# Introduction Researchers have developed a new machine learning framework that can solve complex quantum problems with high precision. The framework, based on artificial intelligence, uses neural networks to learn Bloch functions and their corresponding energies simultaneously. # Problem Statement The problem the researchers sought to solve is the Floquet-Bloch eigenvalue problem associated with particles in two-dimensional periodic potentials, with a focus on honeycomb lattice geometry due to its distinctive band topology featuring Dirac points and its relevance to materials such as graphene. # Proposed Solution The new machine learning framework uses a neural network to learn Bloch functions and their corresponding energies simultaneously. The model was trained over the Brillouin zone to recover band structures and Bloch modes, with numerical validation against traditional plane-wave expansion methods. # Evaluations and Applications The model demonstrated its ability to capture changes in band structure topology. This work contributes to the growing field of physics-informed machine learning for quantum eigenproblems, providing insights into the interplay between symmetry, band structure, and neural architectures.