  A measurement is performed of Higgs bosons produced with high transverse
momentum ($p_\mathrm{T}$) via vector boson or gluon fusion in proton-proton
collisions. The result is based on a data set with a center-of-mass energy of
13 TeV collected in 2016-2018 with the CMS detector at the LHC and corresponds
to an integrated luminosity of 138 fb$^{-1}$. The decay of a
high-$p_\mathrm{T}$ Higgs boson to a boosted bottom quark-antiquark pair is
selected using large-radius jets and employing jet substructure and
heavy-flavor taggers based on machine learning techniques. Independent regions
targeting the vector boson and gluon fusion mechanisms are defined based on the
topology of two quark-initiated jets with large pseudorapidity separation. The
signal strengths for both processes are extracted simultaneously by performing
a maximum likelihood fit to data in the large-radius jet mass distribution. The
observed signal strengths relative to the standard model expectation are
4.9$^{+1.9}_{-1.6}$ and 1.6$^{+1.7}_{-1.5}$ for the vector boson and gluon
fusion mechanisms, respectively. A differential cross section measurement is
also reported in the simplified template cross section framework.
