Real-Time Sensing of Inaccessible Physical Fields via an Edge-Deployable Hardware-Portable Graph Neural Operator

Real-time inference of inaccessible interior physical fields from sparse boundary observations is a fundamental but unresolved problem in scientific machine learning, with direct relevance to safety-critical monitoring across many engineering applications. Existing neural operators achieve high accuracy but leave deployment to embedded edge platforms unaddressed. Here we introduce VIRSO (Virtual Irregular Real-Time Sparse Operator), the first neural operator with a unique spatial-spectral architecture that explicitly addresses edge-deployment hardware. VIRSO learns a nonlinear mapping from sparse, geometrically disjoint boundary inputs to spatially continuous interior multiphysics fields on irregular unstructured meshes through a spectral-spatial decomposition explicitly aligned with hardware execution: a compute-bound graph spectral pathway and a memory-bandwidth-bound spatial-aggregation pathway, each independently characterized on datacenter and embedded accelerators. The design reduces the inference energy-delay product by 29$\times$ relative to the vanilla graph-operator baseline (206 J$\cdot$ms $\to$ 7.0 J$\cdot$ms on an NVIDIA H200) and enables 17.0 samples/s embedded inference on an NVIDIA Jetson Orin Nano within 7.06 W board-level power, without modification. A mesh-density-adaptive graph construction strategy (V-KNN) simultaneously improves accuracy and reduces graph edge count by 34%. Across three benchmarks with reconstruction ratios from 47:1 to 156:1, VIRSO achieves mean relative $L_2$ errors below 1% with fewer parameters than operator baselines and delivers an inference speedup of $\approx 10^4$ times over the high-fidelity reference solver. To our knowledge, this is the first demonstration of a single-digit-watt neural operator, establishing hardware co-design as a missing ingredient in operator-based inference and a tractable path to real-time deployment.