AI Surrogate Modeling for Real-Time Tokamak Equilibrium Prediction: Benchmarking Neural Architectures and Validation on EXL-50U

The boundary and divertor plasma govern how a tokamak exhausts power and particles, setting heat fluxes, target conditions, and the onset of detachment. Predicting these quantities is essential for operating current and future devices, but edge simulations that resolve them are too slow for parameter scans, optimization, or real-time control. Machine-learning surrogates offer a fast alternative, yet most are forward-only: they cannot recover input parameters from observations or assess the reliability of their predictions. We introduce a cycle-consistent neural surrogate for edge plasmas, combining a conditional U-Net forward model with an optimization-based inverse method built on the frozen forward network. The forward model maps five control parameters to two-dimensional plasma-state fields on the SOLPS-ITER mesh; the inverse method enforces consistency between forward and inverse predictions, a self-supervised quality check needing no ground-truth labels at inference. An ensemble of multilayer perceptrons also predicts electron temperature and density profiles at the outboard midplane and divertor targets, with uncertainty estimates that flag where more simulations are needed. The forward model achieves normalized root-mean-square errors below 2.6% and Pearson correlations above 0.95 for all fields. Cycle-consistency regularization raises the average cyclical $R^2$ from 0.59 to 0.99 without degrading forward accuracy and enables recovery of the core fueling rate; all five control parameters are recovered with Pearson $r\ge0.97$. A $k$-d tree warm start yields a database completion rate above 95%, versus roughly 30% outright failures when cold-started. With about $4\times10^6$ parameters, the model produces full 2D predictions in milliseconds, five to six orders of magnitude faster than SOLPS-ITER, enabling real-time control, parameter scans, uncertainty analysis, and digital twins.

Fast surrogates for tokamak boundary-plasma simulation are typically deterministic regressors mapping a global operating point to a flattened vector of cell values. Near the divertor detachment transition the steady state is not reliably single-valued. A point estimate must average over qualitatively different plasma states, and it arrives with no statement of confidence. Moreover, the flattened vector representation discards the geometric structure of the SOLPS-ITER mesh. This work addresses both problems. We unroll the curvilinear mesh into three fixed-size image tensors whose layout preserves cell adjacency and inverts exactly, letting a convolutional network act on the geometry without loss of information. A conditional flow matching model, well suited to highly sensitive systems, is then trained on this representation. The result is an efficient, scalable surrogate that captures multiple plausible outcomes even at sensitive operating points. Along a gas-puff scan, the predictive distribution splits into a hot and a cold mode across an early regime transition. A further check on synthetic data with an injected bifurcation of known size confirms the model recovers both branches rather than their average.

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.