Black Hole Spectroscopy with Conditional Variational Autoencoder

Gravitational waves provide a unique opportunity to test general relativity in the strong-field regime, enabling the extraction of key physical parameters from observational data. Traditional likelihood-based inference methods, while robust, become computationally expensive in high-dimensional parameter spaces, such as when incorporating multiple ringdown modes or beyond Kerr deviations. In this paper, we explore the implementation of a conditional variational autoencoder-based machine-learning framework for accelerated ringdown parameter estimation. As a first application, we use the neural network to infer the remnant properties of a final black hole under the Kerr hypothesis. We demonstrate the performance of this algorithm with simulated ringdown waveforms consistent with advanced LIGO sensitivity and compare with Bayesian analysis results. We further extend the framework beyond the Kerr paradigm by incorporating deviations predicted in braneworld gravity.