Silicate liquids play a critical role in the thermal evolution of Earth, at scales ranging from dikes and sills to magma oceans. In the present-day Earth, silicate melts exist transiently in the crust and upper mantle, and are thought to exist at depths as great as the core-mantle boundary (CMB). The rate of transport of heat through a magma is governed by the thermal conductivity. The value of the thermal conductivity, k is important for understanding processes ranging from double diffusive convection in magma chambers to the earliest thermal evolution of a putative molten Earth (Elkins-Tanton, 2012;Huppert & Sparks, 1984). Yet, the thermal conductivity of silicate liquids at pressures greater than 1 bar is unknown. The pressure dependence of k may be large: the thermal conductivity of crystals may vary by an order of magnitude over the pressure range of the Earth's mantle at elevated temperature (Stackhouse et al., 2010). Even at 1 bar, the thermal conductivity of silicate liquids is still highly uncertain, with different experimental techniques yielding values that may differ by as much as a factor of 10 (Hasegawa et al., 2012;Kang & Morita, 2006).Here, we predict the thermal conductivity of a silicate liquid, with an approach combining the Green-Kubo method with ab initio electronic structure calculations and the development of a machine learning potential. The Green-Kubo method is the most widely used means of determining the thermal conductivity in materials simulations based on classical potentials because it is an equilibrium method that is readily controlled (Sellan et al., 2010). Combining the Green-Kubo method with ab initio theory however has proved challenging because there is no simple way of decomposing the total energy into individual contributions from each atom. Because of this limitation, previous ab initio calculations of the thermal conductivity have used alternatives to the Green-Kubo method, including nonequilibrium methods (Stackhouse et al., 2010), which have also been combined with classical potentials in studies of silicate liquids (Tikunoff & Spera, 2014). It