Virtual Sensing to Enable Real-Time Monitoring of Inaccessible Locations & Unmeasurable Parameters

Abstract

Real-time monitoring of safety-critical interior states is an open problem across energy, environmental and industrial systems where direct instrumentation is infeasible. Approaches based on governing equations, discrete state vectors or fixed sensor locations cannot deliver mesh-independent, field-level reconstruction at arbitrary interior coordinates in real time. Here we introduce neural operator-based virtual sensing, a framework for recovering inaccessible interior fields from sparse boundary measurements, instantiated with MIMONet, a multi-input, multi-output neural operator that fuses heterogeneous inputs and decodes coupled fields through a shared latent representation. Across three engineering-grade evaluations of escalating complexity - confined recirculating flow, pressurized water reactor subchannels and compact power-system heat exchangers - MIMONet attains relative reconstruction error below 5% with sub-millisecond inference, with calibrated uncertainty and noise resilience. We validate the framework on three independent real-world datasets spanning electrochemical energy, atmospheric science and physical oceanography: current-density mapping in a hydrogen fuel cell, wind-speed profiling on meteorological towers, and North Atlantic ocean state from a global reanalysis. MIMONet improves on classical virtual-sensing baselines by 72-84%, including 84% for fuel-cell internal fields recovered from 10% sensor coverage and 83% for hub-height wind speed recovered from lower-level tower sensors. Most notably, it recovers sea-surface height, a field with no direct sensors, from its learned coupling to observed temperature and salinity at 4.1x lower error than the best classical predictor. These results establish operator-based virtual sensing as a practical route to real-time field observability in systems where the states that matter most cannot be measured directly.