  Understanding many processes, e.g. fusion experiments, planetary interiors
and dwarf stars, depends strongly on microscopic physics modeling of warm dense
matter (WDM) and hot dense plasma. This complex state of matter consists of a
transient mixture of degenerate and nearly-free electrons, molecules, and ions.
This regime challenges both experiment and analytical modeling, necessitating
predictive \emph{ab initio} atomistic computation, typically based on quantum
mechanical Kohn-Sham Density Functional Theory (KS-DFT). However, cubic
computational scaling with temperature and system size prohibits the use of DFT
through much of the WDM regime. A recently-developed stochastic approach to
KS-DFT can be used at high temperatures, with the exact same accuracy as the
deterministic approach, but the stochastic error can converge slowly and it
remains expensive for intermediate temperatures (<50 eV). We have developed a
universal mixed stochastic-deterministic algorithm for DFT at any temperature.
This approach leverages the physics of KS-DFT to seamlessly integrate the best
aspects of these different approaches. We demonstrate that this method
significantly accelerated self-consistent field calculations for temperatures
from 3 to 50 eV, while producing stable molecular dynamics and accurate
diffusion coefficients.
