  A search is presented for the pair production of heavy vector-like quarks,
$T\bar T$ or $B\bar B$, that decay into final states with jets and no
reconstructed leptons. Jets in the final state are classified using a deep
neural network as arising from hadronically decaying $W/Z$ bosons, Higgs
bosons, top quarks, or background. The analysis uses data from the ATLAS
experiment corresponding to 36.1 fb$^{-1}$ of proton-proton collisions with a
center-of-mass energy of $\sqrt{s} = 13$ TeV delivered by the Large Hadron
Collider in 2015 and 2016. No significant deviation from the Standard Model
expectation is observed. Results are interpreted assuming the vector-like
quarks decay into a Standard Model boson and a third-generation-quark,
$T\rightarrow Wb,Ht,Zt$ or $B\rightarrow Wt,Hb,Zb$, for a variety of branching
ratios. At 95% confidence level, the observed (expected) lower limit on the
vector-like $B$-quark mass for a weak-isospin doublet ($B, Y$) is 950 (890)
GeV, and the lower limits on the masses for the pure decays $B\rightarrow Hb$
and $T\rightarrow Ht$, where these results are strongest, are 1010 (970) GeV
and 1010 (1010) GeV, respectively.
