This note reports studies of Higgs boson production with sizeable transverse momentum decaying to a $b\bar{b}$ quark pair. The analyzed data were recorded with the ATLAS detector in proton-proton collisions with a center-of-mass energy of $\sqrt{s}=13$~TeV at the Large Hadron Collider between 2015 and 2018, corresponding to an integrated luminosity of 136~fb$^{-1}$. Higgs bosons decaying to $b\bar{b}$ are reconstructed as single large-radius jets and identified by the experimental signature of two $b$-hadron decays. The experimental techniques are validated in the same kinematic regime using the $Z\rightarrow b\bar{b}$ process. For Higgs boson production at transverse momenta above 450 GeV, the production cross section is found to be 13\pm 57 \text{(stat.)} \pm 22 \text{(syst.)} \pm 3 \text{(theo.)} \mathrm{~fb}. The differential cross section 95% confidence level upper limits as a function of Higgs boson transverse momentum are \sigma_{H}(300< p_{\text{T}}^{H}<450~\mathrm{~GeV}) < 2.8~\mathrm{~pb}, \sigma_{H}(450< p_{\text{T}}^{H}<650~\mathrm{~GeV}) < 91~\mathrm{~fb}, \sigma_{H}(p_{\text{T}}^{H}>650~\mathrm{~GeV}) < 40.5~\mathrm{~fb}, and \sigma_{H}(p_{\text{T}}^{H}>1~\mathrm{~TeV}) < 10.3~\mathrm{~fb}. All results are consistent with the Standard Model predictions.

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