Physics-informed Neural Operator Learning for Nonlinear Grad-Shafranov Equation

Realizing the symbiotic potential of AI and fusion energy requires bridging a critical "sim-to-real" gap. Models trained on simulations must generalize reliably under distribution shifts in safety-critical workflows. Focusing on the strongly nonlinear Grad-Shafranov equation (GSE) for tokamak equilibria, we propose a physics-anchored operator learning framework. Through systematic benchmarking across neural operator instantiations, we identify the Transformer-KAN Neural Operator (TKNO) as the state-of-the-art performer. Crucially, we adopt a semi-supervised paradigm that synergizes sparse data supervision with physical loss constraints. This approach significantly mitigates the catastrophic collapse often observed in purely data-driven methods under boundary-shape distribution shifts, thereby ensuring robust extrapolation. Validated on experimental discharge data from the EXL-50U tokamak, the model achieves high-fidelity equilibrium prediction (RMSE < 1.3%) with millisecond-level inference. These results demonstrate that AI has the potential to significantly accelerate fusion research and development.