  The prospects of observing the non-resonant di-Higgs production in the
Standard Model at the proposed high energy upgrade of the LHC, $viz.$ the
HE-LHC$~$($\sqrt{s}=27~{\rm TeV}$ and $\mathcal{L} = 15~{\rm ab^{-1}}$) is
studied. Various di-Higgs final states are considered based on their
cleanliness and signal yields. The search for the non-resonant double Higgs
production at the HE-LHC is performed in the $b\bar{b}\gamma\gamma$,
$b\bar{b}\tau^{+}\tau^{-}$, $b\bar{b}WW^{*}$, $WW^{*}\gamma\gamma$,
$b\bar{b}ZZ^{*}$ and $b\bar{b}\mu^{+}\mu^{-}$ channels. The signal-background
discrimination is performed through multivariate analyses using the Boosted
Decision Tree Decorrelated$~$(BDTD) algorithm in the$~$TMVA framework, the
XGBoost toolkit and Deep Neural Network$~$(DNN). The variation in the
kinematics of Higgs pair production as a function of the self-coupling of the
Higgs boson, $\lambda_{h}$, is also studied. The ramifications of varying
$\lambda_{h}$ on the $b\bar{b}\gamma\gamma$, $b\bar{b}\tau^{+}\tau^{-}$ and
$b\bar{b}WW^{*}$ search analyses optimized for the SM hypothesis is also
explored.
