# Reinforcement Learning for Power-Flow Network Analysis

arXiv: https://arxiv.org/abs/2603.05673 · HTML: https://mlsanity.com/paper/2603.05673/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for energy, networks and operations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 7 of its 52 references that are in the map.
- First posted on arXiv 5 Mar 2026.

## Placed in

- Deep reinforcement learning methods / [RL for energy, networks and operations](https://mlsanity.com/deeprl/rl-for-energy-networks-and-operations/)

## Builds on (most cited first, 7 of 7)

- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [A Review of Safe Reinforcement Learning Methods for Modern Power Systems](https://mlsanity.com/paper/2407.00304/) (2024)
- [Recent Advances in Computational Methods for the Power Flow Equations](https://mlsanity.com/paper/1510.00073/) (2015)
- [The Distribution of the Number of Real Solutions to the Power Flow Equations](https://mlsanity.com/paper/2010.03069/) (2020)
- [Tangent Quadrics in Real 3-Space](https://mlsanity.com/paper/2010.10879/) (2020)
- [Nodes on quintic spectrahedra](https://mlsanity.com/paper/2011.13860/) (2020)
- [Exploiting Symmetry in the Power Flow Equations Using Monodromy](https://mlsanity.com/paper/2011.14977/) (2020)

## Abstract (arXiv)

The power flow equations are non-linear multivariate equations that describe the relationship between power injections and bus voltages of electric power networks. Given a network topology, we are interested in finding network parameters with many equilibrium points. This corresponds to finding instances of the power flow equations with many real solutions. Current state-of-the art algorithms in computational algebra are not capable of answering this question for networks involving more than a small number of variables. To remedy this, we design a probabilistic reward function that gives a good approximation to this root count, and a state-space that mimics the space of power flow equations. We derive the average root count for a Gaussian model, and use this as a baseline for our RL agents. The agents discover instances of the power flow equations with many more solutions than the average baseline. This demonstrates the potential of RL for power-flow network design and analysis as well as the potential for RL to contribute meaningfully to problems that involve complex non-linear algebra or geometry. footnoteAuthor order alphabetic, all authors contributed equally.