# Meta-model Neural Process for Probabilistic Power Flow under Varying N-1 System Topologies

arXiv: https://arxiv.org/abs/2509.12281 · HTML: https://mlsanity.com/paper/2509.12281/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 23 references that are in the map.
- First posted on arXiv 14 Sep 2025.

## Builds on (most cited first, 4 of 4)

- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [The Neural Process Family: Survey, Applications and Perspectives](https://mlsanity.com/paper/2209.00517/) (2022)
- [Constructing Convex Inner Approximations of Steady-State Security Regions](https://mlsanity.com/paper/1708.06845/) (2017)
- [Non-parametric Probabilistic Load Flow using Gaussian Process Learning](https://mlsanity.com/paper/1911.03093/) (2019)

## Built on by (most cited first, 1 of 1)

- [Gradient-Free Topology Adaptation for Power Flow Surrogates via In-Context Whitening](https://mlsanity.com/paper/2607.12241/) (2026)

## Abstract (arXiv)

The probabilistic power flow (PPF) problem is essential to quantifying the distribution of the nodal voltages due to uncertain injections. The conventional PPF problem considers a fixed topology, and the solutions to such a PPF problem are associated with this topology. A change in the topology might alter the power flow patterns and thus require the PPF problem to be solved again. The previous PPF model and its solutions are no longer valid for the new topology. This practice incurs both inconvenience and computation burdens as more contingencies are foreseen due to high renewables and a large share of electric vehicles. This paper presents a novel topology-adaptive approach, based on the meta-model Neural Process (MMNP), for finding the solutions to PPF problems under varying N-1 topologies, particularly with one-line failures. By leveraging context set-based topology representation and conditional distribution over function learning techniques, the proposed MMNP enhances the robustness of PPF models to topology variations, mitigating the need for retraining PPF models on a new configuration. Simulations on an IEEE 9-bus system and IEEE 118-bus system validate the model's performance. The maximum %L1-relative error norm was observed as 1.11% and 0.77% in 9-bus and 118-bus, respectively. This adaptive approach fills a critical gap in PPF methodology in an era of increasing grid volatility.