Can synthetic pre-training improve tokamak equilibrium reconstruction with scarce data?

The bottleneck is labels, not model capacity

A tokamak's internal plasma state cannot be measured directly. It has to be inferred from external magnetic diagnostics, a task called equilibrium reconstruction. The standard tool, EFIT, iteratively solves the Grad–Shafranov equation until a self-consistent equilibrium matches the measurements, but its cost and its dependence on good initialization make real-time use difficult.

Fast neural surrogates can replace that iteration, yet they are normally trained on high-quality labeled experimental equilibria. Those labels come from expensive discharge shots, and at the start of a new campaign or on a new device almost none exist. The paper's question is therefore narrow and practical: can cheap simulated equilibria supply the prior that missing labels would otherwise provide?

Simulated equilibria are anchored to real EFIT statistics

The authors build an end-to-end sim-to-real pipeline for free-boundary Grad–Shafranov reconstruction. They perturb profile coefficients along the leading principal components anchored to real EFIT statistics, solve the free-boundary problem with the FreeGSNKE solver, and keep only solutions that pass convergence and physical-consistency filters. This yields 213,924 aligned synthetic input–output pairs without manual labeling.

The real side comes from the open-access FAIR-MAST dataset covering the M5–M9 campaigns. Raw discharges are screened in four steps: complete diagnostics and EFIT reconstructions, restriction to the flat-top phase where the plasma current is above 85% of the shot peak, one matched synthetic equilibrium per retained slice, and retention of only converged, physically consistent solutions. The cascade reduces 11,573 raw discharges to 213,924 real slices from 7,286 discharges.

The model is then trained in two stages: pre-train on synthetic pairs, fine-tune on a limited fraction of real data. The comparison throughout is against a model trained from scratch on exactly the same real fraction, so any gain is attributable to the synthetic prior rather than to more real labels.

Synthetic-only models fail on real discharges

The paper first shows why pre-training, not pure simulation, is the strategy. A model trained on clean synthetic data and tested directly on real discharges produces the highest nRMSE of the compared models — a pronounced sim-to-real gap. Adding simulated diagnostic noise to the synthetic training data partially mitigates the mismatch, but every synthetic-only model still underperforms a model trained on all real data.

That result sets the logic of the method: synthetic data alone cannot reproduce real measurement characteristics, so it is used as a starting point that real fine-tuning then adapts to experimental conditions and device specifics.

In-distribution gains appear only at scarce fractions

On the random in-distribution split, the benefit of pre-training depends strongly on how much real data is available. At 1% real data, fine-tuning after synthetic pre-training improves nRMSE by roughly 22–29% across three noise variants relative to from-scratch training; at 5% the gain is about 10–12%.

The direction reverses as labels accumulate. At 25% and above, gains become negligible or slightly negative — for example −5.6% at 25% and −4.1% at 100% for the clean variant. The authors interpret this as a fully converged from-scratch model already being saturated when the test distribution matches a well-labeled training set. The practical reading is that a transferable prior pays off precisely where labels are missing, not where they are abundant.

The benefit is also largely insensitive to the injected diagnostic noise: clean and noisily pre-trained arms end up with nearly identical fine-tuned accuracy, with nRMSE differing by less than 0.1 at scarce fractions.

Unseen plasma shapes keep the pre-training advantage

The second setting drops the identical-distribution assumption. Using upper and lower triangularity descriptors of the last closed flux surface, the authors define a shape asymmetry δasym = δu − δl and mark the out-of-distribution region as δasym below the 10th percentile of the real diverted-equilibrium distribution, −0.214. Discharges, not individual time slices, are split so that neighboring correlated slices cannot leak across sets; the resulting OOD test set holds 19,009 slices from 775 discharges. These shape quantities are used only to build and analyze the benchmark, not fed to the model.

The synthetic distribution overlaps the dense region of real equilibria but has broader support in the triangularity plane, extending into regions real data sparsely populate. The authors offer this as a plausible mechanism for the robustness they observe. With 1% real data, pre-training cuts nRMSE by roughly 58% under these out-of-distribution shapes, and the gain persists at every real-data fraction rather than vanishing as it did in-distribution.

A future campaign is where the gain is largest

The temporal split is the most application-like test. Discharges are partitioned by campaign: pre-training and fine-tuning use past campaigns M5–M7, and evaluation is on the unseen M9 campaign, mirroring deployment at the start of a new campaign before any of its equilibrium labels exist. The test set contains 17,498 slices from 507 discharges.

Here pre-training wins at every fraction. As real data drops from 5% to 1%, the fine-tuned model's nRMSE stays close to 2.3%, while the from-scratch baseline rises from 3.80% to 6.42%; the relative error reduction grows from 38.6% to 64.0%. At 100% real data the gain is still +11.4%. Visual comparisons on shot 29412 show the from-scratch model distorting the boundary at 1% real data while the pre-trained model tracks the EFIT reference across all four time slices.

Physical consistency is checked separately: predicted flux correlates with EFIT references at R ≈ 0.995, and the plasma current recovered by integrating Jϕ over the EFIT-defined plasma region matches the measured Rogowski-coil signal at R ≈ 0.99.

Inference speed clears the real-time bar

The trained surrogate processes a time slice in about 0.036–0.039 ms on an NVIDIA GeForce RTX 5090 GPU, a throughput of roughly 2.6–2.8 × 10⁴ slices per second. The paper compares this with reported EFIT/EFIT++ runtimes of approximately 0.1–2 s per time slice, depending on grid resolution and hardware. Because inference is a single forward pass, speed stays nearly unchanged across real-data fractions and training strategies.

This matters because the accuracy gains would be of limited use if they came at the cost of the real-time budget that motivates surrogates in the first place.

The prior earns its keep under shift and scarcity together

The paper's own comparison across settings gives the decision rule. When the test distribution matches a well-labeled training set, pre-training is a wash or slightly harmful once real data reach 25% and beyond. When distribution shift and label scarcity coincide — unseen plasma shapes, or a later campaign — pre-training improves accuracy at every real-data fraction tested, and the gap widens as labels shrink.

The authors note that the synthetic pipeline requires no manual labeling and is designed to be transferable to other tokamaks and operating regimes, but they also list cross-machine validation as an open direction, so the results here are established on MAST. Uncertainty quantification is likewise named as future work. For a team deciding whether to invest in simulation-based pre-training, the paper's specific threshold is the one that matters: the payoff is concentrated in the low-label, shifted-distribution regime, with the 1% real-data, cross-campaign case showing the largest reduction at 64.0%.

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