  We present a framework for computing the shock Hugoniot using on-the-fly
machine learned force field (MLFF) molecular dynamics simulations. In
particular, we employ an MLFF model based on the kernel method and Bayesian
linear regression to compute the electronic free energy, atomic forces, and
pressure; in conjunction with a linear regression model between the electronic
internal and free energies to compute the internal energy, with all training
data generated from Kohn-Sham density functional theory (DFT). We verify the
accuracy of the formalism by comparing the Hugoniot for carbon with recent
Kohn-Sham DFT results in the literature. In so doing, we demonstrate that
Kohn-Sham calculations for the Hugoniot can be accelerated by up to two orders
of magnitude, while retaining ab initio accuracy. We apply this framework to
calculate the Hugoniots of 14 materials in the FPEOS database, comprising 9
single elements and 5 compounds, between temperatures of 10 kK and 2 MK. We
find good agreement with first principles results in the literature while
providing tighter error bars. In addition, we confirm that the inter-element
interaction in compounds decreases with temperature.
