  Though the 125-GeV scalar, as the Higgs boson of the standard model, is
disfavoured as a dark matter portal by direct searches and the observations on
relic density, a heavier scalar in an extended electroweak sector can fit into
that role. We explore this possibility in the context of two Higgs doublet
models (2HDM). Taking Type I and Type II 2HDM as illustration, and assuming a
scalar gauge singlet dark matter particle, we show that the heavy neutral
CP-even scalar ($H$) can (a) serve as dark matter portal consistently with all
data, and (b) have a substantial invisible branching ratio, over a wide region
of the parameter space. Using this fact, we estimate rates of LHC signals where
$H$ is produced via ({\it i}) gluon fusion, in association with a hard jet, and
({\it ii}) vector boson fusion. Invisible decays of the $H$ can then lead to
monojet + $\slashed{E_T}$ in ({\it i}), and two forward jets with large
rapidity gap + $\slashed{E_T}$ in ({\it ii}). The second kind of signal usually
yields better significance for the high-luminosity run. We also supplement our
cut-based analyses with those based on gradient boosted decision trees
(XGboost) and artificial neural network (ANN) techniques, where the statistical
significance distinctly improves, especially for Type II 2HDM.
