Ab initio simulations with Density Functional Theory (DFT) are now routinely employed across scientific disciplines to unravel the intricate electronic characteristics and properties of materials at the atomic level. Over the past decade, deep learning has revolutionized multiple areas such as computer vision, natural language processing, healthcare diagnostics, and autonomous systems. The combination of these two fields presents a promising avenue to enhance the accuracy and efficiency of complex materials properties predictions, bridging the gap between quantum-level understanding and data-driven insights for accelerated scientific discovery and innovation. Many efforts have been devoted to build deep learning interatomic potentials that learn the potential energy surface (PES) from DFT simulations and can be employed in large-scale molecular dynamics (MD) simulations. Generalizing such deep learning approaches to predict the electronic structure instead of just the energy, forces and stress tensor of a system is an appealing idea as it would open up new frontiers in materials research, enabling the simulation of electron-related physical properties in large systems that are important for microelectronic applications. The goal of this PhD is to develop new methodologies relying on equivariant neural networks to predict the DFT Hamiltonian (i.e. the most fundamental property) of complex materials (including disorder, defects, interfaces, etc.) or heterostructures.