Plasmas are many-body systems of interacting charged particles that exist naturally and can be created experimentally. For example, plasmas are found in many astrophysical systems like the corona of the sun, the Earth's ionosphere, and in the interior of white-dwarf stars. In engineering and medicine, plasmas are used during the design process of semi-conductors or for inactivating viruses like COVID-19. Plasmas also occur in nuclear fusion experiments which promise a nearly infinite supply of clean, renewable energy. Quantifying the behaviors of plasmas experimentally can be challenging due to the short time- scales and small length-scales that interactions between the plasma particles occur. In many cases, computational approaches are used to simulate the dynamics of plasmas to supplement the dearth of experimental data. The accuracy of these computational methods is largely unknown across the entire parameter regimes plasmas occupy limiting their predictive capabilities. This dissertation is composed of four distinct projects all with the common goal of developing numerical methods for rapidly and accurately computing properties of non-ideal plasmas.First, we focus on the data-driven discovery of pair interaction potentials for molecular dynamics simulations of dense plasmas across a wide range of temperatures and elements. We find that our pair interaction potentials simulate the ionic interactions in a plasma with accuracy comparable to Kohn-Sham molecular dynamics but with orders of magnitude less computation cost. Second, we develop theoretical models that avoid the need for numerical simulations of plasma mixtures altogether. Our theoretical models show reasonable agreement with molecular dynamics data across the both the weak and strong coupling regimes. Third, we use techniques in machine learning to interpolate plasma properties data with multiple sources of data. We find that our machine learning method accurately predicts trends in data even in the absence of high-fidelity calculations. Lastly, we implement a numerical scheme for solving kinetic equations with applications to ultracold neutral plasma mixtures and high-energy-density plasmas. With our simulation results, we suggest plasma conditions for future experiments and we discuss natural extensions of our numerical method that will be the basis of future work.
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