  We present a proximal algorithm that performs a variational recursion on the
space of joint probability measures to propagate the stochastic uncertainties
in power system dynamics over high dimensional state space. The proposed
algorithm takes advantage of the exact nonlinearity structures in the
trajectory-level dynamics of the networked power systems, and is nonparametric.
Lifting the dynamics to the space of probability measures allows us to design a
scalable algorithm that obviates gridding the underlying high dimensional state
space which is computationally prohibitive. The proximal recursion implements a
generalized infinite dimensional gradient flow, and evolves
probability-weighted scattered point clouds. We clarify the theoretical nuances
and algorithmic details specific to the power system nonlinearities, and
provide illustrative numerical examples.
