Anticipating the effects of random inputs over a Complex System is a natural question arising in many engineering and dynamical systems applications. In the context of the electrical grids, the growing uncertainty coming from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify these effects and assess the risks it poses.
I will introduce the motivations for this work, as well as the Polynomial Chaos Expansion method. It produces results that are highly accurate but are computationally challenging to scale to large systems. To determine the Polynomial Expansion, we propose learning algorithms that can take advantage of the sparsity to significantly improve computational efficiency while retaining the desired high level of accuracy.