We present a new machine learning technique for the classification of scattering processes which include invisible particles missing in detector. With this purpose, new high-level feature variables are introduced, which can be obtained in the process of topological augmentation – a general reconstruction procedure of invisible missing momenta subject to various hypothetical decay topologies. Given visible particle information, each augmented feature can be used as an optimized event projection basis, and we utilize them all in together for the classification of many hypothetical topologies possibly involved. As an important application, we focus on the (non-resonant) di-Higgs production in the channel of 2 b-jets, 2 leptons + MET, and demonstrate our new multi-class classification analysis using deep neural networks supervised by the topologically augmented features. We provide an update on the future expectation of di-Higgs discovery at the LHC, and discuss on the importance of our method for general scattering processes with missing information, which can even improve the conventional deep learning technique which works well with full visible low-level information.