Physics-Informed Neural Networks for Solving Two-Flavor Neutrino Oscillations in Vacuum and Matter Environments for Atmospheric and Reactor Neutrinos

Abstract

Neutrino oscillations provide crucial insights into fundamental particle physics, with two-flavor approximations effectively describing reactor and atmospheric phenomena. This paper investigates the application of Physics-Informed Neural Networks (PINNs), which have several advantages over traditional solvers. Traditional methods typically depend on mesh-based techniques or dimensionality reduction approaches to solve the governing differential equations for neutrino evolution in vacuum and matter environments. We review the theoretical framework, including vacuum mixing and the Mikheyev-Smirnov-Wolfenstein (MSW) effect in matter, and demonstrate PINN implementations for vacuum and constant-density profiles. This Machine learning based approach for reactor (low-energy) and atmospheric (high-energy) neutrinos shows high precision similar to analytical solutions, with mean squared errors of the order of 10^{-3}~10^{-4}. We have also discussed the robustness of PINNs in solving coupled ODE systems, along with future extensions to three-flavor effects.