Advantage-level Aggregation Reinforcement Learning for X-point Target Magnetic Configuration Control in an EXL-50U Experiment-Calibrated Simulation Environment
Organizations: Beijing ENN Fusion Energy Science and Technology Co., Ltd., Beijing 101111, China · Beijing Key Laboratory of High Magnetic Field Spherical Torus Fusion Energy, Beijing 101111, China · Hebei Key Laboratory of Compact Fusion, Langfang 065000, China · Key Laboratory of Materials Modification by Beams of the Ministry of Education, School of Physics, Dalian University of Technology, Dalian 116024, China · School of Nuclear Science and Engineering, East China University of Technology, Nanchang 330013, Jiangxi, China · School of Mechanics and Engineering Science, Peking University, Beijing 100084, China
Managing divertor heat loads is a central challenge for compact, high-power tokamaks. To increase local flux expansion and decouple the dissipation volume from the core, EHL-2 adopts the X-point target (XPT) divertor. This requires the secondary X-point to remain on the divertor leg; displacement degrades the topology and exhaust geometry. Current experiments, including EXL-50U discharges, rely on precomputed feedforward waveforms with PID loops on global quantities. Lacking dedicated closed-loop feedback for the secondary null, XPT operation is repeatable but not routine. We formulate XPT feedback as a multi-objective reinforcement learning (RL) control problem in a free-boundary environment calibrated to EXL-50U discharge #13906. To address strong coupling among plasma current, shape, and null constraints - where reward scalarisation collapses objective-specific temporal credit - we develop Advantage Aggregation (AdvA). AdvA preserves objective-wise temporal credit before worst-objective-aware nonlinear scalarisation and introduces a residual correction to policy updates. AdvA-PPO is evaluated against Reward-PPO and a feedforward-plus-PID baseline under nominal operation, measurement uncertainties, and unseen initial equilibria. On a 500 ms rollout, AdvA-PPO raises the mean worst-channel score from 0.23 to 0.81 over Reward-PPO, reducing X-point flux RMSE by ~20x. Under combined measurement uncertainties, it is the only learned controller completing the horizon while retaining a usable XPT shape. Multi-initialization fine-tuning enables a single AdvA-PPO policy to complete full-horizon operation across divertor and limiter initial equilibria. These results provide a simulation-based foundation for future real-time XPT validation on EXL-50U.
Figures & tables
Figure 1: Representative experimental XPT equilibrium in EXL-50U discharge #13906 at t=500ms . The reconstructed magnetic topology demonstrates experimental access to XPT operation.
Device
Method
FB targets
Real-time secondary null in FB
TCV [ 14 , 7 , 8 , 10 ]
Divertor shape control
Ip , boundary / shape
No
MAST-U [ 13 , 9 ]
LEMUR + FF Br,z→0
ROUT , RIN , ZX
No
EXL-50U (this exp.)
FF+PID
Ip , R , Z
No
Table 1: Experimental XPT magnetic control to date. “Real-time secondary null in FB” asks whether a real-time estimate of the secondary null enters the feedback law (as opposed to feedforward coil programming alone).
Figure 2: End-to-end architecture for reconstructed-null XPT control. Simulation closes the loop through FGE; deployment swaps FGE observations for real-time reconstruction while keeping the same state and coil-command interfaces (11 policy coils; VS under PID).
Figure 3: Free-boundary equilibria from the FGE validation run of EXL-50U discharge #13906 at t=0.50 , 0.55 , 0.63 , and 0.69s (left to right). Each panel overlays the simulated separatrix (solid blue) and X points (blue crosses) on the experimental LIUQE-reconstructed separatrix (dashed black) and X points (open circles); thin gray curves show simulated flux surfaces and the dark gray contour marks the limiter.
Figure 4: Time traces from the FGE validation run of EXL-50U discharge #13906 (solid blue) compared with the experimental LIUQE reconstruction (dashed black): (a) plasma current Ip ; (b) plasma radial position R ; (c) outer radial extent Rmax of the LCFS; (d) LCFS elongation κ .
Quantity
Bias
RMSE
Maximum
Ip (kA)
+1.4
3.1
6.5
R (mm)
+4.7
5.3
11.4
Rmax (mm)
+7.6
8.7
16.7
κ
+0.045
0.051
0.101
LCFS distance (mm)
—
13.8
30.5
Primary X points X2 , X3 (mm)
—
18.3
38.0
Table 2: Deviations between the FGE validation run and the LIUQE reconstruction of discharge #13906 over 0.5 – 0.7s : time-averaged signed deviation (bias, simulation minus reconstruction), root-mean-square error (RMSE), and maximum absolute deviation. The LCFS row is based on the symmetrized mean distance between the simulated and reconstructed boundary contours, and the X-point rows on the Euclidean position offsets averaged over the upper and lower X point of each type; these distances are nonnegative by construction, so no bias is reported.
Figure 5: Baseline FF+PID control structure.
Figure 6: Policy update and environment interaction for AdvA-PPO. The FGE environment provides the reconstructed magnetic observation and component rewards. Per-objective value heads and GAE preserve temporal credit assignment before SmoothMax aggregation; the PPO anchor is then corrected by the norm-capped residual of Eqs. ( 15 )–( 16 ). Reliability gating and gradient projection are ablation options and are off in AdvA-PPO.
Name
Locus
α
Gate
β
Proj.
K
da/do
Reward-PPO
reward
−3
off
0
off
10
11/45
Adv-mean
advantage
0
off
0
off
10
11/45
Adv-SmoothMax
advantage
−3
off
0
off
10
11/45
+ gate
advantage
−3
on
0
off
10
11/45
+ resid (AdvA-PPO)
advantage
−3
off
0.2
off
10
11/45
+ proj
advantage
−3
off
0
on
10
11/45
Table 3: Controllers in the component ablation, in the same order as the Results ablation (Sec. 3.2 ). “Locus” is where nonlinear aggregation occurs relative to objective-wise temporal credit. For AdvA rows, Gate/ β /Proj. act on advantage weights or the residual of Eqs. ( 15 )–( 16 ). All rows share the same da=11 / do=45 interface (Sec. 2.3.2 ; VS under PID). Reward-PPO is the reward-level SmoothMax baseline of Sec. 2.3.4 .
ID
Shot
t0
Topology
Ip⋆
I1
#13906
≈500ms
XPT (training / test)
≈400kA
I2
#13705
≈500ms
divertor (test)
≈500kA
I3
#13844
≈500ms
divertor (test)
≈500kA
I4
#15892
≈500ms
limiter (test)
≈500kA
Table 4: Evaluation initials I1–I4. All windows start at t0≈500ms (CSV start 0.502s ) and use the frozen #13906 XPT geometric target; Ip⋆ is the current reference for that cell.
Figure 7: Closed-loop evolution on #13906 ( 500ms ). Grey: FF+PID; blue: Reward-PPO; red: AdvA-PPO. (a) Ip ; (b) LCFS error; (c)–(d) primary X distance and flux ( X2 , X3 ); (e)–(f) secondary X distance and flux ( X1 , X4 ).
Figure 8: Flux snapshots on #13906 at t=500 – 900ms (shot clock; control from t0=500ms ). Rows: FF+PID, Reward-PPO, AdvA-PPO. Blue solid: current LCFS; black dashed: target; open circles: target X ; blue crosses: actual X .
Quantity
FF+PID
Reward-PPO
AdvA-PPO (ours)
Ip (A)
454 / 1488
735 / 1310
260 / 624
Primary X dist. (mm)
39.0 / 58.3
22.8 / 39.2
6.3 / 9.5
Secondary X dist. (mm)
30.1 / 38.3
19.0 / 31.8
28.2 / 44.2
Mean X flux ( 10−4Wb )
77.38 / 117.02
13.06 / 18.89
0.66 / 1.93
LCFS ( ×10−3 )
120.1 / 430.3
14.7 / 21.9
12.2 / 17.2
SmoothMax uˉ↑
0.093
0.563
0.925
Table 5: Nominal tracking on I1 (#13906, 500ms ); metrics as in Sec. 2.4.2 . FF+PID X-point and LCFS rows are open-loop observations.
Variant
Ip (A)
mean dX (mm)
mean flux ( 10−4Wb )
LCFS ( ×10−3 )
uˉ↑
r↑
Reward-PPO
735 / 1310
20.9 / 35.5
13.06 / 18.89
14.7 / 21.9
0.563
0.232
Adv-mean
1615 / 2149
34.2 / 45.8
1.77 / 2.70
8.7 / 14.9
0.830
0.665
Adv-SmoothMax
1630 / 2545
17.6 / 27.3
2.44 / 5.22
13.4 / 18.0
0.879
0.760
+ gate
2779 / 3384
18.5 / 29.0
1.30 / 2.76
15.3 / 21.7
0.899
0.760
+ resid = AdvA-PPO
260 / 624
17.3 / 26.9
0.66 / 1.93
12.2 / 17.2
0.925
0.810
+ proj
1601 / 1916
18.9 / 29.7
1.27 / 2.10
8.5 / 11.3
0.894
0.765
Table 6: Component ablation on I1 (#13906, 500ms ). Names as in Table 3 ; metrics as in Sec. 2.4.2 .
Method
Surv. (ms)
Ip (A)
Prim. X (mm)
Prim. flux ( 10−4Wb )
Sec. X (mm)
Sec. flux ( 10−4Wb )
LCFS ( ×10−3 )
R1: delay 1 – 3ms
FF+PID
500
637
38.1
2.16
29.6
149.81
160.8
Reward-PPO
500
11997
23.0
28.38
41.1
36.88
229.6
AdvA-PPO
500
4521
26.6
13.04
24.8
17.85
18.8
R2: full diagnostic noise
FF+PID
500
74817
46.1
23.02
22.3
55.54
222.0
Table 7: Zero-shot noise/delay on I1 (#13906); RMSE over the survived horizon (Sec. 2.4.2 ).
Figure 9: R3: delay + noise on I1 (#13906). Panel layout as Figure 7 .
Figure 10: Zero-shot cross-init flux under frozen #13906 XPT. Rows: #13705, #13844, #15892. Columns: initial equilibrium and FF+PID / Reward-PPO / AdvA-PPO at episode end. Grey: initial LCFS/ X ; blue: final; black dashed/circles: target.
Init.
Controller
Surv.
Ip (kA)
mean dX (mm)
mean flux ( 10−4Wb )
LCFS ( ×10−3 )
uˉ↑
r↑
I2 #13705 divertor
FF+PID
full
9.4 / 42.3
125 / 178
1315 / 5054
232 / 596
0.02
0.00
Reward-PPO
full
32.8 / 79.3
85 / 179
889 / 5013
46 / 70
0.07
0.00
AdvA-PPO
full
31.8 / 75.6
69 / 179
909 / 5187
63 / 129
0.11
0.01
I3 #13844 divertor
FF+PID
full
2.8 / 6.1
126 / 174
1305 / 5009
97 / 119
0.02
0.00
Reward-PPO
full
19.6 / 56.8
72 / 168
990 / 5333
50 / 110
0.10
0.00
AdvA-PPO
full
17.6 / 57.3
60 / 176
1061 / 5781
79 / 241
0.14
0.00
Table 8: Zero-shot cross-init to frozen #13906 XPT (I2–I4); metrics as in Sec. 2.4.2 (full survival =500ms ). FF+PID feedforward is re-anchored as described in the text.
Figure 11: AdvA-PPO multi-initialization fine-tune ( 100 iterations, frozen #13906 XPT). Grey dashed: zero-shot; red: fine-tuned. Top: uˉ ; bottom: mean dX . Early stop marked by a dotted vertical line.
Init.
Controller
Surv.
Ip (kA)
mean dX (mm)
LCFS ( ×10−3 )
uˉ↑
r↑
I1 #13906 (XPT / training)
zero-shot
full
0.3
17
12
0.92
0.81
fine-tuned
full
0.7
24
17
0.77
0.58
I2 #13705 (divertor)
zero-shot
full
31.8
69
63
0.11
0.01
fine-tuned
full
26.2
67
64
0.11
0.00
I3 #13844 (divertor)
zero-shot
full
17.6
60
79
0.14
0.00
fine-tuned
full
13.7
58
66
0.13
0.00
Table 9: AdvA-PPO before/after multi-initialization fine-tuning ( 100 iterations, frozen #13906 XPT). Errors and uˉ / r on the common window of each pair; survival separate. On #15892 the common window is the 96 zero-shot steps; over its own 500ms the fine-tuned run reaches uˉ=0.08 , Ip RMSE 20.8kA , mean dX=74mm .
Reinforcement learning control uses reward-driven learning to make decisions in dynamic systems, from robots and vehicles to energy and infrastructure.
Scenario development, the design of the waveforms that take a tokamak discharge from breakdown to flat-top, is still an iterative, labour-intensive process. Every candidate scenario has to be simulated with a controller in the loop, and the classical shape and current controllers need low-level actuator references. So the process is iterative and includes a number of trial-and-error steps. We propose to replace the per-scenario controller tuning by a single goal-conditioned reinforcement-learning controller trained once, in advance, against a free-boundary equilibrium and transport simulator. A scenario is then specified only by the target waveforms of the physical quantities of interest (plasma current, line-averaged electron density, LCFS shape, x-point positions), and the controller produces the coil-current and fueling commands that realize them. We demonstrate the approach on an EAST plasma-current ramp-up: the controller takes over a small limited plasma, ramps the current and the density, grows the cross-section, forms two x-points and holds a double-null diverted configuration against sampled shape targets for the rest of a 1.2 s episode. The neural network controller is trained using TQC algorithm. On 1024 test scenarios sampled from a low-discrepancy scrambled Sobol sequence in 11-dimensional target space, the controller forms the divertor in 86% of the cases, holds it for more than 0.5 s in 67% and reaches the end of the episode in a diverted state in 58%, with flat-top tracking errors of a few kA in plasma current, ∼0.15×1019 m−3 in density, ∼2 cm in position and ∼8 cm in x-point location; the failures concentrate at the high-current density (J) region which is believed to be physically or from engineering perspective not feasible within ohmic mode.
Plasma shape control in tokamaks requires a real-time controller that tracks dynamically changing shape targets while tolerating diagnostic failures. Classical approaches decompose the problem into equilibrium reconstruction followed by a linear controller, and assume a fixed, fully operational sensor set. We present a reinforcement learning agent that addresses both limitations simultaneously. The agent is trained in NSFsim, a high-fidelity tokamak simulator configured for DIII-D, on a curated dataset of 120 experimental plasma shapes. The shape targets are resampled as random step changes every 0.25 s, exposing the agent to diverse transitions across the full shape envelope. At test time the agent zero-shot tracks dynamic shape sequences; on a held-out static configuration in simulation it achieves a mean shape error of 2.01 cm, and dynamic trajectory following is demonstrated qualitatively in simulation and on the physical device. Diagnostic dropout randomly masks 30% of magnetic sensors per episode, yielding a single policy robust to arbitrary sensor subsets without backup controllers or mode-switching logic. An asymmetric actor-critic architecture with privileged equilibrium information improves value estimation under partial observability; an auxiliary shape reconstruction head on the actor enables end-to-end shape reconstruction from raw diagnostics and serves as an interpretability tool for policy analysis. The policy transfers to experimental DIII-D shots, where it directly commands the coil actuators on two dynamic shape maneuvers, and to the independent GSevolve simulator.
D. Sorokin, M. Stokolesov, A. Granovskiy +7
Next Step Fusion, Bertrange, L-8070, Luxembourg · Center for Energy Research, University of California San Diego, CA 92093, USA
Tokamaks remain leading candidates for achieving practical fusion energy, yet many important control problems inside these devices are still difficult or unsolved. One such challenge is controlling the plasma rotation profile, which strongly influences stability, confinement, and transport. While the average rotation can be controlled, controlling the full profile is challenging due to high dimensionality, response to multiple actuators and dependence on plasma condition. Learning-based control methods, such as reinforcement learning (RL), provide a potential solution to this challenging problem with ability to model complex interactions leading to effective multi-input multi-output control. However, learning such policies is challenging due to the lack of accurate simulators that can model the rotation profile dynamics. In this work, we investigate the use of offline RL and offline model-based RL algorithms for rotation profile control, training them solely on historical data from the DIII-D tokamak. Our final method uses probabilistic models of plasma dynamics to generate rollouts for RL training. We deploy this policy on the DIII-D Tokamak and observe promising real-world results. We conclude by highlighting key challenges and insights from training and deploying an RL policy on a complex physical device while using only limited past data.