Statistical Analysis of a Complex Plasma System From a Small Number of Simulations

This work aims to enhance the small amount of data obtained from simulations using statistical methods, in order to improve the analysis of the underlying physical properties of plasma behavior, particularly electron density and electron temperature in the boundary region of the tokamak. Electron density and electron temperature are important observables for characterizing plasma behavior in the boundary region of the tokamak, as they influence transport properties and confinement regimes. While the simulations used in this work are fully deterministic, we aim to extract statistical information by interpreting numerical simulations as samples from underlying random fields. This approach allows for the construction of marginal and joint probability density functions (PDFs) that provide physical insight beyond standard deterministic interpretation and capture key structural features of the plasma behavior in the boundary region of the tokamak, including the role of triangularity, the impact of the diffusion coefficient, and the implications for plasma behavior. Numerical simulations are performed with the Gkeyll gyrokinetic code. Despite their resolution, the computational cost limits the number of available simulation data, suggesting a role for advanced analysis techniques capable of extracting meaningful physical insights from a small dataset. To this end, we explore a statistical framework based on probabilistic learning on manifolds (PLoM), a nonparametric method designed for small-sample inference.