CARONTE: a Physics-Informed Extreme Learning Machine-Based Algorithm for Plasma Boundary Reconstruction in Magnetically Confined Fusion Devices

TL;DR

CARONTE introduces a real-time plasma boundary reconstructor based on a single physics-informed Extreme Learning Machine to solve the homogeneous Grad-Shafranov equation in the vacuum, enabling online adaptation to evolving tokamak equilibria using magnetic sensors. The method combines a fast ELM with physics constraints, providing a stable, low-parameter model that directly estimates the poloidal flux ψ and thereby the LCFS boundary without extensive offline training. Validation on CREATE-ground-truth equilibria demonstrates robust boundary reconstruction across small circular devices and large-scale tokamaks, with TANH-based tuning achieving sub-centimeter RMSD in challenging DTT configurations and outperforming traditional XLOC-like approaches in noise resilience. The approach offers substantial practical impact for real-time magnetic control, with potential extensions to full equilibrium reconstruction and isoflux control strategies in future work.

Abstract

In this work, we propose a novel physics informed neural network based algorithm for real time plasma boundary reconstruction in tokamak devices. The approach is based on a single Extreme Learning Machine network used to solve the homogeneous Grad Shafranov equation, which is required to identify the plasma boundary. This architecture enables the real time training of the network parameters using the available magnetic sensor data and, consequently, dynamically adapting the network output to the evolving plasma equilibrium. We demonstrate that, the network performs accurate plasma boundary reconstruction for complex configurations, outperforming well established methods, such as the algorithm used for decades at the Joint European Torus, the world's largest tokamak, until it ceased operation in 2023. Indeed, compared to the latter, the proposed solution better generalizes the poloidal flux function, without requiring algorithm retuning across different plasma equilibria. The proposed neural network reconstructor demonstrates also greater robustness with respect to noise on the magnetic measurements. Moreover, this method takes advantage of the generalization power of neural networks but without the need for extensive, time consuming training based on a huge amount of experimental data, making its implementation on existing devices straightforward.

Figures (9)

• Figure 1: Simplified scheme of a tokamak fusion device.
• Figure 2: The cylindrical coordinate system and the surface $S(\mathbf{r})$ obtained by rotating $\mathbf{r}$ around the $r=0$ axis.
• Figure 3: Plasma flux surfaces for a RFX-mod2 diverted plasma computed with CREATE-L. The LCFS highlighted in blue defines the plasma boundary. The arrows represent the plasma-wall gaps.
• Figure 4: The basic ELM is made up of the reservoir and the output layer. The reservoir consists of nonlinear neurons randomly connected to the network input, while the output layer is connected to the nonlinear neurons through the weights to be optimized during the network's training.
• Figure 5: Simplified scheme of the CARONTE algorithm workflow.