Two approaches to the calculation of phase diagrams for materials under high pressures and temperatures with the use of ab initio molecular dynamics are discussed. The first is based on calculations of vibrational free energies of crystal phases with the temperature-dependent effective potential, and the second is based on calculations of thermodynamic potentials with the thermodynamic integration technique combined with machine learning accelerated quantum molecular dynamics with moment tensor potential. Detailed consideration is given to methodical issues. The emphasis of the paper is on phase diagram calculation for uranium in the region where its three solid phases (orthorhombic $\alpha$, body-centered-cubic $\gamma$, and body-centered-tetragonal ${\gamma }^{\prime }$) exist ($P<400\text{GPa}$ and $T<6000\text{K}$). It is shown that the position of equilibrium lines on the phase diagram is sensitive to the choice of theoretical approximation [density functional theory (DFT), $\mathrm{DFT}+U$], but phase diagram topology (the phases and their relative positions) on the $P\text{−}T$ plane is not if the accuracy of thermodynamic potential calculations is below 3–$5\text{meV/at}$. Comparison with calculations by other authors and with available experimental data is provided. The prediction of a triple point $\alpha \text{−}\gamma \text{−}{\gamma }^{\prime }$ at $P\sim 100\text{GPa}$ and $T\sim 2400\text{K}$ in the calculation may be of interest in view of its possible verification in experiments in laser-heated diamond anvil cells.

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• Lattice dynamics
• Phase diagrams
• Actinides
• Ab initio molecular dynamics