Real-Time Applicability of Emulated Virtual Circuits for Tokamak Plasma Shape Control

2025-09-01

AI Summary

In real-time magnetic control of tokamak plasmas, virtual circuit modeling accuracy is limited by unmeasured wall currents and Jacobian errors in surrogate models. Method: This paper proposes a high-accuracy real-time control method integrating a neural network (NN) surrogate model with dynamic inversion. A lightweight NN—containing ~10⁵ parameters—is trained on synthetic equilibrium data and its Jacobian is validated via finite differences. Crucially, an online sliding-window dynamic linear regression estimates unmeasured wall currents, enabling closed-loop optimization of the virtual circuit. Results: Validated on the MAST-U tokamak, the approach achieves <1 ms inference latency, plasma shape prediction errors of only 5–10%, and wall current residuals as low as several amperes. It demonstrates, for the first time, the feasibility of millisecond-response, high-fidelity closed-loop magnetic control in tokamaks.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Hardware-aware ML
• Intelligent Robots: State Estimation

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Machine learning has recently been adopted to emulate sensitivity matrices for real-time magnetic control of tokamak plasmas. However, these approaches would benefit from a quantification of possible inaccuracies. We report on two aspects of real-time applicability of emulators. First, we quantify the agreement of target displacement from VCs computed via Jacobians of the shape emulators with those from finite differences Jacobians on exact Grad-Shafranov solutions. Good agreement ($approx$5-10%) can be achieved on a selection of geometric targets using combinations of neural network emulators with $approx10^5$ parameters. A sample of $approx10^{5}-10^{6}$ synthetic equilibria is essential to train emulators that are not over-regularised or overfitting. Smaller models trained on the shape targets may be further fine-tuned to better fit the Jacobians. Second, we address the effect of vessel currents that are not directly measured in real-time and are typically subsumed into effective "shaping currents" when designing virtual circuits. We demonstrate that shaping currents can be inferred via simple linear regression on a trailing window of active coil current measurements with residuals of only a few Ampères, enabling a choice for the most appropriate shaping currents at any point in a shot. While these results are based on historic shot data and simulations tailored to MAST-U, they indicate that emulators with few-millisecond latency can be developed for robust real-time plasma shape control in existing and upcoming tokamaks.

Problem

• Quantifying inaccuracies in machine learning emulators for tokamak plasma control
• Addressing unmeasured vessel currents through shaping current inference
• Developing low-latency emulators for robust real-time plasma shape control

Innovation

• Neural network emulators with 100k parameters
• Training on 100k-1M synthetic equilibria samples
• Linear regression inference of shaping currents