Developable surfaces find extensive applications in various fields such as Computer-Aided Design (CAD), computer graphics, architecture geometry, and manufacturing. In this report, we propose two novel geometry-informed neural networks, namely GINN-SP and GINN-DA, for efficient surface partition and developable approximation of an input triangular mesh. GINN-SP utilizes a graph neural network to divide a complex surface into several semi-developable surface patches, which have simple topology, few critical points, and are amenable to deep learning-based aggregation of geometric information. On the other hand, GINN-DA parameterizes the two-dimensional surface, reduces Gaussian curvature, and incorporates geometric information for better approximation. We demonstrate the superior performance of GINN-SP and GINN-DA over existing methods through extensive benchmarking examples.