounds. The QNM fitting formulas come from previous work, including papers by the same author (Refs. [29,33]), but they are used as inputs, not derived here.

free parameters (2)
  • Network hyperparameters (latent dimension, GMM components, filter counts, strides, dense widths, dropout, L2 rate… = ld=16, Md=24, dropout 0.2, L2 0.001, batch 1024, epochs 55000; see Table I and Section III
    Hand-tuned to make the CVAE train; they define the method but are not physical parameters. Different choices could change posterior quality.
  • Training prior ranges for injected parameters = Mf in [20,150] solar masses, chi in [0.01,0.99], A22n in [1e-22,1e-20], phases in [0,2pi]; braneworld q in [0,-1], chi…
    Chosen by hand as astrophysically relevant intervals (Section II); the posterior is conditioned on this prior and results may not generalize outside it.
assumptions (6)
  • domain assumption The ringdown waveform is a linear superposition of damped sinusoids for the (2,2,0) and (2,2,1) modes, with counter-rotating modes neglected.
    Section II, Eq. (II.1): this model defines the signal content and omits retrograde modes and higher overtones.
  • domain assumption QNM frequencies and damping times are computed from fitting formulas: Berti et al. for Kerr and Mishra et al. for braneworld tidal charge.
    Section II: the training waveforms and the Bayesian benchmark both use these formulas, so any inaccuracy is inherited by both.
  • domain assumption Detector noise is Gaussian, stationary, and fully described by the advanced LIGO noise covariance matrix used for whitening.
    Section II: whitening with the noise covariance and the likelihood in Bayesian comparison assume this noise model.
  • domain assumption The CVAE architecture and training objective from Ref. [57] yield a calibrated approximation to the posterior distribution when trained with sufficient samples.
    Section III: the paper relies on this standard simulation-based inference assumption; calibration is checked empirically rather than proven.
  • domain assumption Sky location, inclination, polarization, azimuth, and ringdown start time are known and fixed during training and inference.
    Section II: 'For simplicity, we keep the sky locations fixed' and set (psi,iota,phi)=(0.82,pi,0.0), t0=0; real data requires estimating these.
  • standard math Variational autoencoder reparameterization and Bayes' theorem.
    Used implicitly in the loss function Eq. (III.1) and in the Bayesian benchmark.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Black Hole Spectroscopy with Conditional Variational Autoencoder." pith.science (2026). https://pith.science/paper/4IADJFRK

@misc{pith2026250617618,
  author       = {Pith},
  title        = {Pith review of: Black Hole Spectroscopy with Conditional Variational Autoencoder},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4IADJFRK}},
  note         = {Machine review of arXiv:2506.17618}
}
read the original abstract

Gravitational waves provide a unique opportunity to test general relativity in the strong-field regime, enabling the extraction of key physical parameters from observational data. Traditional likelihood-based inference methods, while robust, become computationally expensive in high-dimensional parameter spaces, such as when incorporating multiple ringdown modes or beyond Kerr deviations. In this paper, we explore the implementation of a conditional variational autoencoder-based machine-learning framework for accelerated ringdown parameter estimation. As a first application, we use the neural network to infer the remnant properties of a final black hole under the Kerr hypothesis. We demonstrate the performance of this algorithm with simulated ringdown waveforms consistent with advanced LIGO sensitivity and compare with Bayesian analysis results. We further extend the framework beyond the Kerr paradigm by incorporating deviations predicted in braneworld gravity.

Figures

Figures reproduced from arXiv: 2506.17618 by the authors.

Figure 1
Figure 1. FIG. 1. A visual overview of the training and testing algo [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. This figure shows the evolution of the loss components as a function of training epochs for both the Kerr (left panel) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. In this figure, we present the CVAE constructed posterior (crimson) distribution and compare it with that of the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. In this figure, we present the CVAE constructed posterior (crimson) distribution and compare it with that of the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. In this figure, we show the PP plot for Kerr inference (left panel) and braneworld inference (right panel) using the [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

83 extracted references · 13 canonical work pages

  1. [57]

    Denoising gravitational-wave signals from binary black holes with a dilated convolutional autoencoder,

    P. Bacon, A. Trovato, and M. Bejger, “Denoising gravitational-wave signals from binary black holes with a dilated convolutional autoencoder,”Mach. Learn. Sci. Tech.4 no. 3, (2023) 035024,arXiv:2205.13513 [gr-qc]

    arXiv 2023

  2. [62]

    Merger-ringdown consistency: A new test of strong gravity using deep learning,

    S. Bhagwat and C. Pacilio, “Merger-ringdown consistency: A new test of strong gravity using deep learning,” Phys. Rev. D 104 no. 2, (2021) 024030, arXiv:2101.07817 [gr-qc]

    arXiv 2021

  3. [1]

    Parameter Estimation

    Samples drawn from this latent space are then com- bined with the ringdown data and passed through the 5 58.48+14.86 9.44 62.48+14.61 11.80 0.2 0.4 0.6 0.8 0.41+0.32 0.33 0.54+0.26 0.38 1.5 3.0 4.5 6.0 A220(×10 21) 3.85+1.23 1.49 3.62+1.44 1.56 2 4 6 8 A221(×10 21) 3.70+2.52 2.25 3.90+2.64 2.30 1.5 3.0 4.5 6.0 220 2.09+0.63 0.50 2.05+0.71 0.56 50 60 70 80...

  4. [2]

    Observation of Gravitational Waves from a Binary Black Hole Merger,

    LIGO Scientific, VirgoCollaboration, B. P. Abbott et al., “Observation of Gravitational Waves from a Binary Black Hole Merger,”Phys. Rev. Lett. 116 no. 6, (2016) 061102, arXiv:1602.03837 [gr-qc]

    arXiv 2016

  5. [3]

    Properties of the Binary Black Hole Merger GW150914,

    LIGO Scientific, VirgoCollaboration, B. P. Abbott et al., “Properties of the Binary Black Hole Merger GW150914,” Phys. Rev. Lett. 116 no. 24, (2016) 241102, arXiv:1602.03840 [gr-qc]

    arXiv 2016

  6. [4]

    GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run,

    LIGO Scientific, VirgoCollaboration, R. Abbott et al., “GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run,”Phys. Rev. X 11 (2021) 021053, arXiv:2010.14527 [gr-qc]

    arXiv 2021

  7. [5]

    GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the Third Observing Run,

    KAGRA, VIRGO, LIGO ScientificCollaboration, R. Abbott et al., “GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo during the Second Part of the Third Observing Run,”Phys. Rev. X 13 no. 4, (2023) 041039,arXiv:2111.03606 [gr-qc]

    arXiv 2023

  8. [6]

    Tests of general relativity with GW150914,

    LIGO Scientific, VirgoCollaboration, B. P. Abbott et al., “Tests of general relativity with GW150914,” Phys. Rev. Lett. 116 no. 22, (2016) 221101, arXiv:1602.03841 [gr-qc] . [Erratum: Phys.Rev.Lett. 121, 129902 (2018)]

    arXiv 2016

Show all 83 references
  1. [7]

    Tests of General Relativity with GWTC-3,

    LIGO Scientific, VIRGO, KAGRACollaboration, R. Abbott et al., “Tests of General Relativity with GWTC-3,” arXiv:2112.06861 [gr-qc]

    arXiv

  2. [8]

    GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral,

    LIGO Scientific, VirgoCollaboration, B. P. Abbott et al., “GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral,”Phys. Rev. Lett. 119 no. 16, (2017) 161101,arXiv:1710.05832 [gr-qc]

    2017 arXiv

  3. [9]

    Population Properties of Compact Objects from the Second LIGO-Virgo Gravitational-Wave Transient Catalog,

    LIGO Scientific, VirgoCollaboration, R. Abbott et al., “Population Properties of Compact Objects from the Second LIGO-Virgo Gravitational-Wave Transient Catalog,” Astrophys. J. Lett. 913 no. 1, (2021) L7, arXiv:2010.14533 [astro-ph.HE]

    2021 arXiv

  4. [10]

    Population of Merging Compact Binaries Inferred Using Gravitational Waves through GWTC-3,

    KAGRA, VIRGO, LIGO ScientificCollaboration, R. Abbott et al., “Population of Merging Compact Binaries Inferred Using Gravitational Waves through GWTC-3,” Phys. Rev. X 13 no. 1, (2023) 011048, arXiv:2111.03634 [astro-ph.HE]

    2023 arXiv

  5. [11]

    Stability of a Schwarzschild singularity,

    T. Regge and J. A. Wheeler, “Stability of a Schwarzschild singularity,” Phys. Rev. 108 (1957) 1063–1069

    1957

  6. [12]

    Scattering of Gravitational Radiation by a Schwarzschild Black-hole,

    C. V. Vishveshwara, “Scattering of Gravitational Radiation by a Schwarzschild Black-hole,”Nature227 (1970) 936–938

    1970

  7. [13]

    Perturbation analysis for gravitational and electromagnetic radiation in a reissner-nordstroem geometry,

    F. J. Zerilli, “Perturbation analysis for gravitational and electromagnetic radiation in a reissner-nordstroem geometry,” Phys. Rev. D 9 (1974) 860–868

    1974

  8. [14]

    S. A. Teukolsky, “Perturbations of a rotating black hole

  9. [15]

    Fundamental equations for gravitational electromagnetic and neutrino field perturbations,” Astrophys. J. 185 (1973) 635–647

    1973

  10. [16]

    On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA,

    E. Berti, V. Cardoso, and C. M. Will, “On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA,”Phys. Rev. D 73 (2006) 064030, arXiv:gr-qc/0512160

    2006 arXiv

  11. [17]

    Event horizons in static electrovac space-times,

    W. Israel, “Event horizons in static electrovac space-times,” Commun. Math. Phys. 8 (1968) 245–260

    1968

  12. [18]

    Axisymmetric Black Hole Has Only Two Degrees of Freedom,

    B. Carter, “Axisymmetric Black Hole Has Only Two Degrees of Freedom,”Phys. Rev. Lett. 26 (1971) 331–333

    1971

  13. [19]

    Uniqueness of the Kerr black hole,

    D. C. Robinson, “Uniqueness of the Kerr black hole,” Phys. Rev. Lett. 34 (1975) 905–906

    1975

  14. [20]

    Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum: II. Black-Hole Images,

    T. Johannsen and D. Psaltis, “Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum: II. Black-Hole Images,”Astrophys. J. 718 (2010) 446–454, arXiv:1005.1931 [astro-ph.HE]

    2010 arXiv

  15. [21]

    Testing the no-hair theorem with black hole ringdowns using TIGER,

    J. Meidam, M. Agathos, C. Van Den Broeck, J. Veitch, and B. S. Sathyaprakash, “Testing the no-hair theorem with black hole ringdowns using TIGER,”Phys. Rev. D 90 no. 6, (2014) 064009,arXiv:1406.3201 [gr-qc]

    2014 arXiv

  16. [22]

    Testing the no-hair theorem with GW150914,

    M. Isi, M. Giesler, W. M. Farr, M. A. Scheel, and S. A. Teukolsky, “Testing the no-hair theorem with GW150914,” Phys. Rev. Lett. 123 no. 11, (2019) 111102, arXiv:1905.00869 [gr-qc]

    2019 arXiv

  17. [23]

    Black-hole spectroscopy, the no-hair theorem, and GW150914: Kerr versus Occam,

    J. Calderón Bustillo, P. D. Lasky, and E. Thrane, “Black-hole spectroscopy, the no-hair theorem, and GW150914: Kerr versus Occam,”Phys. Rev. D 103 no. 2, (2021) 024041,arXiv:2010.01857 [gr-qc]

    2021 arXiv

  18. [24]

    Observational Black Hole Spectroscopy: A time-domain multimode analysis of GW150914,

    G. Carullo, W. Del Pozzo, and J. Veitch, “Observational Black Hole Spectroscopy: A time-domain multimode analysis of GW150914,”Phys. Rev. D 99 no. 12, (2019) 123029, arXiv:1902.07527 [gr-qc] . [Erratum: Phys.Rev.D 100, 089903 (2019)]

    2019 arXiv

  19. [25]

    Analyzing black-hole ringdowns,

    M. Isi and W. M. Farr, “Analyzing black-hole ringdowns,” arXiv:2107.05609 [gr-qc]

    arXiv

  20. [26]

    Analysis of Ringdown Overtones in GW150914,

    R. Cotesta, G. Carullo, E. Berti, and V. Cardoso, “Analysis of Ringdown Overtones in GW150914,”Phys. Rev. Lett. 129 no. 11, (2022) 111102, arXiv:2201.00822 [gr-qc]

    2022 arXiv

  21. [27]

    Ringdown of GW190521: Hints of multiple quasinormal modes with a precessional interpretation,

    H. Siegel, M. Isi, and W. M. Farr, “Ringdown of GW190521: Hints of multiple quasinormal modes with a precessional interpretation,”Phys. Rev. D 108 no. 6, (2023) 064008, arXiv:2307.11975 [gr-qc]

    2023 arXiv

  22. [28]

    Probing Spacetime Symmetries Using Gravitational Wave Ringdown,

    R. Ghosh, A. K. Mishra, and S. Sarkar, “Probing Spacetime Symmetries Using Gravitational Wave Ringdown,” arXiv:2412.08942 [gr-qc]

    arXiv

  23. [29]

    Testing the Black-Hole Area Law with GW150914,

    M. Isi, W. M. Farr, M. Giesler, M. A. Scheel, and S. A. Teukolsky, “Testing the Black-Hole Area Law with GW150914,” Phys. Rev. Lett. 127 no. 1, (2021) 011103, arXiv:2012.04486 [gr-qc]

    2021 arXiv

  24. [30]

    Constraints on Kerr-Newman black holes from merger-ringdown gravitational-wave observations,

    G. Carullo, D. Laghi, N. K. Johnson-McDaniel, W. Del Pozzo, O. J. C. Dias, M. Godazgar, and J. E. Santos, “Constraints on Kerr-Newman black holes from merger-ringdown gravitational-wave observations,” Phys. Rev. D 105 no. 6, (2022) 062009, arXiv:2109.13961 [gr-qc]

    2022 arXiv

  25. [31]

    Constraining extra dimensions using observations of black hole quasi-normal modes,

    A. K. Mishra, A. Ghosh, and S. Chakraborty, “Constraining extra dimensions using observations of black hole quasi-normal modes,”Eur. Phys. J. C 82 no. 9, (2022) 820,arXiv:2106.05558 [gr-qc] . 9

    2022 arXiv

  26. [32]

    Identifying modified theories of gravity using binary black-hole ringdowns,

    C. Pacilio and S. Bhagwat, “Identifying modified theories of gravity using binary black-hole ringdowns,” Phys. Rev. D 107 no. 8, (2023) 083021, arXiv:2301.02267 [gr-qc]

    2023 arXiv

  27. [33]

    Black-hole ringdown as a probe of higher-curvature gravity theories,

    H. O. Silva, A. Ghosh, and A. Buonanno, “Black-hole ringdown as a probe of higher-curvature gravity theories,” Phys. Rev. D 107 no. 4, (2023) 044030, arXiv:2205.05132 [gr-qc]

    2023 arXiv

  28. [34]

    Measuring deviations from the Kerr geometry with black hole ringdown,

    K. Dey, E. Barausse, and S. Basak, “Measuring deviations from the Kerr geometry with black hole ringdown,” Phys. Rev. D 108 no. 2, (2023) 024064, arXiv:2212.10725 [gr-qc]

    2023 arXiv

  29. [35]

    Bounds on tidal charges from gravitational wave ringdown observations,

    A. K. Mishra, G. Carullo, and S. Chakraborty, “Bounds on tidal charges from gravitational wave ringdown observations,” Phys. Rev. D 109 no. 2, (2024) 024025, arXiv:2311.03556 [gr-qc]

    2024 arXiv

  30. [36]

    Higher-derivative corrections to the Kerr quasinormal mode spectrum,

    P. A. Cano, L. Capuano, N. Franchini, S. Maenaut, and S. H. Völkel, “Higher-derivative corrections to the Kerr quasinormal mode spectrum,” Phys. Rev. D 110 no. 12, (2024) 124057, arXiv:2409.04517 [gr-qc]

    2024 arXiv

  31. [37]

    Black hole spectroscopy: from theory to experiment,

    E. Berti et al., “Black hole spectroscopy: from theory to experiment,” arXiv:2505.23895 [gr-qc]

    arXiv

  32. [38]

    BILBY: A user-friendly Bayesian inference library for gravitational-wave astronomy,

    G. Ashtonet al., “BILBY: A user-friendly Bayesian inference library for gravitational-wave astronomy,” Astrophys. J. Suppl. 241 no. 2, (2019) 27, arXiv:1811.02042 [astro-ph.IM]

    2019 arXiv

  33. [39]

    An introduction to bayesian inference in gravitational-wave astronomy: Parameter estimation, model selection, and hierarchical models,

    E. Thrane and C. Talbot, “An introduction to bayesian inference in gravitational-wave astronomy: Parameter estimation, model selection, and hierarchical models,” Publications of the Astronomical Society of Australia 36 (2019) . http://dx.doi.org/10.1017/pasa.2019.2

    2019 doi

  34. [40]

    Inferring Binary Properties from Gravitational Wave Signals,

    J. Roulet and T. Venumadhav, “Inferring Binary Properties from Gravitational Wave Signals,” arXiv:2402.11439 [gr-qc]

    arXiv

  35. [41]

    pyRing: a time-domain ringdown analysis python package

    G. Carullo, W. Del Pozzo, and J. Veitch, “pyRing: a time-domain ringdown analysis python package.” git.ligo.org/lscsoft/pyring, July, 2023. https://doi.org/10.5281/zenodo.8165508

    2023 doi

  36. [42]

    dynesty: a dynamic nested sampling package for estimating bayesian posteriors and evidences,

    J. S. Speagle, “dynesty: a dynamic nested sampling package for estimating bayesian posteriors and evidences,” Monthly Notices of the Royal Astronomical Society493 no. 3, (Feb., 2020) 3132–3158. http://dx.doi.org/10.1093/mnras/staa278

    2020 doi

  37. [43]

    johnveitch/cpnest: v0.11.4,

    J. Veitch, W. D. Pozzo, A. Lyttle, M. J. Williams, C. Talbot, M. Pitkin, G. Ashton, Cody, M. Hübner, A. Nitz, D. Mihaylov, D. Macleod, G. Carullo, G. Davies, and ttw, “johnveitch/cpnest: v0.11.4,” Apr.,

  38. [44]

    Matching matched filtering with deep networks for gravitational-wave astronomy,

    H. Gabbard, M. Williams, F. Hayes, and C. Messenger, “Matching matched filtering with deep networks for gravitational-wave astronomy,” Phys. Rev. Lett. 120 no. 14, (2018) 141103,arXiv:1712.06041 [astro-ph.IM]

    2018 arXiv

  39. [45]

    emcee: The MCMC Hammer

    D. Foreman-Mackey, A. Conley, W. Meierjurgen Farr, D. W. Hogg, D. Lang, P. Marshall, A. Price-Whelan, J. Sanders, and J. Zuntz, “emcee: The MCMC Hammer.” Astrophysics source code library, record ascl:1303.002, Mar., 2013

    2013

  40. [46]

    Probabilistic programming in python using pymc3,

    J. Salvatier, T. V. Wiecki, and C. Fonnesbeck, “Probabilistic programming in python using pymc3,” PeerJ Computer Science 2 (2016) e55

    2016

  41. [47]

    Rapid identification of time-frequency domain gravitational wave signals from binary black holes using deep learning*,

    Y.-X. Wang, S.-J. Jin, T.-Y. Sun, J.-F. Zhang, and X. Zhang, “Rapid identification of time-frequency domain gravitational wave signals from binary black holes using deep learning*,”Chin. Phys. C 48 no. 12, (2024) 125107, arXiv:2305.19003 [gr-qc]

    2024 arXiv

  42. [48]

    Detecting and denoising gravitational wave signals from binary black holes using deep learning,

    C. Murali and D. Lumley, “Detecting and denoising gravitational wave signals from binary black holes using deep learning,” Phys. Rev. D 108 no. 4, (2023) 043024, arXiv:2210.01718 [gr-qc]

    2023 arXiv

  43. [49]

    Convolutional neural networks for signal detection in real LIGO data,

    O. Zelenka, B. Brügmann, and F. Ohme, “Convolutional neural networks for signal detection in real LIGO data,”Phys. Rev. D 110 no. 2, (2024) 024024, arXiv:2402.07492 [astro-ph.IM]

    2024 arXiv

  44. [50]

    Nonlinear Noise Cleaning in Gravitational-Wave Detectors With Convolutional Neural Networks,

    H. Yu and R. X. Adhikari, “Nonlinear Noise Cleaning in Gravitational-Wave Detectors With Convolutional Neural Networks,” Front. Artif. Intell. 5 (2022) 811563, arXiv:2111.03295 [astro-ph.IM]

    2022 arXiv

  45. [51]

    Noise Reduction in Gravitational-wave Data via Deep Learning,

    R. Ormiston, T. Nguyen, M. Coughlin, R. X. Adhikari, and E. Katsavounidis, “Noise Reduction in Gravitational-wave Data via Deep Learning,”Phys. Rev. Res. 2 no. 3, (2020) 033066,arXiv:2005.06534 [astro-ph.IM]

    2020 arXiv

  46. [52]

    Machine-learning nonstationary noise out of gravitational-wave detectors,

    G. Vajente, Y. Huang, M. Isi, J. C. Driggers, J. S. Kissel, M. J. Szczepanczyk, and S. Vitale, “Machine-learning nonstationary noise out of gravitational-wave detectors,” Phys. Rev. D 101 no. 4, (2020) 042003, arXiv:1911.09083 [gr-qc]

    2020 arXiv

  47. [53]

    NNETFIX: an artificial neural network-based denoising engine for gravitational-wave signals,

    K. Mogushi, R. Quitzow-James, M. Cavaglià, S. Kulkarni, and F. Hayes, “NNETFIX: an artificial neural network-based denoising engine for gravitational-wave signals,” Mach. Learn. Sci. Tech. 2 no. 3, (2021) 035018,arXiv:2101.04712 [gr-qc]

    2021 arXiv

  48. [54]

    Gravitational Wave Denoising of Binary Black Hole Mergers with Deep Learning,

    W. Wei and E. A. Huerta, “Gravitational Wave Denoising of Binary Black Hole Mergers with Deep Learning,” Phys. Lett. B 800 (2020) 135081, arXiv:1901.00869 [gr-qc]

    2020 arXiv

  49. [55]

    Application of dictionary learning to denoise LIGO’s blip noise transients,

    A. Torres-Forné, E. Cuoco, J. A. Font, and A. Marquina, “Application of dictionary learning to denoise LIGO’s blip noise transients,”Phys. Rev. D 102 no. 2, (2020) 023011,arXiv:2002.11668 [gr-qc]

    2020 arXiv

  50. [56]

    NRSurNN3dq4: A Deep Learning Powered Numerical Relativity Surrogate for Binary Black Hole Waveforms,

    O. Gramaxo Freitas, A. Theodoropoulos, N. Villanueva, T. Fernandes, S. Nunes, J. A. Font, A. Onofre, A. Torres-Forné, and J. D. Martin-Guerrero, “NRSurNN3dq4: A Deep Learning Powered Numerical Relativity Surrogate for Binary Black Hole Waveforms,” arXiv:2412.06946 [gr-qc]

  51. [58]

    Gravitational-wave surrogate models powered by artificial neural networks,

    S. Khan and R. Green, “Gravitational-wave surrogate models powered by artificial neural networks,”Phys. Rev. D 103 no. 6, (2021) 064015,arXiv:2008.12932 [gr-qc]

    2021 arXiv

  52. [59]

    Use of conditional variational auto encoder to analyze ringdown 10 gravitational waves,

    T. S. Yamamoto and T. Tanaka, “Use of conditional variational auto encoder to analyze ringdown 10 gravitational waves,” arXiv:2002.12095 [gr-qc]

    2002 arXiv

  53. [60]

    Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy,

    H. Gabbard, C. Messenger, I. S. Heng, F. Tonolini, and R. Murray-Smith, “Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy,” Nature Phys. 18 no. 1, (2022) 112–117, arXiv:1909.06296 [astro-ph.IM]

    2022 arXiv

  54. [61]

    Gravitational-wave parameter estimation with autoregressive neural network flows,

    S. R. Green, C. Simpson, and J. Gair, “Gravitational-wave parameter estimation with autoregressive neural network flows,”Phys. Rev. D 102 no. 10, (2020) 104057,arXiv:2002.07656 [astro-ph.IM]

    2020 arXiv

  55. [63]

    Complete parameter inference for GW150914 using deep learning,

    S. R. Green and J. Gair, “Complete parameter inference for GW150914 using deep learning,”Mach. Learn. Sci. Tech.2 no. 3, (2021) 03LT01,arXiv:2008.03312 [astro-ph.IM]

    2021 arXiv

  56. [64]

    Real-Time Gravitational Wave Science with Neural Posterior Estimation,

    M. Dax, S. R. Green, J. Gair, J. H. Macke, A. Buonanno, and B. Schölkopf, “Real-Time Gravitational Wave Science with Neural Posterior Estimation,” Phys. Rev. Lett. 127 no. 24, (2021) 241103, arXiv:2106.12594 [gr-qc]

    2021 arXiv

  57. [65]

    Simulation-based inference of black hole ringdowns in the time domain,

    C. Pacilio, S. Bhagwat, and R. Cotesta, “Simulation-based inference of black hole ringdowns in the time domain,”Phys. Rev. D 110 no. 8, (2024) 083010, arXiv:2404.11373 [gr-qc]

    2024 arXiv

  58. [66]

    Statistically-informed deep learning for gravitational wave parameter estimation,

    H. Shen, E. A. Huerta, E. O’Shea, P. Kumar, and Z. Zhao, “Statistically-informed deep learning for gravitational wave parameter estimation,”Mach. Learn. Sci. Tech. 3 no. 1, (2022) 015007,arXiv:1903.01998 [gr-qc]

    2022 arXiv

  59. [67]

    Rapid Mass Parameter Estimation of Binary Black Hole Coalescences Using Deep Learning,

    A. McLeod, D. Jacobs, C. Chatterjee, L. Wen, and F. Panther, “Rapid Mass Parameter Estimation of Binary Black Hole Coalescences Using Deep Learning,” arXiv:2201.11126 [astro-ph.IM]

    arXiv

  60. [68]

    Learning structured output representation using deep conditional generative models,

    K. Sohn, H. Lee, and X. Yan, “Learning structured output representation using deep conditional generative models,” in Advances in Neural Information Processing Systems, C. Cortes, N. Lawrence, D. Lee, M. Sugiyama, and R. Garnett, eds., vol. 28. Curran Associates, Inc.,

  61. [69]

    Rapid likelihood free inference of compact binary coalescences using accelerated hardware,

    D. Chatterjee et al., “Rapid likelihood free inference of compact binary coalescences using accelerated hardware,” Mach. Learn. Sci. Tech. 5 no. 4, (2024) 045030, arXiv:2407.19048 [gr-qc]

    2024 arXiv

  62. [70]

    Parameter estimation of microlensed gravitational waves with conditional variational autoencoders,

    R. Bada-Nerin, O. Bulashenko, O. Gramaxo Freitas, and J. A. Font, “Parameter estimation of microlensed gravitational waves with conditional variational autoencoders,” Phys. Rev. D 111 no. 8, (2025) 084067, arXiv:2412.00566 [gr-qc]

    2025 arXiv

  63. [71]

    An introduction to variational autoencoders,

    D. P. Kingma and M. Welling, “An introduction to variational autoencoders,” Foundations and Trends ® in Machine Learning 12 no. 4, (2019) 307–392. http://dx.doi.org/10.1561/2200000056

    2019 doi

  64. [72]

    Tutorial on variational autoencoders,

    C. Doersch, “Tutorial on variational autoencoders,”

  65. [73]

    Controlling structured output representations from attributes using conditional generative models,

    M. Debbagh, “Controlling structured output representations from attributes using conditional generative models,” 2025. https://arxiv.org/abs/2305.00980

    2025 arXiv

  66. [74]

    Auto-encoding variational bayes,

    D. P. Kingma and M. Welling, “Auto-encoding variational bayes,” 2022. https://arxiv.org/abs/1312.6114

    2022 arXiv

  67. [75]

    Exciting black hole modes via misaligned coalescences: II. The mode content of late-time coalescence waveforms,

    H. Lim, G. Khanna, A. Apte, and S. A. Hughes, “Exciting black hole modes via misaligned coalescences: II. The mode content of late-time coalescence waveforms,” Phys. Rev. D 100 no. 8, (2019) 084032, arXiv:1901.05902 [gr-qc]

    2019 arXiv

  68. [76]

    Angular emission patterns of remnant black holes,

    X. Li, L. Sun, R. K. L. Lo, E. Payne, and Y. Chen, “Angular emission patterns of remnant black holes,” Phys. Rev. D 105 no. 2, (2022) 024016, arXiv:2110.03116 [gr-qc]

    2022 arXiv

  69. [77]

    Brane world gravity,

    R. Maartens, “Brane world gravity,”Living Rev. Rel. 7 (2004) 7, arXiv:gr-qc/0312059

    2004 arXiv

  70. [78]

    Advanced LIGO,

    LIGO ScientificCollaboration, J. Aasiet al., “Advanced LIGO,” Class. Quant. Grav. 32 (2015) 074001, arXiv:1411.4547 [gr-qc]

    2015 arXiv

  71. [79]

    Advanced LIGO detector performance in the fourth observing run,

    E. Capote et al., “Advanced LIGO detector performance in the fourth observing run,”Phys. Rev. D 111 no. 6, (2025) 062002,arXiv:2411.14607 [gr-qc]

    2025 arXiv

  72. [83]

    An Introduction to extra dimensions,

    A. Perez-Lorenzana, “An Introduction to extra dimensions,” J. Phys. Conf. Ser. 18 (2005) 224–269, arXiv:hep-ph/0503177

    2005 arXiv

  73. [2015]

    https: //proceedings.neurips.cc/paper_files/paper/2015/ file/8d55a249e6baa5c06772297520da2051-Paper.pdf

    2015

  74. [2021]

    https://arxiv.org/abs/1606.05908

    arXiv

  75. [2022]

    https://doi.org/10.5281/zenodo.6460935

    doi

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.