Data-Driven Approximation of Binary-State Network Reliability Function: Algorithm Selection and Reliability Thresholds for Large-Scale Systems

While exact reliability computation for binarystate networks is NP-hard/#P-hard, existing approximation methods face critical tradeoffs between accuracy, scalability, and data efficiency. This study evaluates 20 machine learning methods across three reliability regimes--full range (0.0-1.0), high reliability (0.9-1.0), and ultra-high reliability (0.99-1.0)--to address these gaps. We demonstrate that large-scale networks with arc reliability 0.9 exhibit near-unity system reliability, enabling computational simplifications. Further, we establish a datasetscale-driven paradigm for algorithm selection: Artificial Neural Networks (ANN) excel with limited data (size < m), while Polynomial Regression (PR) achieves superior accuracy in data-rich environments (size m). Our findings reveal ANN's Test-MSE of 7.24E 05 at 30,000 samples and PR's optimal performance (5.61E 05) at 40,000 samples, outperforming traditional Monte Carlo simulations. These insights provide actionable guidelines for balancing accuracy, interpretability, and computational efficiency in reliability engineering, with implications for infrastructure resilience and system optimization. Keywords: Binary-State Networks; Network Reliability Approximated Function; Reliability Thresholds; Dataset Scalability; Artificial Neural Networks (ANN); Polynomial Regression; Monte Carlo Simulation (MCS); Binary-Addition-Tree Algorithm (BAT); BAT-MCS 1. INTRODUCTION Modern infrastructure systems--from power grids and communication networks to IoT ecosystems--demand rigorous reliability analysis to ensure operational resilience. These systems are often modeled as binary-state networks, where components (arcs/nodes) operate in either functional (1) or failed (0) states [1, 2, 3]. Within this paradigm, network reliability--the probability of maintaining 2 connectivity between specified nodes under given conditions--serves as a critical performance metric [4, 5-7].