Network State Prediction and Fault Detection in IoT Using Green’s Theorem and Maxwell’s Equations

Abstract—IoT-based Wireless Sensor Networks (WSNs) are highly susceptible to node faults and energy depletion, which can disrupt critical monitoring applications. In this paper, we present a novel approach for proactive fault detection and network state prediction based on vector-field modeling using Green’s Theorem and Maxwell’s Equations. We propose a clustering scheme with an aggregator at the center of each region and use Green’s Theorem to detect closed-loop imbalances in cluster state. We also incorporate Maxwell’s equations to characterize energy flow and fault dynamics. The mathematical framework provides detailed derivations for network field behavior, and we show how it enables early fault localization and enhanced lifetime. Simulation results confirm that the Green’s Theorem Fault-Detection (GTFD) protocol accurately predicts network stability and dynamically re-stabilizes after faults.