Neutrino Mass Predictions with an AI-based Algorithm under $A_4$ Modular Symmetry

This research undertakes a comprehensive exploration of neutrino mass model grounded in $A_4$ discrete non-Abelian modular symmetry formulated within a linear seesaw framework that modifies the conventional type-I seesaw structure with a focus on optimizing the model parameters using incomprehensible but intelligible-in-time logics optimization algorithm (ILA), an AI-based algorithm. In contrast to traditional discrete flavor symmetry frameworks, modular symmetry significantly reduces the number and complexity of flavon fields needed to generate realistic fermion mass textures. The key predictions include neutrino masses, $U_{PMNS}$ matrices, effective neutrino masses for neutrinoless double beta decay, beta decay, Dirac and Majorana CP violation phases for normal (NO) and inverted mass ordering (IO), offering testable implications. The working efficiency of the ILA optimization technique is also estimated. The optimized neutrino oscillation parameters are well consistent with recent experimental data. Our analysis also aligns with Planck cosmological constraints on the sum of neutrino masses $0.06<Σm<0.12$.