# Stochastic Uncertainty Propagation in Power System Dynamics using Measure-valued Proximal Recursions

arXiv: https://arxiv.org/abs/2108.13405 · HTML: https://mlsanity.com/paper/2108.13405/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2021.

## Built on by (most cited first, 3 of 3)

- [On the Hopf-Cole Transform for Control-affine Schr"odinger Bridge](https://mlsanity.com/paper/2503.17640/) (2025)
- [Proximal Mean Field Learning in Shallow Neural Networks](https://mlsanity.com/paper/2210.13879/) (2022)
- [Learning Concave Bid Shading Strategies in Online Auctions via Measure-valued Proximal Optimization](https://mlsanity.com/paper/2509.10693/) (2025)

## Abstract (arXiv)

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.