  We develop a framework for on-the-fly machine learned force field (MLFF)
molecular dynamics (MD) simulations of warm dense matter (WDM). In particular,
we employ an MLFF scheme based on the kernel method and Bayesian linear
regression, with the training data generated from Kohn-Sham density functional
theory (DFT) using the Gauss Spectral Quadrature method, within which we
calculate energies, atomic forces, and stresses. We verify the accuracy of the
formalism by comparing the predicted properties of warm dense carbon with
recent Kohn-Sham DFT results in the literature. In so doing, we demonstrate
that ab initio MD simulations of WDM can be accelerated by up to three orders
of magnitude, while retaining ab initio accuracy. We apply this framework to
calculate the diffusion coefficients and shear viscosity of CH at a density of
1 g/cm$^3$ and temperatures in the range of 75,000 to 750,000 K. We find that
the self- and inter-diffusion coefficients as well as the viscosity obey a
power law with temperature, and that the diffusion coefficient results suggest
a weak coupling between C and H in CH. In addition, we find agreement within
standard deviation with previous results for C and CH but disagreement for H,
demonstrating the need for ab initio calculations as presented here.
