In this paper, we propose a novel semi-supervised machine learning approach2 to approximate general Einstein metrics on a broad class of manifolds. We demonstrate its potential by focusing on spheres in various dimensions, with the aim of shedding light on longstanding open problems, providing new perspectives for analysis, and stimulating further research into the numerical and analytical aspects of Einstein geometry. After this successful validation of our method, we aim at applying to other settings with larger relevance in theoretical physics, by looking for black hole solutions and moving to Lorentzian signature.