TCV · HERMES-3 · UPSTREAM → DIVERTOR

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Upstream observations → divertor predictions. Ridge currently performs best.

Follow-up to September 4 · updated September 9, 2026
Summary
September 12–17: models and results

EXPERIMENT 2 · PREDICTION

Upstream plane → native target planes

Study

Two observed fields in; four downstream fields out. Each time uses a fresh upstream observation.

Output fieldTargetModelSamplingColor quantity

Loading native arrays…

Observed upstream

Downstream · same simulation timeTruth → prediction → what was missed

Hover over a target to compare the same cell.

Movie details

Coordinates, colors and scoring protocol

Vertical: native radial index x=16 at the bottom to x=63 at the top. Larger x goes farther into the scrape-off layer. These are cell addresses, not metres. Horizontal: toroidal sample centers ζ=0–71.11° in a periodic 72° wedge. Ben’s raw radial indices include two guards: 18–65 are our 16–63. Selecting inner/outer changes the poloidal slice y, not the radial axis.

Every target retains all 48×81 native cells. Smooth view evaluates their periodic Fourier series at eight display samples per toroidal cell, with radial rows unchanged and no alignment shift. Native view remains available. Both views use identical scores; smooth interpolation can overshoot. Target truth and prediction share one fixed color scale across the 48 displayed frames. Residual uses the same magnitude limit on a signed scale. Fluctuation limits are the 99th percentile of displayed truth amplitude; absolute-field limits use its maximum. Saturated cells are counted under each image. Inputs have separately labeled scales.

Full-field errors use all scored frames and equal weight per native target cell; changing the color transformation never changes those scores. The toroidally varying score removes the instantaneous toroidal mean of each training-mean anomaly (n≠0), with its own zero-anomaly reference. These inspected trajectories do not establish transfer to an independent plasma condition.

What we can predict

Temperature is easier than density. The right-hand panel isolates the toroidally varying structure, so a good broad-profile prediction cannot hide the missed filaments.

Does training along the winding help?

Yes for this GAOT comparison; ridge still wins. Aligned training lowers native-cell MAE and RMSE on all four outputs compared with the matched native-target model. Both completed 400 epochs, with epoch 40 selected by validation. Earlier GAOT already aligned targets: this adds the missing native control.

Full-field RMSE removed relative to the fitting-mean target. Higher is better; 0% means no improvement over that reference.
Target	Native GAOT	Aligned GAOT	Ridge
Inner density	16.6%	22.0%	28.5%
Inner temperature	41.2%	50.4%	58.2%
Outer density	2.6%	3.5%	15.8%
Outer temperature	38.5%	41.3%	46.5%

Component errors and comparison scope

For toroidally varying structure alone, aligned GAOT removes 8.5% / 18.8% of inner density / temperature RMSE and −0.2% / 3.0% at the outer target. Ridge removes 17.7% / 30.9% and 12.1% / 12.0%, respectively. The hard remaining problem is reconstructing those varying structures, especially outer density.

Same upstream Ne/Te, same refined geometry, model and seed; target coordinates alone differ. Predictions are inverted to original native cells before scoring, without display interpolation. One seed, 648 previously inspected regression frames; this is not independent generalization evidence. Existing movie choices retain their historical model identities. ·.

Full-field errors: native GAOT, aligned GAOT and ridge; RMSE reduction in percent — Figure 11. Matched native/aligned GAOT and ridge · refined geometry · 648 regression frames · September 9. Both neural runs completed 400 epochs; validation selected epoch 40. One seed; previously inspected data.

Toroidally varying errors: native GAOT, aligned GAOT and ridge; RMSE reduction in percent — Figure 11. Matched native/aligned GAOT and ridge · refined geometry · 648 regression frames · September 9. Both neural runs completed 400 epochs; validation selected epoch 40. One seed; previously inspected data.

Magnetic map + fitted gain versus ridge

Full-field RMSE reduction for magnetic map with fitted gain and Fourier ridge, four downstream outputs. — **Figure 2.** Controlled plane benchmark, the same 648 scored times. A fitted gain improves the magnetic copy, but Fourier ridge removes more error. Full-field and n≠0 scores have separate fitting-mean references. Higher RMSE reduction is better; negative is worse than the reference.

Toroidally varying RMSE reduction for the same two models and outputs. — **Figure 2.** Controlled plane benchmark, the same 648 scored times. A fitted gain improves the magnetic copy, but Fourier ridge removes more error. Full-field and n≠0 scores have separate fitting-mean references. Higher RMSE reduction is better; negative is worse than the reference.

Exact baseline scores, including the unchanged-amplitude map

Controlled rerun: regression-block RMSE reduction versus the fitting-mean reference ↑
Target	Mapped anomaly	Map + gain	Fourier ridge
Inner nₑ	-525.0%	1.2%	28.5%
Inner Tₑ	-32.8%	32.0%	58.2%
Outer nₑ	-350.3%	3.1%	15.8%
Outer Tₑ	-47.3%	21.4%	46.5%

Where errors sit radially

Inner density physical RMSE versus native radial cell, including the fitting-mean reference. — **Figure 3.** 648 regression times × 81 toroidal cells per radial row. Compare models within each panel: density uses 10¹⁹ m⁻³, temperature eV. The dashed curve is the fitting-mean reference. Radial x=16–63 is a native cell address, not metres.

Inner temperature physical RMSE versus native radial cell, including the fitting-mean reference. — **Figure 3.** 648 regression times × 81 toroidal cells per radial row. Compare models within each panel: density uses 10¹⁹ m⁻³, temperature eV. The dashed curve is the fitting-mean reference. Radial x=16–63 is a native cell address, not metres.

In the archived matched pilot, ridge beats GAOT on all four outputs. GAOT stopped at epoch 192 of 400; that does not establish the ceiling of neural prediction.

Predicted field	Mean reference MAE ↓	Linear ridge MAE ↓	GAOT MAE ↓	Ridge MAE removed ↑
Inner density 10¹⁹ m⁻³	0.01685	0.01212	0.01401	28.1%
Inner temperature eV	1.481	0.5343	0.6703	63.9%
Outer density 10¹⁹ m⁻³	0.02288	0.01831	0.02429	20.0%
Outer temperature eV	1.379	0.5714	0.726	58.6%

Full-field RMSE and prediction correlation

Correlation compares predicted and true target anomalies, pooling matching cells and times after subtracting each cell’s training-time mean. It is not upstream-versus-downstream correlation or percent accuracy.

Field	Ridge: correlation / RMSE reduction	GAOT: correlation / RMSE reduction	Physical RMSE: ridge / GAOT
Inner density	0.695 / 27.5%	0.594 / 17.7%	0.0157 / 0.01783
Inner temperature	0.910 / 58.8%	0.873 / 51.3%	0.7636 / 0.9029
Outer density	0.533 / 15.7%	0.228 / -11.6%	0.02523 / 0.03338
Outer temperature	0.848 / 47.1%	0.780 / 36.5%	0.9397 / 1.129

Physical units match the MAE table. Reference RMSE is the error of the cellwise training mean. MSE skill = 1 − MSE/reference MSE; RMSE reduction uses the square root and is a different number.

How much varying structure was recovered?

Varying pattern only (n≠0)	Ridge RMSE removed ↑	GAOT RMSE removed ↑
Inner density	17.8%	1.9%
Inner temperature	31.3%	20.9%
Outer density	12.4%	-19.6%
Outer temperature	13.1%	-6.8%

· Summary
September 12–17: models and results.

What the restricted view tells us

The older pilot predicts complete target planes from a strip at one toroidal angle. Four input frames improve the recorded full-field scores. This is an exploratory result with the validation limitation stated above.

Observed simulation-window cell centers on the actual older 85604 poloidal mesh. — **Figure 4.** Older 85604 pilot. Left: the actual 48×9 observed field strip on its older mesh. Right: complete native target-plane errors for one versus four input times, scored over 189 later frames. Inputs are exact Ne/Te/φ, without optics. Different data and preprocessing make this exploratory, not a controlled comparison with the full-plane benchmark.

Older window-to-plane prediction RMSE reduction using one versus four input frames. — **Figure 4.** Older 85604 pilot. Left: the actual 48×9 observed field strip on its older mesh. Right: complete native target-plane errors for one versus four input times, scored over 189 later frames. Inputs are exact Ne/Te/φ, without optics. Different data and preprocessing make this exploratory, not a controlled comparison with the full-plane benchmark.

Exact window scores and scope

Window pilot: RMSE reduction versus the training-mean reference ↑
Target	1 input frame	4 input frames
Inner nₑ	20.6%	22.2%
Inner Tₑ	44.4%	46.9%
Outer nₑ	7.2%	12.6%
Outer Tₑ	46.4%	48.6%

The plane and window runs use different records and inputs, so their scores do not isolate the effect of restricting the view. A real camera adds emissivity, line-of-sight integration and an optical footprint. None of those is implemented in this field-strip pilot.

EXPERIMENT 1 · CONNECTION

Was the mapping wrong?

Our geometry-only forward copy had a reversed shift; that is fixed. The separate target-to-upstream alignment used for the lag curves already had the correct sign. Ben’s script and the now-accessible refined mesh confirm the convention. We score only the connected SOL rows x=16–63.

Axisymmetric revolution of the verified refined 85604 mesh, with upstream and both target rings identified. — **Figure 9.** Verified refined 85604 mesh. Left: fixed-y rings around the torus at radial cell x=32; the purple curve is a poloidal coordinate path, not a field line. Right: the same mesh in physical R and Z (metres). The prediction movies retain native radial/toroidal coordinates..

Physical R-Z cross-section of the verified refined mesh, showing native radial and poloidal locations. — **Figure 9.** Verified refined 85604 mesh. Left: fixed-y rings around the torus at radial cell x=32; the purple curve is a poloidal coordinate path, not a field line. Right: the same mesh in physical R and Z (metres). The prediction movies retain native radial/toroidal coordinates..

Figure 13 · Explore the mesh and plasma volume

Unmodified frame from Ben’s torus movie at the same simulation time — **Figure 13.** The actual simulation on Yichen’s newly accessible refined mesh. Surface mode shows one radial row with cross-sections at the cut boundaries; volume mode includes the data between all SOL rows. Cut angle moves the boundary around the torus; Visible arc sets the retained sector (360° restores the full torus). In Poloidal cross-section view, Cut angle selects the displayed slice. Smooth geometry passes through the supplied R/Z samples, and field interpolation follows the magnetic winding between poloidal planes. Original samples are preserved. The source is a periodic 72° wedge; a 360° view repeats it five times. These 48 frames are simulation truth; plane predictions and scores are unchanged..

Upstream pattern mapped to the target

OMP = outer midplane; B = magnetic field. Shift the upstream pattern along the magnetic connection, keeping its amplitude unchanged.

Native upstream electron-temperature fluctuation at 13.7000 ms. — **Figure 8.** Ben’s snapshot time, 13.7000 ms: upstream temperature fluctuation → the same field pushed along B → actual outer target. All panels use one symmetric ±4.44 eV scale, with native cells and no smoothing. The unchanged-amplitude copy has 1.88× the zero-fluctuation reference RMSE. Geometry connects locations; it does not preserve the target amplitude.

The same upstream fluctuation pushed to the outer plane with run-specific zShift. — **Figure 8.** Ben’s snapshot time, 13.7000 ms: upstream temperature fluctuation → the same field pushed along B → actual outer target. All panels use one symmetric ±4.44 eV scale, with native cells and no smoothing. The unchanged-amplitude copy has 1.88× the zero-fluctuation reference RMSE. Geometry connects locations; it does not preserve the target amplitude.

Ben’s original movies

Figure 6a · Ben’s poloidal cross-section

Left: electron density nₑ in m⁻³ on a logarithmic color scale; successive labeled powers of ten differ by a factor of 10. Right: (nₑ − ⟨nₑ⟩ζ)/⟨nₑ⟩ζ, a dimensionless departure from the toroidal mean. A value of +0.10 means 10% above that mean; −0.10 means 10% below. Red is above, blue below, and white near the mean. Here R is distance from the machine’s axis and Z is physical height, both in metres. These axes differ from Figure 5’s radial index and toroidal angle.

Figure 6b · Ben’s half-torus reference

The colorbar again shows (nₑ − ⟨nₑ⟩ζ)/⟨nₑ⟩ζ, not density in m⁻³. Its displayed range differs from the poloidal movie, so identical redness across the two movies need not mean the same fractional amplitude. The torus shape gives spatial context; a rotation of the view is not plasma motion. No one-to-one radial-index assignment to its exposed surface is asserted here.

Figure 7 · Ben’s original five-row snapshot and source script

Ben’s original five-row snapshot: inner truth, mapped upstream to inner, upstream, mapped upstream to outer, outer truth; density left and temperature right — Figure 7. Original Toroidal Snapshot.png, unchanged, at 13.7000 ms. Purple rows are geometry-only mapped upstream fluctuations. Each panel has its own physical-unit color scale. The 486 horizontal display samples are Fourier resampling of 81 native toroidal samples; smoothing adds no simulation resolution.. Reproduced scores and amplitude-sensitive errors:.

Did the outer leg become more connected?

The stronger inner-leg match remains in this record after the checked mapping. Temperature is more connected than density, and the varying-pattern peak remains near zero sampled delay. Those are measured relationships; the map check does not establish the physical cause of the asymmetry.

Density: aligned upstream-target correlation versus time lag, paired with mapped-copy RMSE. — **Figure 1.** Experiment 1, full 85604, 1936 frames, SOL only. Top: mapped upstream–target correlation of the toroidally varying time-mean anomaly. Bottom: unchanged-copy RMSE divided by zero-anomaly RMSE; lower is better, 1 is the reference. Positive lag samples the target later. A near-zero pattern peak does not measure a transport speed.

Temperature: aligned upstream-target correlation versus time lag, paired with mapped-copy RMSE. — **Figure 1.** Experiment 1, full 85604, 1936 frames, SOL only. Top: mapped upstream–target correlation of the toroidally varying time-mean anomaly. Bottom: unchanged-copy RMSE divided by zero-anomaly RMSE; lower is better, 1 is the reference. Positive lag samples the target later. A near-zero pattern peak does not measure a transport speed.

Why a lag peak is not a sound-speed measurement

Ben’s distinction matters: advection and conduction/diffusion act together, and conditions vary along the field line. A local target sound speed is not a path-integrated transit model. These passive correlation curves do not measure an imposed perturbation’s travel time. The n=0 component is the toroidal average and can still evolve in time; it is not automatically a static equilibrium.

September 4 follow-up

The refined mesh and magnetic shift are checked. Field alignment improves GAOT across all four target outputs; Fourier ridge still has lower errors. Recovering toroidally varying structure remains the main challenge.

One seed on a previously inspected 85604 regression block. The window results are an older exploratory pilot, not an optical-camera benchmark. Same-time reconstruction, not a future-time forecast.

The physics and the models, simply

A tokamak confines plasma with a twisting magnetic field. Outside the confinement boundary, open field lines lead to the divertor targets. The plasma can change along those lines through flows, heat transport, sources and losses; a connected line need not carry an unchanged image.

Experiment 1: compare actual upstream and target fluctuations after accounting for magnetic geometry. Experiment 2: learn from earlier upstream/target pairs, then predict later target fields using only upstream observations. These movies reconstruct each observed instant; they do not integrate a complete plasma state forward in time.

The models: a magnetic map copies a pattern with the correct twist; a fitted gain also changes its amplitude. Fourier ridge learns how upstream radial profiles combine into downstream profiles, separately at each toroidal wavelength. GAOT learns a nonlinear mapping. The controlled comparison tests whether its coordinate correction improves prediction under the same fitting and scoring protocol.

Next: use the verified comparison and errors by radial row and wavelength to choose the next change, then define a physically meaningful camera footprint and measurement before claiming camera performance.