Sophelio/fusion-equilibrium-challenge

⚛️ The Fusion Equilibrium Challenge

Predict the shape of a fusion plasma (the magnetic equilibrium, $\psi$) from control inputs and diagnostics alone — without magnetic sensors. Data comes from two tokamaks:

• DIII-D — General Atomics tokamak (San Diego, USA)
• MAST — Mega Ampere Spherical Tokamak (Culham, UK)

In data-science terms this is an image-regression / control problem: predict a 2-D poloidal flux map (efit_psirz) at each EFIT timestep from coil currents (the actuators), Thomson-scattering temperature/density profiles (the sensors), and the machine's fixed coil and diagnostic geometry.

One row per shot. All time-series, profiles, and flux maps are stored as nested arrays within that row. Every time array is in milliseconds (both machines).

⚠️ Diverted plasmas only

Every timeslice in this dataset is a diverted plasma. Limited frames — where the plasma's boundary is set by physical contact with a material surface rather than by a magnetic X-point — have been removed from efit_times and from every column that lives on it, on both machines and all splits.

This makes the problem well-posed. On a limited plasma the last closed flux surface is determined by the wall, and wall geometry is not contained in ψ(R,Z) — so a boundary extracted from the flux map alone systematically overshoots (91% of DIII-D limited frames overshot plasma volume by more than 0.5 m³). Scoring a boundary you cannot infer is not a useful test, so those frames are gone rather than silently down-weighted.

How the frames were classified — the same physical criterion, each machine's best evidence:

	criterion	kept
DIII-D	magnetics_dsep > 0. That column is EFIT's a-file DSEP, a separatrix↔limiter clearance whose sign encodes the configuration (>0 diverted gap, <0 limited). 0% NaN over the corpus.	88.0% of frames
MAST	EFIT++ reports X-point coordinates (efm/xpoint{1,2}) only on frames where it found one. Cross-checked against the flux itself: |ψ(X-point) − ψ_boundary| / |ψ_boundary − ψ_axis| agrees on 97.3% of 184,396 frames, median offset 0.0006.	66.4% of frames

The full-rate input time series (magnetics_*, thomson_*) are not subset — you still get the complete discharge and resample onto efit_times as before. efit_times is simply no longer contiguous.

A caution on MAST's magnetics_dsep. It is not the same quantity as DIII-D's. MAST ships esm/dr_sep_out, the upper/lower divertor balance (δR_sep), which straddles zero for perfectly ordinary diverted plasmas. Its sign is not a diverted/limited indicator — do not use it as one. It remains in train as context only.

🏆 The competition

This dataset backs the Fusion Equilibrium Challenge, a NeurIPS 2026 competition. You do not have to enter to use the data — but if you want to:

• Leaderboard & submission: Codabench competition #17456
• Starter kit (baselines, submission skeleton, local validator): Sophelio/fusion-equilibrium-challenge-starter
• Website (full rules, scoring, glossary): https://fusion-equilibrium-challenge.sophelio.io

There are two challenges, and each grants exactly one award — the mapping is one to one. Both share this dataset, one submission format, and one leaderboard (the challenges are two sortable columns on it).

	Challenge 1 — Intra-machine	Challenge 2 — Cross-machine
What you do	Reconstruct the equilibrium on DIII-D, the machine you trained on.	Take that model zero-shot to MAST — which has no training data at all.
Scored by	S_model on the hidden DIII-D test set	G_ratio = S_MAST / S_DIII-D
Award	Award #1 — $500	Award #2 — $500

S_model = 0.55·R²ψ + 0.15·R²{q95,βN} + 0.10·(1 − D_LCFS) + 0.20·Consistency, where Consistency scores the seven ψ-derived scalars — magnetic axis R_axis/Z_axis, elongation κ, triangularities δ_top/δ_bot, plasma volume, and internal inductance li — computed from your submitted flux map against the same computation on the true flux. You submit only psirz, q95, and betaN. Challenge 2 needs predictions for both machines: a DIII-D-only entry scores G_ratio = 0. A compute-light badge (trains in under 2 h on one GPU/CPU) applies across both challenges.

Phase	Window
Development — public leaderboard, iterate freely	Jul 27 – Oct 18, 2026
Final — blind private fold, decides the winners	Oct 19 – Oct 26, 2026

Note that mast_train does not exist, and that is deliberate: MAST has zero training shots. That is the whole point of Challenge 2.

Splits & configs

Each (machine, role) is its own config, so every config has a clean schema — the two machines have different coil layouts, and the test configs genuinely omit the target column rather than null-filling it:

Config	Split	Shots	Contents
diii_d_train	train	7,041	Full — includes all targets (efit_psirz, EFIT scalars)
diii_d_public_test	public_test	874	Inputs only — all EFIT-derived columns withheld
mast_public_test	public_test	1,206	Inputs only — all EFIT-derived columns withheld

Shot counts are lower than the previous release because the diverted-only re-cut removed shots left with no diverted frames at all: DIII-D 9,113 → 8,794 shots and 2,216,380 → 1,949,000 timeslices; MAST 2,416 → 2,414 shots and 207,066 → 137,563 timeslices.

from datasets import load_dataset

REPO = "Sophelio/fusion-equilibrium-challenge"

# DIII-D training data (with targets)
train = load_dataset(REPO, "diii_d_train", split="train")

# Public test (inputs only — predict efit_psirz at each efit_times step)
d3d_test  = load_dataset(REPO, "diii_d_public_test", split="public_test")
mast_test = load_dataset(REPO, "mast_public_test",  split="public_test")

import numpy as np
shot = train[0]
psirz = np.array(shot["efit_psirz"])   # (T, 65, 65) for DIII-D
times = np.array(shot["efit_times"])   # (T,) ms — predict a flux map at each

Notes on the design:

• No MAST training data. Cross-machine generalization (DIII-D → MAST) is zero-shot by construction — the mast config has only a test split.
• All EFIT-derived quantities are withheld on the test splits. Anything computed by the EFIT reconstruction leaks the equilibrium you must predict, so every one is removed from public_test: the flux map efit_psirz, the EFIT scalars (efit_beta_n, efit_li, efit_q95, efit_r_axis, efit_z_axis, plus the auxiliary/boundary scalars), and magnetics_dsep (EFIT-derived despite its magnetics_ prefix — and on DIII-D its sign is exactly the classification that defined this corpus). Only the coordinate scaffolding is kept — efit_times and efit_grid_R/Z (both machines) — so you know exactly which timestamps and grid to predict on.
• A private test split is held back entirely for final scoring and is not part of this dataset.

The targets — what you predict

The primary target is the 2-D flux map. You submit only the flux map plus q95 and betaN — the two scalars a flux map cannot contain (they need the toroidal field function F(ψ) and the pressure profile p(ψ), neither of which is in the flux geometry). The dataset still ships all EFIT scalar labels (one value per efit_times step) in train as supervision — withheld on the test splits, same as the flux map — but at scoring time the axis, shape and li are derived from your submitted flux map and scored for consistency against the same derivation on the true flux. A good ψ is what earns them.

Key	Shape	Description
efit_psirz	(T, 65, 65) (both machines)	Primary target — poloidal flux map, a 2-D image at each timestep (V·s/rad). Withheld on test.
efit_q95	(T,)	Safety factor at 95% flux surface — submitted scalar. Withheld on test.
efit_beta_n	(T,)	Normalised beta — submitted scalar. Withheld on test.
efit_li	(T,)	Internal inductance ℓi (supervision; derived from your ψ at scoring). Withheld on test.
efit_r_axis / efit_z_axis	(T,)	Magnetic-axis R/Z (m) (supervision; derived from your ψ at scoring). Withheld on test.
magnetics_dsep	(T,)	Context only, not scored. On DIII-D it is EFIT's a-file DSEP (separatrix↔limiter clearance, now >0 on every shipped frame — it is what defined the diverted filter). On MAST it is a different quantity entirely: esm/dr_sep_out, divertor balance. Withheld on test.
(boundary — both machines) efit_lcfs_n, efit_lcfs_r, efit_lcfs_z	(T,) / (T, N)	LCFS boundary contour + valid-point count — provided in train as bonus context. Withheld on test.
(aux — MAST only) efit_beta_p, efit_elongation, efit_psi_axis, efit_psi_boundary, efit_geom_axis_r/z	(T,)	Extra EFIT scalars, MAST only (the DIII-D fetch did not include them). ⚠️ Not in any released config — they are EFIT-derived so they are withheld on test, and there is no mast_train. You will only see them in the starter kit's parquet_data/ demo shots.

dsep is no longer scored at all. It was one of eight consistency scalars in the previous metric and has been dropped, for a reason worth stating plainly: the two machines' dsep columns are not the same physical quantity. DIII-D's is a clearance whose sign encodes the configuration; MAST's is divertor balance (δR_sep). Scoring one functional against both labels was measuring different things per machine. With the corpus now diverted-only, the classification job it also did is gone. Seven scalars remain in Consistency.

Scaffolding (kept on every split):

Key	Shape	Description
efit_times	(T,)	Timestamps (ms) for the target images. Align all inputs to these times.
efit_grid_R / efit_grid_Z	(65,)	Physical R/Z (m) labelling the flux-map columns/rows (both machines).

Both machines ship a clean 65×65 flux map with no NaNs. (MAST's upstream EFIT stores psirz on a doubled 129-column R grid — 65 real columns interleaved with 64 empty ones; this is not a central-column hole but a grid artifact. We drop the empty columns to recover the dense 65×65 grid the data is actually defined on: MAST R ∈ [0.06, 2.0] m, Z ∈ [−2.0, 2.0] m.)

The two machines' flux maps use opposite sign conventions. On MAST the magnetic axis is the maximum of ψ (efit_psi_axis > efit_psi_boundary on 100% of frames); on DIII-D it is the minimum (99.98% of 1,559,340 train frames, with no frame the other way). Amplitudes differ too — a DIII-D flux map has a median frame peak-to-peak of 0.61 Wb/rad against MAST's 0.21, so DIII-D ψ swings roughly 3× wider. This is provenance, not physics: EFIT++/FAIR-MAST stores ψ with the opposite sign to DIII-D's EFIT, and both machines run positive plasma current on essentially every shot. The scorer normalizes the global sign of your submitted flux map, so a correctly-shaped prediction in either convention scores the same. The ~3× amplitude difference is real and is yours to handle.

Inputs

DIII-D actuators — 18 shaping coils magnetics_F{1-9}{A,B} (kA·turn; ~77% of in-window peaks stay within ±200, the extremes reach ~±580), magnetics_ECOILA (ohmic/central solenoid, kA), magnetics_bcoil (toroidal field, kA), magnetics_plasma_current (Ip, kA). MAST actuators — 10 poloidal coils magnetics_p{2-6}{l,u}_current (kA·turn; the set is far more spread than DIII-D's — per-coil median in-window peaks run from ~3 (p3, p6) to ~185 (p2), extremes ~±600), magnetics_sol_current (central solenoid, kA), magnetics_tf_current (toroidal field, kA), magnetics_efps_current (error-field correction, kA), magnetics_plasma_current (Ip, kA).

Both machines — Thomson scattering core + edge profiles (thomson_core_*, thomson_edge_*: electron temperature Te in eV and density ne in m⁻³, with time bases). Each system carries a single spatial-coordinate array, and the axis differs by machine: thomson_core_R is radius (DIII-D constant ≈ 1.94 m vertical chord; MAST per-channel R), and thomson_edge_spatial is Z on DIII-D (−0.09 to −0.04 m across the corpus, near-constant within a shot) but R on MAST (≈ 1.3–1.5 m). There is no separate *_z/tan_z column.

Note: magnetics_dsep used to be listed here as an input. It is EFIT-derived, so it is present in train as context and withheld on test.

Time bases: each machine exposes a shared magnetics_time; on DIII-D, Ip sits on its own ADC (magnetics_plasma_current_times). In train, magnetics_dsep_times equals efit_times on every shot (it and magnetics_dsep are withheld on test).

DIII-D's magnetics_time has two sampling rates. 4,932 of 7,041 train shots (70.0%) carry a ~20 kHz base — 480,256 samples at dt = 0.049927 ms — and the remaining 2,109 (30.0%) a 2 kHz base of 49,152 or 50,176 samples at dt = 0.5 ms. The public-test mix is the same within a few points (586 shots, 67.0%, at ~20 kHz). Six distinct array lengths occur in all, so do not hard-code a sample count or a rate — read magnetics_time per shot. The record spans roughly −9.4 s to +20.1 s (median duration 24.0 s), so only about 20% of its samples fall inside the efit_times window.

MAST's magnetics_time has two populations. 1,092 of 1,206 test shots carry (30000,), a uniform 0.2 ms / 5 kHz grid. The 114 early-campaign shots carry (15482,), which is the union of two acquisition grids — the poloidal set at 5 kHz over a shorter window, the toroidal field coil at 1 kHz over the full record — so on those shots each column is NaN on the samples belonging to the other grid. No data is missing; both native grids fully cover the plasma window on every shot. This is the layout FAIR-MAST's own amc group ships.

Missing values: always NaN, never a parquet null

Every floating-point column in this release is null-free at every nesting depth, and there are no ±inf values anywhere — wherever a value is absent, it is a plain NaN. So every column converts cleanly to a dense float array, on both machines, with no object-dtype surprises:

v = np.asarray(shot["magnetics_tf_current"], dtype=float)

Which columns carry NaN, how much, and what to do about it are yours to find out and decide — that is part of the problem, not a defect in the data.

🆕 Machine geometry — where the coils and chords actually are

A coil current only tells you something once you know where the coil is, and a Thomson measurement only localises a profile once you know where the chord is. Both are now shipped, on every row of every split (they are inputs, so nothing is withheld):

Key	Shape	Description
coil_name	(C,) str	Coil (or conductor element) identifier
coil_input_column	(C,) str	The join key — the current column this geometry belongs to, e.g. magnetics_F1A
coil_R / coil_Z	(C,)	Centre of the conductor rectangle (m)
coil_width / coil_height	(C,)	Its radial / vertical extent (m)
coil_angle1 / coil_angle2	(C,)	Parallelogram skew angles (degrees) — see below
thomson_chord_name	(N,) str	Chord identifier, IMAS-style (TS_core_*, TS_tangential_*, TS_divertor_*)
thomson_chord_R / thomson_chord_Z	(N,)	Chord position (m)

The two machines describe their coil sets at different granularity, and that is not an inconsistency. DIII-D ships C = 19 lumped rectangles (18 F-coils + the ECOILA solenoid) — the representation EFIT's own mhdin.dat uses. MAST ships C = 812 individual conductor elements from the FAIR level-2 pf_active IDS — one row per conductor turn, the solenoid alone accounting for 656 — so a MAST coil's turn count is how many rows share its coil_input_column (P2 = 20, P3 = 8, P4 = 23, P5 = 23, P6 = 4). Use coil_input_column to join either one back to the currents; do not read the row counts as a discrepancy.

There is no coil_turns column, and you do not need one. Coil currents are already in ampere-turns: each DIII-D F-coil's 58 or 55 turns is folded into magnetics_F*, and MAST's p{2-6}{l,u}_current are natively kA·turn. That is the quantity a Green's-function calculation wants — total ampere-turns per rectangle — so F4A and MAST p4u are directly comparable: median in-window peak 137 kA·turn and 171 kA·turn respectively, over every shot in each config. Plasma current is in kA on both machines. Four channels stay in plain kA rather than kA·turn because no trustworthy turn count exists for them: DIII-D ECOILA and bcoil, MAST sol_current and tf_current (and efps_current, which is not a coil).

Six DIII-D F-coils are parallelograms, not rectangles. coil_angle1 / coil_angle2 are EFIT's AF / AF2 shear angles in degrees, and they are non-zero on F5A/F5B (±45°), F6A/F6B (±92.4°) and F7A/F7B (±108.06°). For those six, (R, Z, width, height) alone under-describes the conductor.

0.0 means "no skew — a plain axis-aligned rectangle." It does not mean the sides lie flat. This is EFIT's own convention: its geometry code branches on if angle1 == 0 and angle2 == 0 to emit a rectangle rather than a polygon, and on write-out it normalises 90 → 0, i.e. 90° and 0° denote the same unskewed coil. We ship the canonical 0. So the 13 DIII-D coils at 0.0 and all 812 MAST elements at 0.0 are making the identical statement — this conductor is a rectangle — and you can treat the two machines' geometry with one code path. MAST's zeros are not a missing-value sentinel: its elements come from IMAS element[:].geometry.rectangle, which has no skew degree of freedom, so there is no angle upstream that could have been lost.

To build the conductor outline: if both angles are 0, use the rectangle (R ± width/2, Z ± height/2). Otherwise shear that rectangle — angle1 tilts one pair of sides, angle2 the other — which is what EFIT does when it converts these six coils to polygons.

Not covered: magnetics_bcoil (DIII-D toroidal field) and MAST's magnetics_tf_current / magnetics_efps_current have no poloidal-plane rectangle, so they appear in no geometry row — 19 of 21 DIII-D current columns and 11 of 14 MAST ones are covered.

One caveat on ECOILA: its row is a single lumped rectangle for the ohmic solenoid, and its turn convention is genuinely ambiguous — EFIT's machine file models the same group as 48 single-turn elements spanning R 0.6875–0.7625 m, Z ±1.7255 m (an envelope the shipped rectangle reproduces to ~1.6 cm), and ECOILB is a second co-located group not shipped here. That is why magnetics_ECOILA is left in kA rather than kA·turn: do not apply an ampere-turn multiplier to it. The 18 F-coil rows carry no such ambiguity (see below).

Chord positions are per shot on DIII-D and they genuinely vary — 22 distinct channel-name layouts in train (19 in public test) across 6 distinct subsystem layouts and channel counts from 59 to 138 across the corpus, mostly because the divertor system was reconfigured between campaigns. Do not cache one shot's chord array and reuse it.

This closes a real gap in the previous release. DIII-D's core Thomson is a vertical laser, so thomson_core_R is a constant ≈ 1.94 m and the informative coordinate — Z — was never shipped; the tangential system is the mirror image (thomson_edge_spatial is its nearly-constant Z, and its informative R was missing); and the divertor subsystem had no shipped counterpart at all. thomson_chord_R/_Z carry all three subsystems with both coordinates.

MAST's Thomson is a horizontal midplane laser: per-channel R (already in thomson_core_R and thomson_edge_spatial) and thomson_chord_Z = 0 by construction. There is no Z upstream to ship — FAIR level-2 exposes only thomson_scattering.channel[:].position.r.

import numpy as np
shot = train[0]
# vacuum field contribution of each coil, using the shipped geometry
geom = {c: np.array(shot[c]) for c in ("coil_R", "coil_Z")}
for name, col in zip(shot["coil_name"], shot["coil_input_column"]):
    # already ampere-turns for the F-coils / MAST P-coils -- no turn multiplier needed
    amp_turns = np.array(shot[col])        # this coil's kA*turn time series

👉 Full signal dictionary, machine differences, and a beginner-friendly guide are in the starter kit — its README.md, MODELING_GUIDE.md, and the fusion_data_provider.py visualizer plugin.

License & acknowledgement

Licensed under CC BY 4.0 — use it for the competition or for any research, with attribution. The private (blind) test fold and its ground truth are never released.

Work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, using the DIII-D National Fusion Facility, a DOE Office of Science user facility, under Award No. DE-FC02-04ER54698, and Awards DE-SC0024426, DE-SC0024499, DE-SC0024409, and DE-SC0024571. See the full challenge README for the complete DOE disclaimer.

Citation

@dataset{fusion_equilibrium_challenge,
  title  = {The Fusion Equilibrium Challenge: Predicting Plasma Shape from Control Inputs},
  author = {Michoski, Craig and Waller, Matthew and Sammuli, Brian and Boyes, William
            and Clark, Mitchell and Smith, Sterling and Nakkina, Tapan Ganatma
            and Hatch, David and Nazikian, Raffi},
  year   = {2026},
  note   = {Sophelio and General Atomics}
}