FlowGMAE: Physics-Constrained Virtual Sensing for Anomaly Detection Beyond Sensor Coverage

Real-world flow networks are only partially observed. Sensors are typically installed on only a subset of edges, leaving much of the network without direct measurements. As a result, the network state is only partially known, and anomalous events outside sensor coverage can easily go undetected. We introduce FlowGMAE, a physics-constrained graph learning framework for learning virtual sensors on partially observed networks. We make three main contributions: (1) a physics-guided graph masked autoencoder operating on the full physical network, with incidence-aware message passing and adaptive masking; (2) a decoder in which conservation directly parameterizes the reconstruction space, analytically determining the constrained component of missing flow while learning only the remaining degrees of freedom; and (3) transferable virtual sensing that combines a time-series foundation model (TSFM) with graph learning for zero-shot transfer and anomaly detection beyond sensor coverage. Experiments on physical flow networks show that FlowGMAE substantially improves flow reconstruction over diverse baselines, with particularly strong gains as the distance from observed sensors increases. Moreover, anomalies on unobserved edges remain detectable from the reconstructed flows, demonstrating the potential of virtual sensing to extend monitoring beyond the physical sensor network.