Accelerated Bayesian Inference for Neutron Stars in f(Q) Gravity: Gaussian Processes, Deep Learning, and Ensemble Uncertainty Quantification

Abstract

The study of neutron stars (NSs) in modified gravity theories provides a unique window into the strong-field regime of gravitational physics. While Bayesian inference has proven powerful for constraining general relativity and curvature-based modifications, such analyses in symmetric teleparallel f(Q) gravity remain computationally expensive due to the repeated solution of modified Tolman-Oppenheimer-Volkoff (TOV) equations. In this work, we introduce a comprehensive accelerated Bayesian inference framework for neutron stars in f(Q) gravity, combining Gaussian process emulation, deep learning surrogates, sequential Monte Carlo methods, active learning, and ensemble uncertainty quantification. Our approach achieves a speedup of approximately \(5.2 \times 10^5\) compared to traditional methods, reducing inference time from weeks to hours while maintaining percent-level accuracy. We demonstrate our methodology by re-analyzing NICER observations of PSR J0030+0451, PSR J0740+6620, PSR J0437+4715, and PSR J0614+3329, considering linear, logarithmic, and exponential f(Q) models with the DDME2 equation of state. Our active learning framework identifies the tidal deformability at canonical mass \(\Lambda _{1.4}\) as the most informative observable for constraining the f(Q) scale parameter \(Q_0\), with an expected information gain of 2.34 nats, while the radius at \(2.0 M_\odot \) is most sensitive to the \(\beta \) parameter with EIG of 1.82 nats. The ensemble variance decomposition shows that EoS uncertainty dominates the radius prediction (\(80.6\%\)), followed by gravity-model (\(14.3\%\)), statistical (\(5.0\%\)), and negligible numerical contributions. Our results confirm the statistical preference for the exponential model, with \(\ln (\textrm{BF}) = -1.81\) versus the linear model and \(-0.43\) versus the logarithmic model, while providing significantly tighter parameter constraints with a 11.4–\(17.9\%\) reduction in the full widths of the \(68\%\) credible intervals. This work establishes a foundation for real-time multi-messenger inference of modified gravity theories as new NS observations become available.