Generating optimal Gravitational-Wave template banks with metric-preserving autoencoders

TL;DR

This work introduces metric-preserving autoencoders to create low-dimensional latent representations of gravitational-wave waveform phases, enabling uniform grid placement for template banks with fewer templates and improved detection performance. By enforcing distance preservation in the latent space, the authors demonstrate near-flat induced metrics that allow a two-dimensional grid to effectively cover the GW parameter space, outperforming a purely linear SVD baseline and rivaling nonlinear methods like random forests. The approach is validated on GW banks across mass ranges and extended to cosmology through COBRA, where a decoder (and proposed latent-parameter mappings) can efficiently reconstruct power-spectrum-like coefficients from cosmological parameters. The method promises broader utility in GW data analysis and cosmology, with potential Extensions to higher modes, precession, LVK searches, and fast parameter estimation.

Abstract

Matched filtering for signal detection in noisy data requires template banks that capture variation in signal waveforms while minimizing computational cost. Dimensionality reduction of signal waveforms can be important for building efficient template banks. In various domains of physics, dimensionality reduction is very commonly performed using linear methods such as singular value decomposition (SVD). This can, however, introduce redundancies if the signals span curved, nonlinear manifolds in parameter space. Alternatively, autoencoders are a type of neural networks that can be used for non-linear dimensionality reduction. We use a variation of the autoencoder which preserves the metric in its latent space ($g_{ij}^{\text{latent}} \approx g_{ij}^{\text{physical}}$); this enables template banks to be constructed by simply placing a uniform grid in the autoencoder's low-dimensional latent space. We apply our method for creating geometric template banks for gravitational wave searches and show that our banks require fewer dimensions compared to using the SVD basis. Our method can also be useful for other applications requiring dimensionality reduction, such as gravitational waveform modeling, fast parameter estimation and model-independent tests of general relativity. Finally, we discuss extensions to other domains including cosmological parameter estimation, and we show tests of our method in extreme cases of periodic signal manifolds.

Figures (18)

• Figure 1: A schematic giving an overview of our procedure for constructing the template banks using metric-preserving autoencoders.
• Figure 2: We show the first three SVD coefficients $c^A$ obtained from decomposing the phase of gravitational wave signals: $\Psi_{22}({\bm p},f) = \mathrm{arg}[h({\bm p},f)] = \langle\Psi_{22}\rangle(f) + \sum_{A=0}^{\rm few}c^A({\bm p})\Psi^{\rm SVD}_A(f)$ for a range of binary parameters ${\bm p}$. We show the coefficients for Bank $0$ (teal) and Bank $4$ (orange). We clearly see that the coefficients follow a narrow curved hypersurface instead of broadly filling the space. Such curved hypersurfaces cannot be compressed efficiently by linear methods like SVD. We will therefore use non-linear dimensionality reduction methods like autoencoders instead. The left and right panels are different views of the same plot.
• Figure 3: Phase overlap from Eq. \ref{['eq:phase_overlap']} between the validation phases and their different models in the selected banks ${\cal M}\in[2.6,5.3]\,{M_\odot}$ (Bank $0$), ${\cal M}\in[5.8,10.8]\,{M_\odot}$ (Bank $4$) and ${\cal M}\in[28.4,173.5]\,{M_\odot}$ (Bank $12$). The upper left panel shows the phase overlap between the validation phases and their model using only the first $2$ SVD basis vectors. In the autoencoder case (lower panel), we see a much lower fraction have reconstruction error larger than $0.1\%$. We also compare our results with another machine learning algorithm, the random forest [RF] (upper right panel), where we predict the supposedly-redundant higher-order SVD coefficients $(c^2,c^3,\dots c^9)$ from the first two $(c^0,c^1)$Wadekar:2023kym. We see that both the machine learning algorithms allow for using an effectively two-dimensional parameter space and significantly outperform using just the linear SVD method, especially for low-mass banks.
• Figure 4: Similar to Fig. \ref{['fig:GWs_phase_overlap']}, but showing the effectualness of our banks for the full GW waveform instead of just the phase overlap. We again show the performance of the two dimensional SVD model (upper left panel), autoencoder model (lower panel) and the random forest model (upper right panel). The full bars (dotted lines) show the result before (after) grid refinement (i.e., making the template grid finer). See the main text for details regarding the grid employed for constructing templates in the autoencoder latent space. We again see that both the machine learning algorithms allow for using effectively two-dimensional banks and significantly outperform using just the linear SVD method, especially for low-mass banks.
• Figure 5: Scatter plot of the distances in the autoencoder latent space (y-axis) vs. the Euclidean distances in the SVD space (x-axis) for $1\%$ of the pairs of validation points for the three banks discussed in Section \ref{['subsec:autoencoders_GWs']}. We see that the distances are preserved extremely well in this case.