Autoencoder-Based Parameter Estimation for Superposed Multi-Component Damped Sinusoidal Signals

Momoka Iida; Hayato Motohashi; Hirotaka Takahashi

cs.LGApr 5, 2026

Autoencoder-Based Parameter Estimation for Superposed Multi-Component Damped Sinusoidal Signals

Authors: Momoka Iida, Hayato Motohashi, Hirotaka Takahashi

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 ·

Abstract

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.

Figures & tables

Panel of Figure 1 — Figure 1: Schematic overview of the analysis pipeline, including data generation (left) and the autoencoder architecture (middle and right). For illustration, the figure shows the two-component case.

Case	Explanation	#Components	Training	Validation	Noise level (SNR [dB])	Result	Special setting
2G-sub	2.2.1 , Fig. 2 , Table 3	2	G (8,000)	G (2,000)	$1/2~(8.8)$	3.1 , Fig. 8 , Table 10	Subdominant component
2G-opp	2.2.1 , Fig. 3 , Table 4	2	G (8,000)	G (2,000)	$1/2^{3}~(14.3)$	3.1 , Fig. 9 , Table 10	Nearly opposite phases
5G	2.2.2 , Fig. 4 , Table 5	5	G (8,000)	G (2,000)	$5~(-5.2)$	3.2 , Figs. 10 11 , Table 12
1G	2.2.3 , Fig. 5 , Table 6	1	G (4,000)	G (1,000)	$1/2^{3}~(4.6)$	3.3.1 , Figs. 12 , 14 , Table 13
1U	2.2.3 , Fig. 5 , Table 6	1	U (4,000)	G (1,000)	$1/2^{3}~(4.6)$	3.3.1 , Figs. 13 , 14 , Table 13
2G	2.2.4 , Fig. 6 , Table 7	2	G (990,000)	G (10,000)	$1/2^{3}~(15.7)$	3.3.2 , Fig. 15 , Table 14

Table 2: Summary of the cases considered in this study. In the Training and Validation columns, G and U denote Gaussian and uniform parameter distributions, respectively. Numbers in parentheses indicate the numbers of training and validation samples used in each case. The compact descriptive case labels encode the number of components, the training distribution (G or U), and, where applicable, the special setting in the suffix.

Panel of Figure 2 — Figure 2: Case 1 : A two-component waveform including a rapidly decaying, low-amplitude component.

Panel of Figure 3 — Figure 3: 2G-opp : A two-component waveform with nearly opposite phases.

Panel of Figure 4 — Figure 4: 5G : A five-component superposed damped sinusoidal waveform.

Panel of Figure 5 — Figure 5: 1G and 1U : Training and validation parameter distributions for the single-component case.

Panel of Figure 6 — Figure 6: 2G and 2U : Training and validation parameter distributions for the two-component case.

Panel of Figure 7 — Figure 7: 3U : Training and validation parameter distributions for the three-component case.

Case	Learning rate	Encoder epochs	Decoder epochs
2G-sub	0.001	350	200
2G-opp	0.001	500	500
5G	0.005	350	200
1G	0.001	350	400
1U	0.001	350	400
2G	0.0001	250	150

Table 9: Training settings for 2G-sub – 3U .

Panel of Figure 8 — Figure 8: Results for 2G-sub .

Panel of Figure 9 — Figure 9: Results for 2G-opp .

Panel of Figure 10 — Figure 10: Results for 5G .

Panel of Figure 11 — Figure 11: Scatter plots of the match score against each parameter for 5G .

Panel of Figure 12 — Figure 12: Results for 1G .

Panel of Figure 13 — Figure 13: Results for 1U .

Figure 14: Comparison of match scores for 1G (black) and 1U (cyan).

Panel of Figure 15 — Figure 15: Results for 2G .

Panel of Figure 16 — Figure 16: Results for 2U .

Panel of Figure 17 — Figure 17: Results for 3U .

Parameter Estimation

Parameter estimation studies how to infer unknown quantities in statistical, physical, and machine-learning models from observed data.

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Parameter Estimation of Ringdown Quasinormal Modes with Autoencoder

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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

Parameter Estimation Gravitational-Wave Astronomy Physics-Informed ML Denoising Autoencoders

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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.

Abstract

Parameter Estimation

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