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

2026-06-13

AI Summary

This work addresses the challenges of Grad–Shafranov equilibrium reconstruction in magnetically confined fusion—namely, poor cross-device generalization, reliance on iterative solvers, and incompatibility with real-time control—by formulating it as a cross-device operator learning task. The authors propose a domain-specific neural operator framework that directly maps geometric and profile parameters to the poloidal magnetic flux field. For the first time, they integrate multi-device pretraining with neural operators, leveraging five architectures—including the Wavelet Neural Operator—and four transfer strategies to achieve data-efficient equilibrium reconstruction across eight tokamak configurations. Experiments demonstrate that with only 100 target-device samples, the method attains an average relative L² error below 4% (dropping below 2% after full fine-tuning), enforces divergence-free magnetic fields, and achieves millisecond-level inference, thereby validating its transferability, physical consistency, and real-time applicability.

Abstract

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.

Problem

• Grad-Shafranov equilibrium
• cross-device generalization
• data efficiency
• neural operator
• transfer learning

Innovation

• neural operator
• transfer learning
• Grad-Shafranov equilibrium
• cross-device generalization
• data-efficient learning