Learning Risk and Communities in Complex Systems: A Review of Temporal Models, Graph Neural Networks, and Fourier Approaches

Abstract

Risk assessment and community detection are two central problems in data-driven decision systems, spanning finance, infrastructure, cybersecurity, transportation, and social networks. In modern settings, both tasks are increasingly defined by (i) temporal complexity (non-stationarity, regime shifts, delays), (ii) relational structure (interacting agents and cascading effects), and (iii) multi-scale frequency behavior (smooth trends vs. abrupt anomalies), motivating learning frameworks that unify deep temporal models, graph representation learning, and Fourier/spectral operators. This review synthesizes progress across three complementary axes: deep temporal learning (e.g., sequence models and transformers for forecasting, anomaly detection, and early-warning), graph-based learning (GNNs, graph transformers, spatio-temporal GNNs, and temporal graph neural networks), and Fourier/spectral learning (graph Fourier transform, spectral filters, wavelets, and frequency-aware graph architectures). We provide a taxonomy that maps model families to learning settings and objectives, compare methods under shared evaluation protocols, and highlight practical design trade-offs such as scalability, stability, interpretability, and robustness. Finally, we outline open challenges—dataset realism, dynamic community ground truth, distribution shift, and frequency-domain generalization—and propose a benchmarking checklist to support reproducible research across risk prediction and community discovery.