Uncertainty quantification and data-oriented approaches in collisional kinetic models

In this thesis, we investigate novel perspectives in uncertainty quantification and data-oriented approaches for collisional kinetic models with applications in plasma physics and multiagent systems. In particular, the thesis is divided into two parts: I Stochastic Galerkin particle methods for plasma equations with random inputs, and II Kinetic multiagent systems in the presence of uncertainties: modelling, control, and data calibration. In the first part, comprising Chapter 1-2-3, we present results concerning the particle stochastic Galerkin class of numerical methods. We show the algorithms together with their properties, some regularity results, and several numerical tests in the context of kinetic equations for plasmas. In the second part, comprising Chapter 4-5-6, we present results concerning kinetic models of many interacting agents in the presence of uncertainty. We investigate numerical methods, optimal control strategies, and calibration of model parameters using real-world data.