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 $0.117 \leq z \leq 1.99$. Our analysis yields stringent constraints on both linear and quadratic LIV, with $E_{\mathrm{QG},1} \geq 2.60 \times 10^{15}~\mathrm{GeV}$ and $E_{\mathrm{QG},2} \geq 1.21 \times 10^{10}~\mathrm{GeV}$. 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.