PHGAT: Persistent homology-enhanced graph attention network for IIoT anomaly detection

The operational safety and efficiency of modern Industrial Internet of Things (IIoT) systems, which generate massive volumes of high-dimensional multivariate time series data, hinge on the early detection of anomalies. However, existing graph-based methods often struggle with the structural instability of dynamically learned graphs and are blind to higher-order, multi-component system dependencies. This paper introduces the Persistent Homology-enhanced Graph Attention Network (PHGAT). This novel framework addresses these critical limitations by pioneering a co-learning paradigm that structurally regularizes dynamic graph learning through topological invariants. Unlike prior works that apply persistent homology to static graphs or as a simple feature augmentation step, PHGAT introduces a principled framework where pH-derived topological features provide global structural constraints, forcing the model to learn meaningful and robust sensor relationships from noisy time-series data. The framework integrates three key innovations: (1) an adaptive graph construction mechanism that dynamically learns sensor relationships by fusing spatio-temporal correlations to model evolving system dynamics; (2) a hierarchical graph attention architecture with cross-scale mechanisms to capture multi-resolution temporal dependencies; and (3) a learnable topological vectorization component that leverages persistent homology to extract robust structural invariants, enhancing model resilience. Extensive experiments on four public IIoT benchmarks–SWaT, SMD, WADI, and SMAP–demonstrate that PHGAT consistently outperforms state-of-the-art methods by a significant margin. Notably, PHGAT achieves an F1-score of 0.976 on SWaT, improving upon the best-performing baseline by 2.24 %, which validates the efficacy of topological regularization in dynamic graph learning for IIoT anomaly detection.