# Adaptive network reliability analysis: Methodology and applications to power grid

arXiv: https://arxiv.org/abs/2109.05360 · HTML: https://mlsanity.com/paper/2109.05360/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 65 references that are in the map.
- First posted on arXiv 11 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [bartMachine: Machine Learning with Bayesian Additive Regression Trees](https://mlsanity.com/paper/1312.2171/) (2013)
- [Bayesian Additive Regression Trees using Bayesian Model Averaging](https://mlsanity.com/paper/1507.00181/) (2015)
- [Deep Learning for Accelerated Reliability Analysis of Infrastructure Networks](https://mlsanity.com/paper/1708.08551/) (2017)
- [REAK: Reliability analysis through Error rate-based Adaptive Kriging](https://mlsanity.com/paper/2002.01110/) (2020)
- [Principled Network Reliability Approximation: A Counting-Based Approach](https://mlsanity.com/paper/1806.00917/) (2018)

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

- [A generic physics-informed neural network-based framework for reliability assessment of multi-state systems](https://mlsanity.com/paper/2112.00220/) (2021)
- [Sampling and active learning methods for network reliability estimation using K-terminal spanning tree](https://mlsanity.com/paper/2407.11053/) (2024)
- [Graph Attention Networks Unleashed: A Fast and Explainable Vulnerability Assessment Framework for Microgrids](https://mlsanity.com/paper/2503.00786/) (2025)

## Abstract (arXiv)

Flow network models can capture the underlying physics and operational constraints of many networked systems including the power grid and transportation and water networks. However, analyzing reliability of systems using computationally expensive flow-based models faces substantial challenges, especially for rare events. Existing actively trained meta-models, which present a new promising direction in reliability analysis, are not applicable to networks due to the inability of these methods to handle high-dimensional problems as well as discrete or mixed variable inputs. This study presents the first adaptive surrogate-based Network Reliability Analysis using Bayesian Additive Regression Trees (ANR-BART). This approach integrates BART and Monte Carlo simulation (MCS) via an active learning method that identifies the most valuable training samples based on the credible intervals derived by BART over the space of predictor variables as well as the proximity of the points to the estimated limit state. Benchmark power grids including IEEE 30, 57, 118, and 300-bus systems and their power flow models for cascading failure analysis are considered to investigate ANR-BART, MCS, subset simulation, and passively-trained optimal deep neural networks and BART. Results indicate that ANR-BART is robust and yields accurate estimates of network failure probability, while significantly reducing the computational cost of reliability analysis.