RESEARCH NOTE · 12–17 SEPTEMBER 2026

What can an upstream patch tell us about the divertor?

Nearby sections are predictable. Reconstructing the whole leg from one observation is harder. Ridge remains a strong reference; longer attention training and small-window curricula have not established an advantage.

85604 · seed 0 · already-inspected evaluation record · archived results reviewed 17 September · physics figures updated 18 September

Inspect the reconstructed plasma

Compare the actual fields, their motion and their fluctuation scales. These are the completed experiments from before the new regional benchmark. Within each comparison, both models observe the same y18 cells and fields.

Model comparisonFieldMovie sectionDisplayed component

Scale scopeMovie residual contrast

Loading verified numerical fields…

Hover over a cell to inspect its numerical value.

Movie. First 64 consecutive regression frames, Δt = 2.610 μs, at native resolution. All panels share the same time. Top: observed y18 and downstream truth. Middle: two predictions. Bottom: prediction minus truth. In the default view, each panel has its own instantaneous toroidal mean removed; this exposes non-axisymmetric structure without rescaling its amplitude. Axes are radial index and toroidal angle, not a Cartesian camera image. This is same-time reconstruction repeated through the movie, not temporal forecasting or particle tracking. The row x is a mesh label, not major radius R.

Figure 1. Structure at y31. All 648 regression frames. Radial distance is arc length along the actual mesh at this section, measured from native x16 for every support. Thin strips show signed mean-profile and fluctuation-RMS differences from truth, centered on zero with magnified axes shared by both models. These are differences of profiles, not cellwise absolute errors. The scale selector locks vertical axes across comparisons or focuses them on the selected comparison; it never rescales models separately. Fluctuation RMS removes the instantaneous toroidal mean. One-sided mode power sums to that fluctuation variance; n = 5k because the periodic simulation wedge covers one fifth of the torus. Power is shown without normalization to unit variance. A correct spectrum alone does not establish correct phase or prediction; the accompanying errors test that. PDF · SVG.

Matched truth and predicted toroidal space–time plots at a fixed native radial row — **Figure 2.** **Is the structure moving?** All 648 consecutive regression frames at y31, with one shared colour scale fixed from fitting data. Rows x40, x22 and x54 are declared representative rows for the full, low and high comparisons, respectively. These are f − ⟨f⟩ζ; their signs and amplitude are preserved. Movie panels report the fraction of cells outside the colour range. The scale selector also controls these time maps; amplitudes are never normalized separately by model. PDF · SVG.

Native full-field and toroidally varying prediction errors versus field-line distance — **Figure 3.** **Where does reconstruction fail?** Full-field MAE and toroidally varying RMSE at all thirteen downstream sections, over all 648 frames. Distance is averaged over the selected radial rows; individual field lines have different lengths. Only two matched competitors are overlaid. The attention example is the mixed-pretraining/equal-rollout-loss arm, chosen to identify the method rather than select the lowest regression error. PDF · SVG.

Pressure and parallel particle transport

For the five-field, full-width direct models, form pₑ = e nₑTₑ and Γ∥ = nₑVᵢ entirely from predicted fields. A good temperature image need not preserve either product.

Pressure and signed parallel particle-flux-proxy RMSE and signed bias versus field-line distance — **Figure 4.** All 648 regression frames, native x16–63, five fields in and out. Upper panels: RMSE, with the fitting-time mean of the instantaneous observable as reference. Lower panels: signed prediction bias, with zero marked. The nₑVᵢ quantity is a **cell-centred parallel particle-flux proxy**; it is not radial E×B transport, target-normal loading or total heat flux. No target truth is substituted into predicted products. No full conservation claim is made. This figure always refers to full-width ridge versus U-Net, independently of the movie selector above. PDF · SVG.

Native errors were recomputed from the displayed movie sources and checked against the archived scores. Spectral normalization was checked by Parseval's identity. Numerical checks and source hashes. The inspected record, single seed, fixed historical crops and unequal training budgets remain limitations.

One task, three coordinates

We observe a simulated field at section y18 and reconstruct sections y19–y31 at the same time. This is spatial reconstruction, not a forecast through time or a tracked particle.

Verified refined R-Z mesh with the observed y18 and downstream y25 and y31 sections — **Figure 5.** Actual refined mesh used by the simulation, outer-leg SOL x16–63. x indexes radial layers, y the poloidal sections, and z toroidal samples. The poloidal drawing suppresses toroidal winding; the model mapping uses the run's zShift. R is major radius, not the index x. Inspect the 3D mesh → · PDF.

Full-section models use verified zShift alignment and are scored back on native target cells. The newer nine-cell windows follow winding by selecting native neighbors and supplying fractional offsets; their training truth is not interpolated. Low/high bands refer to radial index on the same outer leg, not inner/outer divertors.

Numerical results and experiment details

Open the archived study tables and route comparisons

1. Additional inputs helped the early ridge screen

At fixed y18 and the same x44–59 target cells, potential improved density and temperature predictions more than pressure alone. This was an early crop, not a demonstrated shear-isolated region.

Input fields	Density MAE [10¹⁹ m⁻³]	Temperature MAE [eV]
nₑ, Tₑ	0.01320	0.2996
+ φ	0.01063	0.2658
+ Vᵢ	0.01146	0.2810
+ Pₑ	0.01314	0.2988
All five	0.01055	0.2622

Table 1. Outer y31 native-cell error; outputs remain nₑ,Tₑ. “+” adds one field to nₑ,Tₑ. All five means nₑ,Tₑ,φ,Pₑ,Vᵢ. Pressure is derived from density and temperature, so it is not an independent exact measurement.

2. Accurate neighboring predictions do not automatically compose

Radial band	Direct y18→31 [eV]	Predicted chain [eV]	Actual y30→31 [eV]
low	0.9098	0.9581	0.0212
high	0.2256	0.2237	0.0081

Table 2. Three-field band ridge, y31 temperature MAE [eV]. Low=x16–28; high=x48–60. The last column receives an extra downstream observation; it diagnoses local learnability and is not an upstream-only competitor.

━━ Direct: only y18 observed · ┄ Chained: predicted predecessor · ·· True-input: actual predecessor

Figure 6. Three-field band ridge. Separate panels avoid mixing field units and radial populations. True-input is an extra-observation diagnostic; its low error is not a deployable chain score. Native-cell MAE over all 648 evaluation frames. Index spacing is not uniform physical distance.

Full-width three-field route	Ridge Tₑ MAE [eV]	U-Net Tₑ MAE [eV]
Direct	0.5403	0.5710
Specialist chain	0.5727	0.7062
Shared chain	0.6979	0.6973

Table 3. Full-width y31 comparison, x16–63. These values are not directly comparable to one-band values above. Both architectures predict the same three fields; their training budgets are not compute-matched.

3. Longer attention training did not resolve the endpoint gap

All eight first-step arms now have completed training records. High-band endpoint temperature MAE spans 0.339–0.360 eV, versus 0.226 eV for same-band direct ridge. Low-band attention spans 0.950–0.996 eV, versus 0.910 eV for ridge. A pass cap is not proof of convergence.

Eight-arm results and training selection

Band	Pretraining	Rollout loss	y31 Tₑ MAE [eV]	Passes / selected
low	mixed	equal	0.9938	5 / 2
low	mixed	first4	0.9957	5 / 2
low	first	equal	0.9836	5 / 2
low	first	first4	0.9500	10 / 9
high	mixed	equal	0.3393	8 / 5
high	mixed	first4	0.3404	8 / 5
high	first	equal	0.3601	8 / 5
high	first	first4	0.3469	10 / 7

Mixed = balanced teacher-forced transitions; first = specialize on y18→19. Equal = equal rollout-step weights; first4 = first step weighted fourfold. Every final checkpoint uses the same unweighted full-rollout validation criterion. The low/first/first4 arm is explicitly marked unconverged in its metadata.

A separate frozen-model intervention replaced the first prediction with ridge or exact y19. It did not clearly improve y31. Better initialization alone did not rescue that frozen chain; this is distinct from retraining.

4. Small native windows: neighboring rows help ridge; curriculum has no consistent win

Five-row native-window MAE across all downstream sections — **Figure 7.** Five-row × nine-cell observations; identical central-row targets within each band. All 648 regression frames. Curves compare direct ridge, full-rollout attention and curriculum attention. These are historical fixed-band local-window fits, not the new regional benchmark. PDF · SVG.

Band	Input rows	Model	Density MAE [10¹⁹ m⁻³]	Temperature MAE [eV]
low	1	Ridge	0.02770	0.9540
low	1	Attention · full	0.02793	1.0294
low	1	Attention · curriculum	0.02810	1.0016
low	5	Ridge	0.02767	0.9106
low	5	Attention · full	0.02792	0.9628
low	5	Attention · curriculum	0.02826	1.0099
high	1	Ridge	0.01227	0.2734
high	1	Attention · full	0.01248	0.2956
high	1	Attention · curriculum	0.01241	0.4039
high	5	Ridge	0.00924	0.2575
high	5	Attention · full	0.01254	0.3147
high	5	Attention · curriculum	0.01267	0.4016

Table 4. Native y31 errors on identical central-row cells within each band. Five-row models also predict their neighboring rows. Curriculum uses horizons 1,2,4,8,13 over successive two-pass stages. No broad neural advantage is established; low-band density remains difficult for every listed method.

What each model actually does

Figure 8. Model machinery, separated from the prediction route. Direct, specialist and shared chains can use ridge or U-Net. Growing-history attention keeps the original observation and all generated sections. During rollout training, downstream truth supplies the loss; it is not fed back as an observation.

Machinery	What it learns	How it was trained
Fourier ridge	A regularized linear map between fields and radial rows, independently for each toroidal Fourier mode.	Fitting-only normalization; penalty selected on chronological validation.
Compact U-Net	A convolutional encoder/decoder linking neighboring cells at several spatial scales.	Field MSE; periodic toroidal padding, replicated radial boundaries; maximum 100 epochs with validation/early stopping.
Growing-history attention	Patch tokens from observed y18 and earlier generated sections; attention predicts the next section.	Original short pilot: 200 warm-up + 100 continuation updates. Follow-ups use complete fitting passes and backpropagation through rollout.
Local-window ridge	A linear map on flattened one/five-row × nine-cell patches.	Direct and specialist-chain fits; no artificial Fourier periodicity across window edges.

Direct

observed 18 → predicted 19…31

One model predicts all requested destinations.

Specialist / shared chain

18 → 19 → 20 → … → 31

Specialist: one model per transition. Shared: one reused model. Each receives only the preceding predicted section.

Growing history

[18] → 19
[18, 19̂] → 20
[18, 19̂, 20̂] → 21

The original observation stays available. Generated history adds computation, not new measurements.

Single radial layer in the first study still contained all 81 toroidal samples. The newer single-row window contains only nine. Full width=x16–63; narrow bands=x16–28 or x48–60. These observation budgets must not be conflated.

Field names: nₑ=density, Tₑ=electron temperature, φ=potential, Pₑ=electron pressure, Vᵢ=ion parallel velocity. Historical three-field state=nₑ,Tₑ,φ; five-field state adds Pₑ,Vᵢ. The new regional C5P state is different: nₑ,Pₑ,Pᵢ,φ,Vᵢ. It includes ion pressure and is not a completed result of this page.

How to read the evidence

MAE is average absolute native-cell error; RMSE penalizes large errors more. These scores aggregate all 648 evaluation frames, not one movie frame. The fitting-mean reference, toroidally varying error and dynamic amplitude distinguish background reconstruction from turbulence. A smooth movie can have a good background and still miss moving structures.

Fit frames: 0–975. Validation: 1006–1257. Inspected regression: 1288–1935. Both 30-frame gaps remain. Results are exploratory on one record and one seed, with unequal model compute. No independent-shot generalization or transport-law discovery follows.

The completed figures support useful local relationships, strong dependence on radial context, and an unresolved long-range reconstruction problem. They do not establish that the plasma is linear, that shear alone causes the gap, or that more training must beat ridge.

Earlier verified plane movies →Model and training guide →Reviewed numerical results →

Audit trail

This page is generated from archived numerical exports and completion metadata. Older narrative notes saying first-step/window runs were pending are superseded by the completed records used here. No new experiment was run.

Source paths, SHA-256 hashes and extracted tables