Organizations: Graduate School of Integrative Science and Engineering, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan · Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan · Department of Physics, Graduate School of Science, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397, Japan · Graduate School of Information and Data Science and Department of Design and Data Science, Tokyo City University, 3-3-1 Ushikubo-Nishi, Tsuzuki-ku, Yokohama, Kanagawa 224-8551, Japan · Earthquake Research Institute, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan
Ringdown gravitational waves from binary black hole mergers can be modeled as superpositions of quasinormal modes (QNMs), whose frequencies and excitation factors encode properties of the remnant Kerr black hole. Reliable extraction of multiple QNM components is challenging because of mode overlap and noise. We develop an autoencoder-based framework for multi-component QNM analysis, in which the latent space is trained to represent the physical parameters of individual modes, enabling waveform denoising and parameter estimation within a common framework. Using controlled model waveforms constructed as finite sums of Kerr QNMs with recently established high-precision frequencies and excitation factors, including their nontrivial spin dependence near resonant excitation, we assess the method across partitioned spin intervals. The model achieves good in-domain waveform reconstruction and parameter recovery for the two longest-lived components of eight-component input waveforms, while its performance degrades when the validation spins lie far outside the training range. In a selected spin interval, the framework also recovers the 32 parameters of an eight-component waveform with good overall agreement. These results demonstrate the feasibility of physics-informed autoencoder-based inference for a prescribed multi-component ringdown waveform family and motivate further tests with progressively more realistic signals.
Figures & tables
Figure 1: Analysis flow and autoencoder architecture.
Spin range ( a/M )
Training samples
Validation samples
[0.0,0.15]
6,000
1,500
[0.10,0.60]
20,000
5,000
[0.55,0.80]
10,000
2,500
[0.75,0.95]
8,000
2,000
[0.92,0.98]
4,800
1,200
[0.975,0.998]
8,000
2,000
Table 1: Same-spin-range configuration: ranges of spin parameter a/M and numbers of training and validation samples.
Training spin range ( a/M )
Validation spin range ( a/M )
Training samples
Validation samples
[0.1,0.6]
[0.55,0.8]
25,000
2,000
[0.75,0.95]
[0.0,0.15]
15,000
2,000
Table 2: Different-spin-range configuration: ranges of spin parameter a/M and numbers of training and validation samples.
Figure 2: Characteristic behavior of B in the spin interval 0.0–0.15
Spin range ( a/M )
Match score
n
Re (Bn) (abs.)
Im (Bn) (abs.)
Re (ωn) [rad/s] (rel.)
Im (ωn) [rad/s] (rel.)
[0.0,0.15]
0.999±1.6×10−3
0
3.6×10−23±2.8×10−23
5.8×10−24±5.1×10−24
−5.6×10−4±1.4×10−2
9.7×10−5±1.3×10−3
1
1.6×10−22±1.3×10−22
1.4×10−23±1.4×10−23
−6.3×10−4±1.7×10−2
1.4×10−4±2.3×10−3
[0.10,0.60]
0.999±1.1×10−3
0
1.5×10−23±1.5×10−23
3.0×10−23±3.3×10−23
1.1×10−3±5.9×10−3
−2.4×10−4±1.5×10−3
1
7.2×10−23±7.2×10−23
2.0×10−22±2.2×10−22
1.2×10−3±6.8×10−3
−3.0×10−4±1.8×10−3
[0.55,0.80]
0.999±1.9×10−3
0
6.1×10−23±5.9×10−23
3.5×10−23±3.2×10−23
3.4×10−4±4.0×10−3
−2.1×10−4±2.4×10−3
1
5.2×10−22±5.0×10−22
1.3×10−22±1.2×10−22
3.7×10−4±4.3×10−3
−2.2×10−4±2.5×10−3
Table 3: Same-spin-range configuration: mean values and standard deviations of the match score, relative errors ( Re(ωn),Im(ωn) ), and absolute errors ( Re(Bn),Im(Bn) ) in the validation data.
Figure 3: Resonance around a spin of 0.9.
Figure 4: Validation results for spins in the range 0.0–0.15. (a) Top: input waveform; Bottom: output waveform (Denoised) and original waveform (Original) (b) Parameters and match score (c) Relationship between match score and spin parameter (d) Distributions of true and estimated parameters (e) Relationship between parameter estimation errors and true values.
Figure 5: Validation results for spins in the range 0.1–0.6.
Figure 6: Validation results for spins in the range 0.55–0.8.
Figure 7: Validation results for spins in the range 0.75–0.95.
Figure 8: Validation results for spins in the range 0.92–0.98.
Figure 9: Validation results for spins in the range 0.975–0.998.
Figure 10: Validation results for spins in the range 0.995–max.
Figure 11: Different-spin-range configuration with training on spins 0.1–0.6 and validation on spins 0.55–0.8.
Figure 12: Different-spin-range configuration with training on spins 0.75–0.95 and validation on spins 0.0–0.15.
Figure 13: Relationship between spin and the peak amplitude of the standardized input data used for training.
Figure 17
Figure 17: Comparison between the distributions of the true parameters (gray) and the estimated parameters for all 32 parameters.
Figure 18: Parameter-estimation errors for the 32 inferred parameters. The absolute errors are shown for the excitation factors, and the relative errors are shown for the QNM frequencies.
The worldwide network of gravitational-wave detectors have detected more than 350 binary coalescence events till date. Future third-generation detectors, like Einstein telescope, are expected to detect orders-of-magnitude more signals from sources with more complicated characteristics, including eccentric orbits and high-mass ratio binaries. It is well-established that the computational cost of parameter estimation for signals from these kinds of sources will be extremely high. In particular, the process could be sped-up if generating theoretical waveform predictions, used for likelihood calculation becomes faster. Recently, various machine-learning techniques has been proposed to this end. In this work, we propose a two-stage deterministic conditional-autoencoder model for generating four-parameter SEOBNRv4 waveforms. The first-stage of the model generates amplitude and phase series of the waveform, while the second-stage calibrates the residual error in the predictions. Our model achieves a median mismatch of around 10−2 with the target polarization waveforms, while the calibrated amplitude/phase series achieve 10−6 level cosine distance error. We then propose a waveform conditioning step to enable use of these surrogate waveforms for downstream parameter estimation tasks. Finally, we perform extensive parameter estimation tests, with ML and EOB waveform injections and try to recover posterior estimates for the source parameters. We find that when ML waveforms are used to recover EOB target parameter estimates, the inferred posterior have some systematic bias. This inherent bias can be estimated and corrected for, and then importance reweighting of posterior samples can enable use of low-accuracy surrogate waveforms at low SNRs.
Suyog Garg, Kipp Cannon
Research Center for Early Universe, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033 JAPAN
Damped sinusoidal oscillations are widely observed in many physical systems, and their analysis provides access to underlying physical properties. However, parameter estimation becomes difficult when the signal decays rapidly, multiple components are superposed, and observational noise is present. In this study, we develop an autoencoder-based method that uses the latent space to estimate the frequency, phase, decay time, and amplitude of each component in noisy multi-component damped sinusoidal signals. We investigate multi-component cases under Gaussian-distribution training and further examine the effect of the training-data distribution through comparisons between Gaussian and uniform training. The performance is evaluated through waveform reconstruction and parameter-estimation accuracy. We find that the proposed method can estimate the parameters with high accuracy even in challenging setups, such as those involving a subdominant component or nearly opposite-phase components, while remaining reasonably robust when the training distribution is less informative. This demonstrates its potential as a tool for analyzing short-duration, noisy signals.
Momoka Iida, Hayato Motohashi, Hirotaka Takahashi
Graduate School of Integrative Science and Engineering, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan · Research Center for Space Science, Advanced Research Laboratories, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan · Department of Physics, Graduate School of Science, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397, Japan +2
Gravitational-wave denoising must handle the full diversity of spinning, precessing binaries, since the recovered waveform underpins parameter estimation, tests of general relativity, and population studies. Matched filtering achieves this at a cost that becomes prohibitive as next-generation detectors push event rates higher; deep learning offers real-time reconstruction, but current methods are developed on narrow parameter spaces, precluding principled comparison and reliable deployment. We present the first controlled comparison of five neural-network architectures for gravitational-wave denoising, trained identically across the full astrophysically-motivated spinning binary-black-hole parameter space. A unifying principle emerges: matching network structure to the spectral anatomy of a coalescence -- inspiral, merger, ringdown -- outperforms brute-force model scaling. Our Multi-Scale Frequency-Aware architecture embodies this via dedicated parallel branches per frequency regime, achieving the best fidelity while using fewer parameters than larger models. It generalizes from simulated training to real LIGO-Virgo-KAGRA data without retraining, recovering merger morphology across confirmed events spanning three observing runs and both detectors, despite training on a single detector's simulated noise. We construct population-level uncertainty bands from denoising residuals, validate their calibration, and stress-test the framework on extended mass ratios and a spin population resembling hierarchical-merger remnants. Applied to real noise with no known signal, the network suppresses its output almost everywhere, with rare exceptions traced to noise transients rather than a general weakness -- indicating the statistic discriminates signal from noise and motivating a future detection study. Released weights give a deployable, reproducible benchmark for future extensions.
Rohan Raha, Prayush Kumar
Department of Physics, Indian Institute of Science, Bangalore 560012, Karnataka, India · International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India