A profound understanding of warm dense matter (WDM) properties is essential to unraveling the mysteries of planetary and stellar formation, evolution, and interior structure, as well as establishing inertial confinement fusion as a potential energy source. In the center of attention is the dynamic behavior of such matter, which can be characterized in terms of material, transport, and optical properties, e.g., conductivity, opacity, and sound speed. Powerful laser facilities such as the National Ignition Facility (NIF) are capable of recreating these high-pressure states in the laboratory. In addition, recent innovations to the spectral resolution at X-ray free electron laser (XFEL) facilities now enable studying ion dynamics in shock compression experiments. The computational side of WDM research is faced with the challenge of leveraging these experimental capabilities. This thesis employs modern machine-learning approaches to overcome some of the challenges. In the context of scattering experiments, the dynamic structure factor (DSF) of the ions and electrons is employed to connect the simulations with scattering experiments on different energy scales.
Neural-network-based potentials are employed to connect the microscopic ion dynamics observed in simulations with material and transport properties in the hydrodynamic limit. Combined with the improved spectral resolution at XFEL facilities, which permits the measurement of the ionic DSF, this enables the study of material and transport properties at extreme conditions.
Furthermore, the DSF of the electrons is computed from sophisticated many-particle simulations and compared to analytic descriptions that are traditionally used in WDM scattering experiments. This enables insights into the ionization state and the electron-ion collision frequency in extreme matter.
Both electron and ion dynamics are simulated in a consistent ab initio framework to analyze an X-ray Thomson scattering experiment at the NIF. On the basis of these simulations, a Bayesian analysis of the scattering spectra, accounting for the influence of the intricate experimental setup on the results, reveals that the experiment reached conditions present in the interior of red dwarfs.
Finally, electrical conductivity, which is one of the properties of interest in collective scattering experiments, is studied. The long-standing question of whether electron-electron collisions are included in the electrical conductivity computed via the Kubo-Greenwood formula is resolved. It is shown that, in the ideal plasma limit, the direct current electrical conductivity only accounts for electron-ion collisions.