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.
Expected and observed upper limits at the 95% CL on the $T\bar T$ cross section as a function of $T$ mass under the assumption BR($T\to Ht$)=1.
Expected and observed upper limits at the 95% CL on the $B\bar B$ cross section as a function of $B$ mass under the assumption BR($B\to Hb$)=1.
Expected and observed upper limits at the 95% CL on the $B\bar B$ cross section as a function of $B$ mass under the assumption of a weak-isospin doublet.
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