Survey of Novel Deep Learning Architectures for Denoising Gravitational-wave Signals

Rohan Raha; Prayush Kumar

gr-qcSep 7, 2026

Survey of Novel Deep Learning Architectures for Denoising Gravitational-wave Signals

Authors: Rohan Raha, Prayush Kumar

Organizations: Department of Physics, Indian Institute of Science, Bangalore 560012, Karnataka, India · International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India

Abstract

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.

Figures & tables

Architecture	Parameters	Layers	Key Components	Receptive Field	Attention	Training Time
LSTM	242,657	10	4 LSTM (128,64 $\to$ 64,128)	Global	No	1.0 $\times$
Encoder-Decoder			+ Dense bottleneck (32)	(recurrent memory)		(baseline)
			+ LayerNorm + Dropout
CNN-LSTM	26,470,737	34	8 Conv1D (k: 512 $\to$ 48)	512 samples	No	8 $\times$
Hybrid			+ 4 LSTM layers	( $\sim$ 125 ms)
			+ BatchNorm (16 $\times$ )

Table 1: Comprehensive comparison of neural network architectures for gravitational wave denoising. All models process input sequences of length

T=8192

samples (2 seconds at 4096 Hz sampling rate). Training time is relative to the baseline LSTM encoder-decoder. The receptive field indicates the maximum temporal span that can influence a single output time step.

Noise fraction	$\mathcal{L}^{*}_{\rm val}$	$e^{*}$	$e_{\rm total}$
$0\%$	$5.68\times 10^{-3}$	10	15
$30\%$	$3.91\times 10^{-3}$	20	25
$50\%$	$4.01\times 10^{-3}$	5	10

Table 2: Training convergence statistics for the baseline LSTM encoder-decoder trained with three pure noise augmentation fractions.

\mathcal{L}^{*}_{\rm val}

is the best validation MSE across all training epochs;

e^{*}

is the epoch at which it was achieved;

e_{\rm total}

is the total number of epochs completed before early stopping.

Figure 1: Training (solid) and validation (dashed) MSE loss curves for the baseline LSTM encoder-decoder trained with three pure noise fractions: $0\%$ (blue), $30\%$ (orange), and $50\%$ (green). All models employ identical optimizer configuration, early stopping patience of 5 epochs, and the same training dataset described in Section Appendix A .

Figure 2: Training (solid) and validation (dashed) MSE loss curves for all five architectures, each trained with $30\%$ pure noise augmentation. Ranked by final validation MSE (lower is better), the hierarchy from worst to best is: LSTM $>$ CNN-LSTM $>$ ACRED-Net $>$ U-Net $>$ Multi-Frequency, with Multi-Frequency achieving the lowest best validation MSE of $1.15\times 10^{-3}$ .

Architecture	Parameters	$\mathcal{L}^{*}_{\rm val}$	$e^{*}$	$e_{\rm total}$
LSTM ED	243K	$3.91\times 10^{-3}$	20	25
CNN-LSTM	26.5M	$1.91\times 10^{-3}$	26	31
ACRED-Net	22.0M	$1.37\times 10^{-3}$	35	40
U-Net	172M	$1.26\times 10^{-3}$	36	41
Multi-Frequency	59.1M	$1.15\times 10^{-3}$	$24$	$29$

Table 3: Training convergence statistics for all neural network architectures trained with

30\%

pure noise augmentation.

\mathcal{L}^{*}_{\rm val}

is the best validation MSE across all training epochs;

e^{*}

is the epoch at which it was achieved;

E_{\rm total}

is the total epochs completed before early stopping.

Figure 3: Cumulative Pearson correlation $r$ (top panels) and noise-weighted mismatch $1-\mathcal{M}$ (bottom panels, logarithmic scale) as a function of time relative to merger for all five architectures, evaluated over a growing sub-window starting at $t=-0.9$ s. The vertical red dashed line marks merger at $t=0$ . Metrics are computed on the same test signals as Figure 4 , all at $\mathrm{SNR}\approx 20$ . Lower mismatch and higher correlation both indicate better reconstruction. Colors follow the legend at top: LSTM (blue), CNN-LSTM (orange), ACRED (green), U-Net (red), Multi-Frequency (purple). The Multi-Frequency and ACRED architectures maintain the lowest mismatch throughout all three configurations. The LSTM baseline exhibits the highest mismatch across all cases. The most distinctive architectural failure is visible in the precessing spin case, where CNN-LSTM shows a sharp correlation drop and mismatch spike during the mid-inspiral, a feature absent for the other four architectures.

Figure 4: Denoised waveform outputs from the Multi-Frequency architecture for representative test signals at $\mathrm{SNR}\approx 20$ , spanning the three spin configurations in our dataset, augmented with population-level uncertainty bands. Each column contains three panels: the top panel shows the whitened noisy input (light blue) with the whitened clean signal (orange) embedded; the middle panel overlays the denoised output (dark blue) on the clean target (orange dashed); the bottom panel shows the residual $r(t)=\hat{h}(t)-h(t)$ (green) on a symmetric logarithmic scale, together with the population $1\sigma$ and $2\sigma$ bands (shaded) centered on zero. The $1\sigma$ and $2\sigma$ bands are broad enough to encompass the raw residual. The vertical red dashed line marks merger at $t=0$ . Source parameters, $\mathrm{MSE}_{\rm norm}$ , and Pearson correlation $r$ for each example are annotated in the top panel. The population bands are constructed independently of these three specific examples, from the per-time-sample residual distribution of an $N=100$ -per-category evaluation ensemble held at fixed $\mathrm{SNR}=20$ ; their statistical calibration is validated in Section 3.5 .

Figure 5: Probability-probability (P-P) calibration diagnostic for the population-level uncertainty bands of Figure 4 . For each spin category, an evaluation ensemble of $N=100$ signals — held out from, and distinct from, the calibration ensemble used to construct the bands in Section 3.4 — is denoised, and at each time sample within the $[-0.9,+0.1]$ s merger window the residual is converted to an empirical probability-integral-transform (PIT) value against the calibration-set residual distribution at that time sample. The pooled empirical coverage $Y(p)$ is shown for each spin category individually (blue: non-spinning; green: aligned-spin; purple: precessing-spin) and for all three categories combined (black, $n=300$ ), plotted against the nominal coverage $p$ ; perfect calibration corresponds to the diagonal (black dashed). The grey shaded region shows the exact $1/2/3\sigma$ sampling-fluctuation band expected under perfect calibration, computed from the binomial distribution with $n=300$ independent trials (one per signal, pooled across all three spin categories, since time samples within a single waveform are highly correlated and cannot be treated as independent draws). All pooled curves lie close to the diagonal and within the shown sampling band, indicating that the population uncertainty bands are, in aggregate, statistically well calibrated across all three spin categories.

Figure 6: Population-level performance of the Multi-Frequency architecture on $N=100$ test injections per category (500 total across five categories). Categories are distinguished by marker shape and color: non-spinning (circles, blue), aligned-spin (triangles, red), precessing-spin (squares, green), extreme mass-ratio $q>6$ (stars, purple, OOS), and Gaussian aligned-spin $\chi\sim\mathcal{N}(0.67,0.1)$ (crosses, orange, OOD). Top panel: SNR distribution for each category, shown as normalized step histograms on a logarithmic vertical axis. The bulk of injections fall in $5\lesssim\mathrm{SNR}\lesssim 70$ for all five categories, consistent with the shared cosmologically weighted distance sampling. Middle left: $\mathrm{MSE}_{\rm norm}$ versus optimal SNR, colored by luminosity distance $d_{L}$ . The side histogram shows the normalized $\mathrm{MSE}_{\rm norm}$ distribution per category. Middle right: Total mass $M_{\rm tot}$ versus SNR, colored by $\mathrm{MSE}_{\rm norm}$ . At fixed SNR, higher-mass systems achieve lower MSE across all five categories. Bottom left: Mismatch versus SNR, colored by chirp mass $\mathcal{M}_{c}$ . The side histogram shows the normalized mismatch distribution per category. Bottom right: Total mass versus SNR, colored by Mismatch . The two out-of-distribution categories broadly track the trained-distribution trend of decreasing error with SNR and total mass, with a modest systematic offset toward higher $\mathrm{MSE}_{\rm norm}$ and Mismatch at fixed SNR, quantified in Tables 4 and 5 .

	Non-spinning		Aligned-spin		Precessing-spin
	$\mathrm{MSE}_{\rm norm}$	Mismatch	$\mathrm{MSE}_{\rm norm}$	Mismatch	$\mathrm{MSE}_{\rm norm}$	Mismatch
Mean	0.070	0.02851	0.112	0.05009	0.141	0.05024
Median	0.020	0.00603	0.024	0.00677	0.025	0.00857
Std	0.169	0.09974	0.236	0.14007	0.425	0.14484
$\textit{Mismatch}<0.01$	–	64%	–	62%	–	55%
$\textit{Mismatch}<0.03$	–	90%	–	80%	–	81%

Table 4: Population-level performance statistics for the Multi-Frequency architecture (

N=100

per spin category). Metrics are computed over the

[-0.9,+0.1]

s evaluation window. SNR bins are defined as low (

5\leq\mathrm{SNR}<15

), mid (

15\leq\mathrm{SNR}<30

), and high (

30\leq\mathrm{SNR}\leq 80

). Percentages give the fraction of events in each category satisfying the quoted mismatch threshold.

	Extreme mass ratio, $q>6$ (OOS)		Gaussian aligned-spin (OOD)
	$\mathrm{MSE}_{\rm norm}$	Mismatch	$\mathrm{MSE}_{\rm norm}$	Mismatch
Mean	0.246	0.0608	0.126	0.0527
Median	0.049	0.0152	0.023	0.0083
Std	0.923	0.1481	0.245	0.1200
$\textit{Mismatch}<0.01$	–	36%	–	52%
$\textit{Mismatch}<0.03$	–	72%	–	76%

Table 5: Population-level performance statistics for the two out-of-distribution validation sets (

N=100

each), evaluated over the

[-0.9,+0.1]

s window using the same metrics and SNR binning as Table 4 . Extreme mass ratio extrapolates beyond the trained mass-ratio range (

q>6

, out-of-support, “OOS”); Gaussian aligned-spin draws component spins from

\chi\sim\mathcal{N}(0.67,0.1)

(hierarchical-merger-remnant-like), a distribution shape not seen in training even though individual spin magnitudes remain within the trained bound (“OOD”).

Figure 7: Cumulative mismatch distribution for the Multi-Frequency architecture across all five categories ( $N=100$ each): non-spinning (blue), aligned-spin (red), precessing-spin (green), extreme mass-ratio $q>6$ (purple, OOS), and Gaussian aligned-spin $\chi\sim\mathcal{N}(0.67,0.1)$ (orange, OOD). The x-axis shows mismatch $1-\mathcal{O}$ on a logarithmic scale. Dotted vertical lines mark the median mismatch for each category; shaded bands span the 16th–84th percentile range. Non-spinning (median $1-\mathcal{O}=0.0054$ ) and aligned-spin (median $0.0055$ ) distributions are nearly indistinguishable, precessing-spin (median $0.0119$ ) shows the modest rightward shift already seen in the three-category comparison, and the two OOS and OOD categories are shifted further still: extreme mass-ratio (OOS, median $0.0152$ ) is the most degraded of all five, while Gaussian aligned-spin (OOD, median $0.0083$ ) falls between the aligned-spin and precessing-spin distributions.

Panel of Figure 8 — Figure 8: Denoised outputs from the Multi-Frequency architecture applied to real LIGO strain data for three binary black hole events spanning three observing runs. Each subfigure shows H1 (top) and L1 (bottom) data. In each panel: LIGO open data after whitening and bandpass filtering (blue), a posterior-ensemble 90% credible-interval band centered on the maximum-likelihood waveform template (grey shading; cf. Fig. 6 of [ 5 ] for the analogous construction applied to GW150914 itself), and the model denoised output (red). The vertical dashed line marks the merger at $t=0$ . The displayed window ( $[-0.1,+0.01]$ s) captures the high-signal-power region near merger; the full 2-second preprocessed segment was used as model input. Metrics in each panel are computed over the $[-0.1,+0.01]$ s window and compared against the maximum-likelihood template.

Event	Run	$m_{1}$	$m_{2}$	$\mathcal{M}_{c}$	$\chi_{\rm eff}$	$d_{L}$	$\rho_{\rm net}$	$f_{\rm merger}$	Waveform	$r_{\rm H1}$	$r_{\rm L1}$	$\mathrm{MSE}_{\rm H1}$ / $\mathrm{MSE}_{\rm L1}$
		$(M_{\odot})$	$(M_{\odot})$	$(M_{\odot})$		(Mpc)		(Hz)
GW150914	O1	38.22	32.21	30.42	$-0.056$	456	26.0	469	IMRPhenomPv2	0.976	0.977	0.069 / 0.073
GW200129 a	O3b	43.83	31.61	31.90	$+0.108$	952	26.8	437	IMRPhenomXPHM	0.982	0.972	0.087 / 0.073
GW231226	O4	48.24	42.46	39.31	$-0.122$	1136	34.7	364	IMRPhenomXPHM	0.951	0.953	0.122 / 0.111

Table 6: Source parameters and denoising metrics for the three real gravitational wave events. Source parameters are maximum-likelihood estimates from the PE data release posteriors, used for template generation.

\mathcal{M}_{c}

is the chirp mass,

q=m_{2}/m_{1}\leq 1

is the mass ratio,

\rho_{\rm net}

is the network SNR, and

f_{\rm merger}

is the approximate merger frequency estimated as

f_{\rm merger}\approx 1.5\times 220\,(100\,M_{\odot}/M_{\rm tot})

Hz. Pearson correlation

r

and energy-normalized MSE against the maximum likelihood template are evaluated over the

[-0.1,+0.01]

s window around merger. The waveform column gives the approximant used for maximum-likelihood template generation.

Figure 9: Median power spectral density of the whitened input (gray) and network output (crimson), computed over the $[-1.0,0.0]$ s analysis window across all $43{,}083$ real H1 noise-only background segments. Shaded bands span the 16th–84th percentile across segments. The output PSD lies orders of magnitude below the input across the entire analysis band, with a maximum output/input ratio of $0.007$ at $1.0$ Hz and no frequency bin exceeding a factor of 3, confirming near-total suppression on real, stationary detector noise.

Figure 10: Whitened network output (solid) for five randomly selected real H1 noise-only background segments (dashed traces show the corresponding whitened input), overlaid on the population $1\sigma$ band from the SNR $=20$ calibration (Section 3.4 ). All five outputs remain suppressed within or below the calibration band throughout the $[-1.0,0.0]$ s analysis window, representative of the network’s behavior on the bulk of the real noise-only background.

Figure 11: Distribution of $\rho_{\rm out}$ for the real H1 noise-only background (gray, $N=43{,}083$ ) and for the stratified SNR $=10$ – $30$ injected signal population (colored, $N=1000$ per spin category), both evaluated over the $[-1.0,0.0]$ s analysis window. The noise-only distribution is sharply peaked near zero with a long non-Gaussian tail populated by glitches; the signal population clusters around $\rho_{\rm out}\sim 16.7$ – $17.2$ , overlapping the background only in that glitch-driven tail. This is a single-detector (H1) characterization with no coincidence testing against a second interferometer to suppress glitches, unlike an operational search.

$\eta$	FAR (Hz)	FAR (/day)	Eff. nons.	Eff. align.	Eff. prec.
0.1	$3.40\times 10^{-1}$	$2.94\times 10^{4}$	100.0%	100.0%	100.0%
1	$9.58\times 10^{-2}$	$8.28\times 10^{3}$	100.0%	100.0%	99.9%
4	$1.16\times 10^{-2}$	$1.00\times 10^{3}$	100.0%	100.0%	99.8%
6	$3.78\times 10^{-3}$	$3.27\times 10^{2}$	100.0%	99.8%	99.6%
8	$2.44\times 10^{-3}$	$2.11\times 10^{2}$	97.9%	97.6%	97.2%
10	$1.93\times 10^{-3}$	$1.66\times 10^{2}$	90.3%	89.7%	88.5%

Table 7: False-alarm rate (from

11.97

hr of real H1 noise-only background) and per-category recovery efficiency (from the stratified SNR

=10

–

30

injected population,

N=1000

per category) as a function of threshold

\eta

\rho_{\rm out}

Figure 12: Left: false-alarm rate as a function of threshold $\eta$ on $\rho_{\rm out}$ , computed from $11.97$ hr of real H1 noise-only background. Right: recovery efficiency (fraction of injected signals with $\rho_{\rm out}\geq\eta$ ) as a function of the corresponding FAR, for the stratified SNR $=10$ – $30$ injected population, per spin category. Efficiency remains near $100\%$ for FAR $\gtrsim 3\times 10^{-3}$ Hz and falls off as the threshold is pushed further into the glitch-populated tail of the background distribution.

Appendix figures & tables18 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 13: Compositional breakdown of both training and testing datasets ( $N=20{,}000$ waveforms each). The three waveform categories are: Precessing-spin systems (red, 50%) with generic 3D spin orientations and $\chi_{p}>0$ ; Aligned-spin systems (green, 25%) with spins parallel or anti-parallel to the orbital angular momentum ( $s_{1x}=s_{1y}=s_{2x}=s_{2y}=0$ ); and Non-spinning systems (blue, 25%) with $|\vec{s}_{1}|=|\vec{s}_{2}|=0$ .

Figure 14: Mass parameter distributions for training (blue) and testing (orange) datasets. Component mass distribution in the $(m_{1},m_{2})$ plane, with $m_{1,2}\in[5,100]\,M_{\odot}$ . The color scale reflects the number of waveforms per bin; the higher density near equal-mass systems arises from uniform sampling in $\eta$ rather than $(m_{1},m_{2})$ space. Overlapping contours in all panels confirm identical and unbiased parameter sampling across datasets.

Figure 15: Spin parameter distributions for training and testing datasets. Left: Effective spin $\chi_{\rm eff}$ (top, logarithmic scale) spanning $[-1,1]$ for all 20000 samples, peaking near zero due to presence of non-spinning samples. Precessing spin $\chi_{p}$ (bottom) for only 10000 precessing samples, peaking at $\chi_{p}\sim 0.3$ – $0.7$ with values bounded below unity, since the suppression factor $q(4+3q)/(3+4q)$ (reaching ${\sim}0.2$ at $q=1/6$ ) reduces the secondary spin contribution at extreme mass ratios. Middle: The 2D $(\chi_{\rm eff},\chi_{p})$ panel shows non-spinning (blue, $N=5000$ ) systems clustered at the origin, aligned-spin (green, $N=5000$ ) along $\chi_{p}=0$ , and precessing (red, $N=10{,}000$ ) spanning the full plane including $\chi_{p}>1$ at high $q$ . Right: In-plane spin components $(s_{1x},s_{1y})$ (top) and $(s_{2x},s_{2y})$ (bottom) for only 10000 precessing systems, confirming isotropic azimuthal coverage within $|\vec{s}|\leq 0.99$ (black dashed circle). The mild central concentration reflects uniform magnitude sampling combined with isotropic direction sampling. Together, these confirm comprehensive and unbiased coverage of the BBH spin parameter space.

Figure 16: Representative waveforms demonstrating morphological diversity across spin configurations and mass ratios for binary black hole systems with total mass $M_{\text{tot}}=70\,M_{\odot}$ , generated with $f_{\text{lower}}=20$ Hz for visualization purposes. Each panel shows the detector strain $h(t)$ at H1 (solid black), along with the plus polarization $h_{+}$ (blue) and cross polarization $h_{\times}$ (red) overlaid as fainter lines. Top row: Non-spinning systems ( $\chi_{\text{eff}}=0.000$ , $\chi_{p}=0.000$ ) for equal-mass ( $q=1$ , $m_{1}=m_{2}=35\,M_{\odot}$ , left) and high mass-ratio ( $q=1/6$ , $m_{1}=60\,M_{\odot}$ , $m_{2}=10\,M_{\odot}$ , right) configurations, generated with SEOBNRv4_opt . Bottom row: High mass-ratio systems ( $q=1/6$ ) with aligned-spin configuration (left; $\chi_{\text{eff}}=0.529$ , $\chi_{p}=0.000$ , SEOBNRv4_opt ) and precessing-spin configuration (right; $\chi_{\text{eff}}=0.529$ , $\chi_{p}=0.860$ , SEOBNRv4P ). The vertical red dashed line marks merger at $t=0$ s. High mass-ratio systems produce shorter observable waveforms compared to equal-mass systems due to faster inspiral evolution. In the precessing system (bottom right), amplitude modulations from orbital plane precession are imprinted distinctly on each polarization, with $h_{+}$ and $h_{\times}$ dephasing visibly relative to one another. These illustrative waveforms highlight the morphological diversity — across mass ratio, spin magnitude, and spin orientation — that motivates comprehensive parameter space coverage in our training dataset.

Configuration	$m_{1}$	$m_{2}$	$\mathcal{M}$	$M$	$q$	$\chi_{\text{eff}}$	$\chi_{p}$	Cycles	Max Amp.	$\tau_{\text{pre}}$
	$(M_{\odot})$	$(M_{\odot})$	$(M_{\odot})$	$(M_{\odot})$				(pre / post)	$(10^{-21})$	(s)
Non-spinning, $q=1$	35	35	30.47	70	1.0	$0.00$	$0.00$	$46.0$ / $27.0$	$3.34$	$2.62$
Non-spinning, $q=6$	60	10	19.86	70	6.0	$0.00$	$0.00$	$102.5$ / $24.5$	$1.50$	$6.96$
Aligned spin, $q=6$	60	10	19.86	70	6.0	$0.53$	$0.00$	$116.5$ / $27.0$	$1.56$	$7.93$
Precessing spin, $q=6$	60	10	19.86	70	6.0	$0.53$	$0.86$	$119.0$ / $41.5$	$1.44$	$8.03$

Appendix

Table 8: Quantitative characteristics of representative BBH waveforms shown in Figure 16 . All waveforms have total mass

M_{\text{tot}}=70\,M_{\odot}

and are generated with

f_{\text{lower}}=20

Hz. Amplitudes are computed at a fiducial distance of 1 Mpc. Cycle counts are determined by zero-crossing analysis: pre-merger cycles counted from

t=0

t=1.9

s, post-merger cycles from

t=1.9

s to

t=2.0

s. The pre-merger duration

\tau_{\text{pre}}

is measured from

f_{\text{lower}}

to merger.

Figure 17: Representative 2-second time series of simulated aLIGO detector noise. The stochastic fluctuations reflect the colored Gaussian noise characteristics prescribed by the aLIGO Zero-Detuned High Power PSD, with amplitude consistent with strain sensitivity at design configuration ( $h\sim 10^{-23}$ – $10^{-22}$ ).

Figure 18: Statistical validation of 50000 simulated noise realizations. Ensemble-averaged power spectral density validation. The empirical PSD computed from the noise realizations (blue solid line) closely matches the target aLIGO Zero-Detuned High Power PSD (red dashed line), confirming accurate reproduction of the desired noise characteristics across the observable frequency band from 10 Hz to 2 kHz.

Figure 19: Frequency-domain representation after PSD-based whitening according to Equation ( 21 ). The colored noise spectrum (red) has been transformed into approximately unit-variance white noise across the observable band, while the clean signal spectrum (blue) exhibits enhanced power at frequencies where the detector has reduced sensitivity. Whitening equalizes the statistical properties of noise fluctuations, enabling the neural network to treat all frequencies on equal footing.

Figure 20: Final preprocessed signals after standard deviation normalization according to Equation ( 23 ). Both the noisy input (red) and clean target (blue) have been scaled to unit variance, with typical amplitude fluctuations now centered around $\pm 1$ in dimensionless normalized units. This normalized time series serves as the direct input to the denoising neural network, with the noisy signal provided as the model input and the clean signal as the target output for supervised learning.

Figure 21: Corner plot showing the joint and marginal distributions of redshift and optimal SNR for the training (blue) and testing (red) datasets. Top left: Marginal redshift distribution, spanning $z\sim 0$ – $0.2$ , consistent with our luminosity distance upper limit of 1000 Mpc under Planck18 cosmology. Bottom left: Joint KDE density in the redshift–SNR plane; contours mark the 10th–90th percentiles of the estimated density, computed in $(z,\,\log_{10}\,\mathrm{SNR})$ space to avoid distortion on the logarithmic SNR axis. Bottom right: Marginal SNR distribution on a log–log scale. Dark-coloured overflow bars indicate samples with $\mathrm{SNR}>100$ , representing a small fraction of nearby, high-mass or favourably oriented systems. Training and testing distributions are consistent across all panels, confirming unbiased dataset splitting.

Panel of Figure 22 — Figure 22: Two-dimensional histograms showing joint distributions for the training dataset, with color scales indicating event density in each bin. (a) Joint distribution of optimal SNR and luminosity distance $d_{L}$ . The expected inverse SNR–distance relationship is clearly visible, with the vertical banding reflecting discrete sampling of the luminosity distance array. The logarithmic vertical scale for SNR spans three orders of magnitude from $\text{SNR}\sim 0.1$ to $\text{SNR}\sim 100$ . (b) Joint distribution of chirp mass $\mathcal{M}_{c}$ and luminosity distance. Coverage is relatively uniform across $\mathcal{M}\sim 10$ – $80\,M_{\odot}$ at all distances, with a mild concentration at $\mathcal{M}\sim 20$ – $40\,M_{\odot}$ arising from the convolution of uniform- $\eta$ sampling with the component mass constraints. Consistent distributions between training and testing datasets confirm unbiased sampling across both mass and distance parameters.

Figure 23: Schematic diagram of the baseline LSTM encoder-decoder architecture. The encoder comprises two stacked LSTM layers (128 and 64 units) that progressively compress the noisy input into a 32-dimensional latent representation via a dense bottleneck. The symmetric decoder mirrors this structure with two LSTM layers (64 and 128 units) that reconstruct the clean waveform. Layer normalization and dropout (rate 0.2) after each LSTM layer ensure training stability and prevent overfitting. The architecture contains approximately 250K trainable parameters.

Figure 24: Schematic diagram of the CNN-LSTM hybrid architecture. The encoder begins with 8 convolutional layers (kernel sizes 512 $\to$ 48, filter counts 128 $\to$ 32) for multi-scale feature extraction, followed by 2 LSTM layers (128 and 64 units) for temporal integration. After a 32-dimensional dense bottleneck, the decoder applies 2 LSTM layers (64 and 128 units) followed by 8 convolutional layers (mirroring the encoder configuration) for hierarchical reconstruction. Batch normalization after each convolution and layer normalization after each LSTM ensure training stability. The architecture contains approximately 26.5M parameters.

Figure 25: Schematic diagram of ACRED-Net, the transformer-based architecture combining convolutional feature extraction, self-attention mechanisms, and recurrent processing. The encoder applies 3 convolutional blocks (filters 256 $\to$ 64, kernels 512 $\to$ 128) followed by sinusoidal positional encoding, multi-head self-attention (1 head, key dimension 4), and 2 bidirectional LSTM layers (256 and 128 units). The decoder begins with positional encoding and self-attention, processes with 1 LSTM layer (256 units), applies cross-attention to encoder outputs, processes with another LSTM layer (128 units), and refines with 3 convolutional blocks (filters 64 $\to$ 256, kernels 512 $\to$ 128). Residual connections and layer normalization stabilize training. The architecture contains approximately 22.0M parameters and operates in float64 precision.

Figure 26: Schematic diagram of the U-Net architecture with attention gates. The encoder path (left, green) comprises 4 blocks of double convolutions (filters 64 $\to$ 512, kernels 512 $\to$ 64) with batch normalization, ReLU activation, and dropout, followed by max-pooling (stride 2) for downsampling. The bottleneck (center, red) applies double convolutions with 512 filters and kernel size 16. The decoder path (right, blue) performs upsampling (stride 2) followed by attention gates (magenta) that weight skip connections from corresponding encoder levels, concatenation, and double convolutions. The attention gates learn to selectively propagate relevant features while suppressing irrelevant encoder activations. The architecture achieves multi-scale feature extraction through progressive downsampling, reducing sequence length from 8192 (input) to 256 (bottleneck) and back to 8192 (output). Total parameters: $\sim$ 172M.

Figure 27: Schematic diagram of the Multi-Frequency architecture. The input is processed by 7 parallel branches: 3 low-frequency branches (left, red/orange/yellow) with large kernels (512, 256, 128) targeting the inspiral band, and 4 high-frequency detail branches (right, green/blue/cyan/yellow) with small kernels (16, 32, 64, 128) capturing merger transients and ringdown. Each branch applies convolution + batch normalization, bidirectional LSTM (128 units), and self-attention (sigmoid gating). The 3 low-frequency branches are concatenated, integrated with a 512-kernel convolution, and combined with the 4 high-frequency branches. Reconstruction proceeds through 3 LSTM layers (bidirectional 512, unidirectional 256 and 128) and a time-distributed dense layer (128 units), concluding with $1\times 1$ convolution. This explicit frequency decomposition enables specialized processing tailored to different spectral components. Total parameters: $\sim$ 59.1M.

Panel of Figure 28 — Figure 28: Representative pure-noise segments from the real H1 background study (Section 4.2 ). Each panel shows the whitened input (gray) and network output (red) over the $[-1.0,0.0]$ s analysis window (top), with spectrograms of the input and output below (shared colorbar). (a,b) Segments near the population median of $\rho_{\rm out}$ ( $\rho_{\rm out}\approx 0.051$ ): the network suppresses the output to a negligible level throughout, the expected behavior on stationary Gaussian noise.

Gravitational-Wave Astronomy

Gravitational-wave astronomy uses ripples in spacetime to detect cosmic events, measure compact objects, and test gravity.

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Dec 2, 2025

Flexible Gravitational-Wave Parameter Estimation with Transformers

Gravitational-wave data analysis relies on accurate and efficient methods to extract physical information from noisy detector signals, yet the increasing rate and complexity of observations represent a growing challenge. Deep learning provides a powerful alternative to traditional inference, but existing neural models typically lack the flexibility to handle variations in data analysis settings. Such variations accommodate imperfect observations or are required for specialized tests, and could include changes in detector configurations, overall frequency ranges, or localized cuts. We introduce a flexible transformer-based architecture paired with a training strategy that enables adaptation to diverse analysis settings at inference time. Applied to parameter estimation, we demonstrate that a single flexible model, called Dingo-T1, can (i) analyze 48 gravitational-wave events from the third LIGO-Virgo-KAGRA Observing Run under a wide range of analysis configurations, (ii) enable systematic studies of how detector and frequency configurations impact inferred posteriors, and (iii) perform inspiral-merger-ringdown consistency tests probing general relativity. Dingo-T1 also improves median sample efficiency on real events from a baseline of 1.4% to 4.2%. Our approach thus demonstrates flexible and scalable inference with a principled framework for handling missing or incomplete data, key capabilities for current and next-generation observatories.

Annalena Kofler, Maximilian Dax, Stephen R. Green +6

Max Planck Institute for Intelligent Systems, Max-Planck-Ring 4, 72076 Tübingen, Germany · ELLIS Institute Tübingen, Maria-von-Linden-Straße 2, 72076 Tübingen, Germany · Tübingen AI Center, Maria-von-Linden-Straße 1, 72076 Tübingen, Germany +4

Transformer Inference Gravitational-Wave Astronomy Bayesian Inference Inverse Problems

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Jun 11, 2026

Binary Black Hole Parameter Estimation with Hybrid CNN-Transformer Neural Networks

The detection of gravitational waves has revolutionized our ability to explore fundamental aspects of the Universe. Traditionally, modeled gravitational-wave signals have been identified using template-based matched filtering, followed by coincidence analysis across multiple detectors in the signal-to-noise ratio time series. Recent advances in Machine Learning and Deep Learning have sparked growing interest in their application to both signal detection and parameter estimation. In this study, a hybrid Deep Learning strategy is proposed that leverages the effectiveness of Transformer encoders alongside well-established Convolutional Neural Network architectures in an attempt to estimate the intrinsic and extrinsic parameters of non-precessing binary black hole systems. The primary focus of this work is point estimation, producing single best-fit values for each parameter rather than full posterior distributions. This method is evaluated on both simulated signals embedded in Gaussian noise and real gravitational-wave events, and it demonstrates strong predictive performance and robustness across key astrophysical parameters.

Panagiotis N. Sakellariou, Spiros V. Georgakopoulos, Sotiris Tasoulis +1

Department of Mathematics, University of Thessaly, 3rd km. Old National Road Lamia-Athens, Lamia, 35100, Greece · Department of Computer Science and Biomedical Informatics, University of Thessaly, 35100, Greece

Gravitational-Wave Astronomy Hybrid CNN-Transformer Architectures

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May 4, 2026

Testing General Relativity Through Gravitational Wave Classification: A Convolutional Neural Network Framework

We present a machine learning framework for testing general relativity (GR) with gravitational wave signals from binary black hole mergers. Using the source parameters of 173 BBH events from the GWTC catalog as a realistic astrophysical population, we generate simulated GR waveforms and construct beyond GR (BGR) waveforms by applying controlled phase deformations. We introduce a response function formalism that provides a systematic framework for quantifying how any observable responds to modifications of GR. We train convolutional neural networks (CNNs) on two input representations: whitened waveforms and a response function type observable derived from the waveform mismatch, which isolates the effect of phase deviations from the bulk signal. Using response functions as the CNN input improves the classification sensitivity by a factor of approximately 33 compared to whitened waveforms, demonstrating that the choice of observable representation is as important as the classifier architecture. We study the fundamental limits of this classification through Bayes optimal error analysis, averaging methods that reveal coherent patterns hidden in noise, and a comparison between CNN accuracy and a single feature classifier as a proxy for human performance. At all deformation scales, the CNN outperforms the best single feature approach. We extend the framework to physically motivated theories using the parameterized post Einsteinian (ppE) formalism and apply it to massive gravity, where the classifier detects deviations for graviton masses of order

m_g \sim 10^{-23}\;\mathrm{eV}/c^2

with aLIGO design sensitivity.

Lavinia Heisenberg, Shayan Hemmatyar, Hector Villarrubia-Rojo

Institute for Theoretical Physics, Heidelberg University, Philosophenweg 16, 69120 Heidelberg, Germany · Departamento de F´ısica Te´orica and IPARCOS, Facultad de Ciencias F´ısicas, Universidad Complutense de Madrid, Plaza de las Ciencias 1, 28040 Madrid, Spain

Gravitational-Wave Astronomy Binary Classification

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Abstract

Gravitational-Wave Astronomy

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Flexible Gravitational-Wave Parameter Estimation with Transformers

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Testing General Relativity Through Gravitational Wave Classification: A Convolutional Neural Network Framework