Cosmological Model Independent Constraints on Lorentz Invariance Violation with Updated Gamma-Ray Burst Observations: An Artificial Neural Network Approach

Searching for Lorentz invariance violation (LIV) using astrophysical sources such as gamma-ray bursts (GRBs) is crucial for probing quantum gravity. However, the dependence of LIV constraints on assumed cosmological models has been largely overlooked. In this work, we present a model-independent reconstruction of the cosmic expansion history using artificial neural networks (ANN), thereby avoiding biases from specific cosmological priors. We analyze 74 GRB time delays, including 37 measurements from GRB~160625B across multiple energy bands at $z=1.41$, and 37 additional bursts spanning redshifts $0.117\le z\le 1.99$. Our analysis yields stringent constraints on both linear and quadratic LIV, with $E_{\mathrm{Q}\mathrm{G},1}\ge 2.60\times {10}^{15}\mathrm{G}\mathrm{e}\mathrm{V}$ and $E_{\mathrm{Q}\mathrm{G},2}\ge 1.21\times {10}^{10}\mathrm{G}\mathrm{e}\mathrm{V}$. The linear limit is within four orders of magnitude of the Planck scale. By leveraging a large sample of GRBs, our approach significantly enhances the robustness of LIV constraints, providing a powerful, cosmological-independent framework for future tests of quantum gravity.