We discuss recent applications of uncertainty quantification techniques to problems in electromagnetics and energy systems. In the first case, the micro-scale variability of the resonant frequency in material models is explicitly represented by a continuous spectrum. We consider the effect of this inclusion of uncertainty on the numerical analysis of discretization methods for the resulting dispersive Maxwell's equations. Extensions to magnetohydrodynamics and viscoelastics are presented.
For energy systems, the increased adoption of renewable sources of power generation adds significant variability to the grid. Probabilistic load flow analysis attempts to resolve the nonlinear load flow equations under high-dimensional input uncertainties. We discuss our contributions to making this problem more tractable using dimension reduction techniques. Extensions to soil liquefaction are also presented.