Electronic-structure methods have a profound impact on several disciplines, especially materials research, as demonstrated by extensive studies in this field and the discovery of numerous advanced materials and devices with widespread applications. However, large-scale electronic structure calculations are prohibitively expensive. Machine learning models can accelerate these simulations, but current models often lack one or more of the following: uncertainty quantification, preservation of symmetries, incorporation of physics, generalizability, accuracy, efficiency, or scalability. This research aims to address all these challenges within a single machine-learning framework. To achieve this goal, this project focuses on gaining fundamental insights into atomic configurations and corresponding electronic structures by developing a machine-learning model to predict electron density for a wide range of materials. The machine learning model facilitates the design of complex materials, which require simulations of larger systems. This fundamental research is expected to have broad applicability beyond materials science in areas where both quantifying uncertainty and respecting rotational-translational symmetry are crucial, such as biomedical imaging and continuum physics problems. The goal of this project is to enable machine learning-based electron density prediction for ultra-large systems and diverse compositions, thereby accelerating materials design. This will be achieved