In traditional finite-temperature Kohn–Sham density functional theory (KSDFT), the partial occupation of a large number of high-energy KS eigenstates restricts the use of first-principles molecular dynamics methods at extremely high temperatures. However, stochastic density functional theory (SDFT) can overcome this limitation. Recently, SDFT and the related mixed stochastic–deterministic density functional theory, based on a plane-wave basis set, have been implemented in the first-principles electronic structure software ABACUS [Q. Liu and M. Chen, Phys. Rev. B 106, 125132 (2022)]. In this study, we combine SDFT with the Born–Oppenheimer molecular dynamics method to investigate systems with temperatures ranging from a few tens of eV to 1000 eV. Importantly, we train machine-learning-based interatomic models using the SDFT data and employ these deep potential models to simulate large-scale systems with long trajectories. Subsequently, we compute and analyze the structural properties, dynamic properties, and transport coefficients of warm dense matter.

We propose an efficient scheme that combines density functional theory (DFT) with deep potentials (DPs), to systematically study convergence issues in the computation of the electronic thermal conductivity of warm dense aluminum (2.7 g/cm³ and temperatures ranging from 0.5 eV to 5.0 eV) with respect to the number of k-points, the number of atoms, the broadening parameter, the exchange-correlation functionals, and the pseudopotentials. Furthermore, we obtain the ionic thermal conductivity using the Green–Kubo method in conjunction with DP molecular dynamics simulations, and we study size effects on the ionic thermal conductivity. This work demonstrates that the proposed method is efficient in evaluating both electronic and ionic thermal conductivities of materials.