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

TL;DR

This work tackles the computational bottleneck of gravitational-wave parameter estimation by introducing a two-stage neural surrogate (DANSur3dq8) for BBH waveforms. The model first learns from large approximant waveform datasets and is then fine-tuned on a small NR waveform set, using PCA-based dimensionality reduction to map three physical parameters to a compact 42-dimensional coefficient space. Results show median NR mismatches around $2$–$5\times10^{-5}$ after fine-tuning, with massive GPU-accelerated generation capabilities (over a million waveforms in under a tenth of a second in batch mode) and successful integration with the Bilby framework for parameter estimation. The approach significantly accelerates waveform generation, enabling large template banks and rapid inference for current and future GW detectors, while acknowledging current limitations such as the absence of higher modes and precession and outlining avenues for extension.

Abstract

Gravitational-wave approximants are essential for gravitational-wave astronomy, allowing the coverage binary black hole parameter space for inference or match filtering without costly numerical relativity (NR) simulations, but generally trading some accuracy for computational efficiency. To reduce this trade-off, NR surrogate models can be constructed using interpolation within NR waveform space. We present a 2-stage training approach for neural network-based NR surrogate models. Initially trained on approximant-generated waveforms and then fine-tuned with NR data, these dual-stage artificial neural surrogate (\texttt{DANSur}) models offer rapid and competitively accurate waveform generation, generating millions in under 20ms on a GPU while keeping mean mismatches with NR around $10^{-4}$. Implemented in the \textsc{bilby} framework, we show they can be used for parameter estimation tasks.

Figures (11)

• Figure 1: An example of a BBH waveform generated using the approximant, in the polarization (top) and amplitude-phase (bottom) representations.
• Figure 2: Mean mismatch values as a function of the number of principal components kept for the amplitude and phase. The arrows show the gradient of the mismatch values, and the yellow circle shows the chosen number of components to build the PCA basis.
• Figure 3: Visualisation of model architecture.
• Figure 4: Validation loss on the approximant datasets during pre-training.
• Figure 5: Distribution of parameters in the NR dataset's train/validation and testing sets.