# Real-time virtual circuits for plasma shape control via neural network emulators

arXiv: https://arxiv.org/abs/2605.14939 · HTML: https://mlsanity.com/paper/2605.14939/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 40 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 5 of 5)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [Towards practical reinforcement learning for tokamak magnetic control](https://mlsanity.com/paper/2307.11546/) (2023)
- [Neural net modeling of equilibria in NSTX-U](https://mlsanity.com/paper/2202.13915/) (2022)
- [Real-Time Applicability of Emulated Virtual Circuits for Tokamak Plasma Shape Control](https://mlsanity.com/paper/2509.01789/) (2025)

## Built on by (most cited first, 2 of 2)

- [Real-time virtual circuits for plasma shape control via neural network emulators: integration and testing in the MAST-U PCS](https://mlsanity.com/paper/2608.26216/) (2026)
- [Real-time virtual circuits for plasma shape control via neural network emulators: experimental demonstration on MAST Upgrade](https://mlsanity.com/paper/2608.28468/) (2026)

## Abstract (arXiv)

Reliable position and shape control in tokamak plasmas requires accurate real-time regulation of several strongly coupled shape parameters. The control vectors that disentangle these couplings, referred to as textitvirtual circuits (VCs), enable independent shape parameter control for a specific Grad--Shafranov (GS) equilibrium. Numerical calculation of VCs is not currently feasible in real time, therefore VCs are usually computed prior to each experiment, using a small number of reference GS equilibria sampled along the desired scenario trajectory, with each VC used to control the plasma within a preset time interval. While effective near the reference equilibrium, this approach can lead to degraded performance as the plasma departs from the reference equilibrium and/or from the desired trajectory, and it complicates the design of robust control strategies for rapidly evolving plasma configurations. In this paper, we construct neural-network-based emulators of plasma shape parameters from which VCs can be derived, to provide the MAST Upgrade (MAST-U) plasma control system with state-aware VCs in real-time. To do this, we develop an extensive library of over a million simulated GS equilibria, covering a substantial portion of the MAST-U operational space. These emulators provide differentiable functions whose gradients can be rapidly computed, enabling the derivation of accurate VCs for real-time shape control. We perform extensive verification of the emulated VCs by testing whether they disentangle the control problem. The neural-network-based approach delivers high accuracy and orthogonality across a diverse range of equilibria. This work establishes the physical validity of emulated VCs as a scalable and general alternative to schedules of precomputed VCs.