Continuous-Time Hazard Forecasting on Networks with Dynamic Ricci Geometry
DOI:
https://doi.org/10.66238/ijrss.v6i2.130Keywords:
Continuous-Time Networks, Hazard Forecasting, Ricci Curvature, emporal Point Processes, Network GeometryAbstract
The prediction of critical events and system failures within complex, evolving networks is a paramount challenge in network science and dynamic systems analysis. Traditional hazard forecasting models predominantly rely on static graph topologies or discrete-time snapshots, thereby failing to capture the intricate, continuous-time evolution of network structures and the underlying geometric deformations that precede structural bottlenecks. This paper introduces a novel framework for continuous-time hazard forecasting on networks by integrating dynamic Ricci geometry. By leveraging the continuous-time evolution of discrete Ricci curvature, specifically adaptations of Ollivier-Ricci and Forman-Ricci curvatures, the proposed methodology quantifies the dynamic geometric properties of edges and nodes as they evolve in real time. We postulate that sharp local curvature drops act as precursor signals for structural vulnerabilities and impending hazards. The framework couples a continuous-time temporal point process with a dynamic message-passing neural network informed by localized curvature metrics. This allows the hazard function to directly ingest geometric deformations, significantly enhancing predictive accuracy for time-to-event outcomes. Extensive experiments across multiple domains, including financial transaction networks, epidemiological spread patterns, and critical infrastructure systems, demonstrate that integrating dynamic Ricci geometry yields substantial improvements in predictive concordance and temporal resolution compared to purely topological or discrete-time baselines. The findings establish a robust mathematical and algorithmic foundation for proactive risk management and anomaly detection in continuously evolving complex systems.
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Copyright (c) 2026 Noémie Garnier, Lucas Noël, Quentin André
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