Towards Data-Efficient Cross-Device Generalization of Grad-Shafranov Equilibria via Transfer Learning Neural Operator

Real-time reconstruction of magnetohydrodynamic equilibria is essential for plasma shaping, stability assessment and feedback control in magnetic confinement fusion. However, Grad-Shafranov equilibrium calculations remain largely device-specific and iterative, limiting their use in latency-constrained control settings. Existing neural approaches can accelerate individual equilibrium predictions, but they do not generally provide reusable models across changing plasma boundaries or tokamak geometries. Here we show that equilibrium reconstruction can be recast as a cross-device operator learning problem. We develop a domain-specific neural operator framework that maps geometry and profile parameters directly to the poloidal flux field, replacing repeated solve-on-demand computation with amortized operator inference. Using the analytically tractable Solov'ev family as a controlled Grad-Shafranov testbed, we generate equilibria across eight geometrically distinct tokamak-like configurations and benchmark five neural operator architectures under four transfer-learning strategies. Single-geometry pretraining gives poor transfer to unseen devices, whereas multi-geometry pretraining enables data-efficient adaptation. The Wavelet Neural Operator gives the strongest cross-geometry performance, reaching mean relative L2 errors below 4% with 100 labelled target equilibria and below 2% with full fine-tuning. The predicted magnetic fields satisfy the divergence-free constraint to numerical precision, and four architectures achieve millisecond or sub-millisecond inference. These results identify neural operator pretraining as a route towards reusable, real-time equilibrium inference across fusion device configurations.

Graph Neural Operator Towards Edge Deployability and Portability for Sparse-to-Dense, Real-Time Virtual Sensing on Irregular Grids

Accurate sensing of spatially distributed physical fields typically requires dense instrumentation, which is often infeasible in real-world systems due to cost, accessibility, and environmental constraints. Physics-based solvers address this through direct numerical integration of governing equations, but their computational latency and power requirements preclude real-time use in resource-constrained monitoring and control systems. Here we introduce VIRSO (Virtual Irregular Real-Time Sparse Operator), a graph-based neural operator for sparse-to-dense reconstruction on irregular geometries, and a variable-connectivity algorithm, Variable KNN (V-KNN), for mesh-informed graph construction. Unlike prior neural operators that treat hardware deployability as secondary, VIRSO reframes inference as measurement: the combination of both spectral and spatial analysis provides accurate reconstruction without the high latency and power consumption of previous graph-based methodologies with poor scalability, presenting VIRSO as a potential candidate for edge-constrained, real-time virtual sensing. We evaluate VIRSO on three nuclear thermal-hydraulic benchmarks of increasing geometric and multiphysics complexity, across reconstruction ratios from 47:1 to 156:1. VIRSO achieves mean relative $L_2$ errors below 1%, outperforming other benchmark operators while using fewer parameters. The full 10-layer configuration reduces the energy-delay product (EDP) from ${\approx}206$ J$\cdot$ms for the graph operator baseline to $10.1$ J$\cdot$ms on an NVIDIA H200. Implemented on an NVIDIA Jetson Orin Nano, all configurations of VIRSO provide sub-10 W power consumption and sub-second latency. These results establish the edge-feasibility and hardware-portability of VIRSO and present compute-aware operator learning as a new paradigm for real-time sensing in inaccessible and resource-constrained environments.