Autoregressive long-horizon prediction of plasma edge dynamics

TL;DR

This work develops transformer-based autoregressive surrogates (MATEY) trained on SOLPS-ITER edge-plasma data to predict 2D, time-dependent SOL/divertor fields with long-horizon rollouts. By varying the autoregressive horizon during training, the authors show substantial improvements in rollout stability and generalization, achieving accurate predictions over hundreds to thousands of steps and dramatic speedups relative to SOLPS-ITER. The approach demonstrates strong 2D field, temporal, and 1D-profile fidelity, reveals physically meaningful attention patterns, and tests robustness under extended, unseen regimes (trajectory 3x). While offering substantial performance gains for rapid scenario exploration and control-oriented studies, the study also identifies limitations in extrapolation beyond training data and calls for physics-informed constraints and uncertainty quantification for real-time fusion applications.

Abstract

Accurate modeling of scrape-off layer (SOL) and divertor-edge dynamics is vital for designing plasma-facing components in fusion devices. High-fidelity edge fluid/neutral codes such as SOLPS-ITER capture SOL physics with high accuracy, but their computational cost limits broad parameter scans and long transient studies. We present transformer-based, autoregressive surrogates for efficient prediction of 2D, time-dependent plasma edge state fields. Trained on SOLPS-ITER spatiotemporal data, the surrogates forecast electron temperature, electron density, and radiated power over extended horizons. We evaluate model variants trained with increasing autoregressive horizons (1-100 steps) on short- and long-horizon prediction tasks. Longer-horizon training systematically improves rollout stability and mitigates error accumulation, enabling stable predictions over hundreds to thousands of steps and reproducing key dynamical features such as the motion of high-radiation regions. Measured end-to-end wall-clock times show the surrogate is orders of magnitude faster than SOLPS-ITER, enabling rapid parameter exploration. Prediction accuracy degrades when the surrogate enters physical regimes not represented in the training dataset, motivating future work on data enrichment and physics-informed constraints. Overall, this approach provides a fast, accurate surrogate for computationally intensive plasma edge simulations, supporting rapid scenario exploration, control-oriented studies, and progress toward real-time applications in fusion devices.

Figures (11)

• Figure 1: Schematic of the poloidal physical domain and its mapping to a rectangular computational domain, with regions color-coded. The scrape-off layer (SOL) is shown in red, the core in cyan, and the two private flux regions (PFRs) in the blue and yellow, respectively. For inference, an example density field is shown in both coordinate systems.
• Figure 2: Input gas-puff trajectories (actuator signals) used in this study, shown as a function of time. Trajectories 1 and 2 are used for training, while trajectory 3 is reserved for testing. Trajectory 3x extends trajectory 3 beyond 7 s (with increased puffing rates) and is used as a separate, more challenging stress-test case.
• Figure 3: Schematic of the MATEY model architecture with ViT. The model takes as input the plasma states from the previous $T$ time steps, $\mathbf{U}_{t,T} =[\mathbf{u}_{t-T+1}, \dots, \mathbf{u}_{t}]$, together with the actuator values from the previous $T$ time steps and the next timestep, $\mathbf{a}_{t+1,T+1}=[a_{t-T+1}, \dots, a_{t}, a_{t+1}]$. It outputs the predicted plasma state at the next timestep, $\hat{\mathbf{u}}_{t+1}$. Spatiotemporal attention enables each patch to attend to all other patches both across space and time steps (see bottom-right panel). The model is trained autoregressively, feeding predictions back as inputs for subsequent time steps.
• Figure 4: Prediction NRMSE $\varepsilon(t, n_{\mathrm{lead}})$ (Eq. \ref{['eq-nrmse']}) versus start time $t$ and rollout horizon $n_{\mathrm{lead}}$ for the four models, Matey-1, Matey-10, Matey-50, and Matey-100, for trajectories 1--3. Each row corresponds to a distinct trajectory, with the first column showing the associated input actuator signal. In panel c), the horizontal dashed black line indicates the point up to which trajectories 2 and 3 overlap. The subsequent columns display results from four models trained with different numbers of autoregressive steps $n_{\mathrm{lead}}$. For panel b) and c), the horizontal axis of the heatmaps is non-uniform. Vertical gray lines denote changes in resolution: the first segment has a resolution of 50 time steps, and the resolution is halved after each gray line. Errors increase clearly with longer rollouts, with Matey-10 achieving the best accuracy on the training trajectories (panels a) and b)) and Matey-100 performing best on the test trajectory (panel c)). Matey-1, which is trained with simple next-step prediction, results in highest error among all models. The prediction error also varies depending on the start time, as discussed in Section \ref{['subsec:global_performance']}.
• Figure 5: Comparison of density, temperature, and radiated power between the Matey-100 prediction and ground truth from SOLPS. Results are shown for Trajectory 3 at $t=7$ s, after 100 rollout steps from $6.9$ s. The last column shows the absolute errors. Predictions align closely with the ground truth, with errors one to two orders of magnitude smaller than the corresponding field values.