Machine Learning Inference of Black Hole Spin from Simulated Quasi-Periodic Oscillations: A Gaussian Process Regression Approach

Quasi-periodic oscillations (QPOs) in the X-ray light curves of accreting black holes provide a powerful, albeit complex, probe into the strong-field regime of General Relativity. Traditionally, constraints on black hole spin from QPOs have relied on phenomenological or relativistic precession models, each burdened by systematic uncertainties and observational limitations. In this work, we explore a complementary approach grounded in data-driven inference: using synthetic QPO datasets generated from theoretically motivated spin-frequency relations, we apply Gaussian Process Regression (GPR) to recover the underlying spin parameter of a stellar-mass black hole. Our method is tailored for computational accessibility, requiring minimal training data, no large-scale simulations, and modest hardware while retaining physical interpretability. The GPR model successfully reconstructs the spin parameter from noisy QPO signals with high confidence, highlighting the potential of non-parametric machine learning in extracting astrophysical parameters where traditional likelihoods fail or become intractable. We discuss the implications for future observations from next-generation X-ray observatories, and advocate for broader use of Bayesian non-parametric techniques in theoretical astrophysics. Our work serves as a prototype for applying modern statistical tools to long-standing theoretical questions in black hole physics, even in resource-constrained research settings.