Graph-Based Latent Dynamical Learning for Distributed Sensor Networks under Partial Observability and Communication Constraints

Abstract

Distributed sensor networks are increasingly deployed in environments where the underlying physical process is high-dimensional, nonlinear, spatially coupled, and only partially observable through noisy local measurements. In such settings, useful inference depends not only on local prediction accuracy but also on the ability to recover coherent global structure from sparse asynchronous observations, preserve stability over long temporal horizons, and operate within communication and computation limits imposed by decentralized hardware. These requirements are difficult to satisfy jointly because spatial dependence, temporal nonstationarity, sensor heterogeneity, and network failures interact in ways that degrade both estimation quality and operational reliability. This paper develops a graph-based latent dynamical framework for distributed sensor networks that integrates spatial topology, latent-state evolution, uncertainty-aware inference, and communication-efficient learning within a common mathematical formulation. The model represents local measurements through graph-coupled latent variables whose dynamics evolve under a structured operator combining diffusion, low-rank global transport, and temporally adaptive residual terms. The resulting formulation supports filtering, smoothing, forecasting, anomaly sensitivity, and network-level state reconstruction while preserving scalability through decentralized optimization and low-dimensional message exchange. The paper analyzes the geometry of the latent representation, the spectral conditioning of the learned transition operators, and the effect of graph regularization on stability and identifiability under missing data and topology perturbations. It also develops a rigorous evaluation protocol for studying adaptation under drift, communication bottlenecks, and sensor faults. The overall perspective emphasizes that reliable learning in distributed sensing systems requires coordinated treatment of latent representation, dynamical structure, and network-aware computation