Augmentation of invisible information with respect to many hypothetical
models of background and signal processes, can highly improve the performance of the
machine learning classifiers for HEP event discrimination. In this regard di-Higgs searches
in the channels with multiple invisible final states, is one of the most important applications.
Focusing on the di-Higgs channels with 2 bottom quarks + 0/1/2-leptons/taus + MET
from $bbWW$ and $bb\tau\tau$ productions, we introduce various augmentation schemes and ways
to build better multi-class classifiers using deep neural networks. We conclude our study
with demonstration how much the new deep learning classifiers supervised by physical
augmentation, can improve the discovery potential of di-Higgs production at the LHC, and
discuss on the implications for future collider study.