Physics-Informed Neural Networks and Data-Driven Models for GRB X-ray Light-Curve Gap Reconstruction

Abstract

Temporal gaps in Swift-XRT X-ray afterglows of gamma-ray bursts (GRBs) limit how precisely the standard empirical plateau function constrains three parameters: the plateau end time $T_a$, the plateau flux $F_a$, and the post-plateau decay index $\alpha$. These parameters underpin the luminosity-time and fundamental-plane correlations of GRB plateaus so that smaller measurement uncertainties can improve the statistical power of GRBs as cosmological probes. As the fifth study in a series on light-curve reconstruction, this work benchmarks four models on a parent sample of 545 Swift-XRT GRBs: a Physics-Informed Neural Network (PINN) with seven afterglow-motivated priors, ReFANN, a Siamese dual-branch network with Monte Carlo dropout, and Polynomial Quantile Regression (PQR). All four reduce the fractional uncertainties in $\log T_a$, $\log F_a$, and $\alpha$ relative to the original observations. The PINN with a broken power-law prior gives the largest reductions ($\sim$41-49\%), at a higher outlier rate ($\sim$15-20\%), while ReFANN, Siamese network and PQR give more modest reductions ($\sim$19-27\%) with outlier fractions $\lesssim$4\%, across a wider range of light-curve morphologies. A reduced-${\chi }^2$ prior-selection scheme recovers a morphological classification consistent with independent labelling, though it does not match the best single-prior reduction. Together, these results provide a systematic benchmark of physics-informed and data-driven reconstruction strategies for irregularly sampled GRB afterglows.

arXiv comment36 pages, 6 figures, 7 tables, journal paper