Reconstruction of Unobserved Core Electron Density in Tokamak Plasmas with a Neural Operator Transport Surrogate and Uncertainty Quantification

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.

Plasma experiments observe coupled physical states through sparse, heterogeneous, and incomplete diagnostics. We present a proof of concept toward a multimodal foundation model for plasma state reconstruction during magnetic reconnection, motivated by the Facility for Laboratory Reconnection Experiments (FLARE). Using 250 synthetic VPIC simulations at fixed reference electron beta $β_{e0}=0.2$, with 225 training runs and 25 disjoint validation runs, we train a 5.5M-parameter residual 3D U-Net to reconstruct three magnetic-field components and electron density from incomplete observations. The model combines spatial-only pooling, which preserves all 24 temporal frames, with global spatiotemporal self-attention and rotary positional encoding. Independently masking magnetic and density modalities across random, grid, block, and temporal patterns enables sparse sensing, cross-modal completion, density super-resolution, and temporal completion with a single set of weights and no task-specific retraining. With density fully hidden, just 0.1% magnetic spatial visibility reduces median density NRMSE from approximately 0.9 to 0.1. Conversely, observed density improves current-density reconstruction when magnetic data are absent or extremely sparse. With no magnetic observations, roughly 1% density visibility approaches the density reconstruction accuracy achieved with fully observed magnetic fields, although current structure remains more dependent on direct magnetic measurements. Full magnetic conditioning also stabilizes completion of missing future density frames. These results demonstrate bidirectional cross-modal predictive coupling within this simulation regime. Generalization across plasma regimes or to experimental measurements remains untested.

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.