Real-time virtual circuits for plasma shape control via neural network emulators: experimental demonstration on MAST Upgrade

Real-time virtual circuits for plasma shape control via neural network emulators: experimental demonstration on MAST Upgrade

arXiv:2608.28468v1 [physics.plasm-ph] 28 Aug 2026

N. C. Amorisco1

K. Pentland1

A. Agnello2

G. K. Holt1

M. J. Marshall2

E. Jones1

G. McArdle1

C. Vincent1

P. Cavestany2

A. Garrod2

S. Pamela1

J. Buchanan1

T. Nunn1

A. Ross2 M. Kochan1

the MAST Upgrade Team3

August 31, 2026

several levels of the control architecture. Neural networks (NNs) have provided real-time estimates for vertical stability control on DIII-D and for fast and adaptive vertical position control on EAST (Rui et al., 2025; Sammuli et al., 2021; Song et al., 2024), building on earlier neural-network-assisted equilibrium control experiments (Bishop et al., 1995; Windsor et al., 1997). Learned predictors and policies have also been deployed on DIII-D for plasma performance control, tearing instability avoidance and prevention of H–L back-transitions (Char et al., 2023; Orozco et al., 2022; Seo et al., 2024). Reinforcement learning has been used to develop policies that map measurements and control targets either to high-level control requests or directly to actuator commands (Char et al., 2023; De Tommasi et al., 2022; Degrave et al., 2022; Kerboua-Benlarbi et al., 2024; Seo et al., 2024; Tracey et al., 2024; Wang et al., 2025) and used to control plasmas on TCV, HL-3, and DIII-D (Degrave et al., 2022; Subbotin et al., 2026; Tracey et al., 2024; Wu et al., 2025). While these developments demonstrate the potential of AI to enhance plasma control and operation, their routine use within a plasma control system (PCS) must satisfy considerations beyond control robustness. In particular, interpretability and operational familiarity remain important, while retraining learned controllers around new scenarios can be costly. In this work, we demonstrate a different approach designed to address these concerns. Rather than replacing the feedback controller, we use neural network emulators to update the local plasma response linearisations from which virtual circuits (VCs) are derived. Shape errors and actuator requests therefore remain connected through the established VC decomposition, retaining the structure and operational familiarity of conventional shape control. Because the emulators are trained over a broad operating space rather than for individual discharge scenarios, the same models can provide real-time VCs across different plasma conditions without scenario-specific retraining or manually prepared VC schedules. Compared with static, pre-set schedules, these real-time updates keep the VCs matched to the evolving plasma response, maintaining the intended orthogonality between shape-control parameters and allowing the existing controller to adapt its actuator response when the plasma departs unexpectedly from the planned trajectory. The timeliness of this approach is reinforced by a con-

Abstract. Conventional plasma shape control in tokamaks relies on virtual circuits (VCs) that are computed offline from linearisations around a small, tailored number of reference equilibria, and deployed as expertly prepared schedules during the discharge. Here, we report on the first experimental deployment of real-time VCs. We replace pre-set look up tables with VCs updated in real time using surrogates of the plasma response. Both the existing control architecture and the interpretability of VC-based control are retained. Previous work showed that neural network emulators can produce accurate VCs, and validated their performance in closed-loop shape control simulations. Here, we report their first experimental validation on MAST Upgrade (MAST-U). Dedicated experiments spanning different scenarios, including prescribed shape perturbations, feedback-driven divertor-leg motion, and strongly evolving plasma configurations, show that real-time VCs can realise plasma shape-control tasks within the MAST-U plasma control system. These results establish the experimental feasibility of real-time linearisations as a practical extension of conventional plasma shape control in tokamaks. The present implementation demonstrates a central step towards a simpler control workflow, in which manually constructed, phased VC schedules are replaced by VCs generated automatically online from a trained surrogate model, without scenario-specific retraining. Keywords. Virtual circuits • Real-time control • Neural-network emulators • Plasma control systems • MAST Upgrade

1 Introduction Accurate control of the plasma position and shape is fundamental to the operation of magnetic confinement fusion experiments, enabling the exploration of high-performance operating scenarios while maintaining safe plasma operation (e.g., Ariola and Pironti, 2016). As fusion devices move towards higher power operation and increasingly demanding engineering constraints, there is growing interest in the application of artificial intelligence (AI) and machine learning to plasma control, with the aim of improving controller performance, reducing the burden of manual controller design and tuning, and enabling increasingly autonomous operation. Applications of AI to tokamak plasma control have significantly progressed in the 2020s, with approaches spanning 1

United Kingdom Atomic Energy Authority, Culham Campus, Abingdon, Oxfordshire, OX14 3DB, United Kingdom (nicola.amorisco@ukaea.uk) 2 STFC Hartree Centre, Sci-Tech Daresbury, Keckwick Lane, Daresbury, Warrington, WA4 4AD, United Kingdom 3 See author list of J.R. Harrison at al 2026 Nucl. Fusion 66 116005

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Figure 1.1 Schematic comparison between conventional virtual-circuit operation and RTVC operation. Conventional operation uses precomputed linearisations scheduled by discharge phase, whereas RTVCs generate the local linearisation from the instantaneous plasma state. The shape reconstruction, shape/VC controllers, and machine safety limits within the PCS interface are unchanged.

temporaneous experimental demonstration of an inverse Grad-Shafranov neural network for tokamak magnetic control (Wang et al., 2026). That method maps requested plasma shapes and real-time estimates of the plasma state directly to PF-coil current references, which are then tracked by lower-level current controllers. RTVC addresses the same broad challenge from a complementary direction: rather than learning the inverse mapping from shape requests to coil currents, it learns the forward plasma response, differentiates this model to construct local VCs, and retains explicit feedback on the reconstructed plasma-shape error. The emergence of these complementary approaches highlights real-time, learned equilibrium models as an increasingly active direction in tokamak shape control.

control algorithm and integrated into the MAST-U PCS. Playback, performance, and non-actuating “piggyback” tests verified real-time execution and consistency with the offline emulator implementation (Marshall et al., 2026). Here, we present the first experimental demonstration of RTVCs on MAST-U. The experiments span progressively more demanding plasma scenarios, from control of conventional plasma shapes, through prescribed shape perturbations and feedback-driven divertor leg motion, to strongly evolving plasma configurations. Together, they establish the feasibility of integrating RTVCs within an existing control architecture and applying the same trained models across distinct scenarios without scenario-specific retraining or manually prepared VC schedules. They also provide a first experimental assessment of the resulting shape control performance and its present limitations.

The methodological and validation foundations of RTVC were established in a sequence of earlier studies. Agnello et al. (2024) introduced a framework for efficiently generating synthetic Grad-Shafranov (GS) equilibria using the FreeGSNKE free-boundary equilibrium solver (Amorisco et al., 2024). Ross et al. (2026) applied this framework at scale to produce a large equilibrium library spanning a broader range of configurations than those explored in previous campaigns on MAST Upgrade (MAST-U; Fishpool et al., 2013; McArdle et al., 2020; Ryan et al., 2023). The resulting library was used to train plasma-shape emulators, whose Jacobians were used to construct VCs, which were then tested against physics-based reference VCs in static validation. Subsequent closed-loop simulations using the FreeGSNKE Pulse Design Tool (FPDT) (Pentland et al., 2026a) showed that these realtime VCs delivered the requested shape corrections across a broad region of the MAST-U operating space (Pentland et al., 2026b). Most recently, the emulators were incorporated into a real-time virtual circuit (RTVC) server and

2 Experimental methodology 2.1 Real-time VCs VCs are conventionally constructed by linearising the controlled plasma shape parameters with respect to the poloidal field (PF) coil currents around a reference GS equilibrium, and inverting, typically through a pseudoinverse, the resulting Jacobian matrix. Each VC is therefore a vector of PF coil current perturbations that, to first order, change one local shape parameter, such as the X-point position, by a prescribed amount while suppressing changes in the other controlled parameters (see, e.g., Wai et al., 2026). In conventional MAST-U operation, these linearisations are computed offline at a limited set of reference equilibria sampled along the planned plasma trajectory. The corre2

Deployment of real-time virtual circuits on MAST-U sponding VCs are then assigned manually to predefined phases of the pulse. Selecting the reference equilibria and the transition times between their VCs is therefore an integral part of expert scenario preparation. Within each phase, the scheduled VCs remain fixed. As the plasma evolves, or departs unexpectedly from the planned trajectory, its local shape response can differ from that of the reference equilibrium. The scheduled VCs then become increasingly mismatched, potentially degrading the intended decoupling between shape control channels and reducing control effectiveness. In the low-latency approach introduced by Ross et al. (2026), neural-network emulators predict the plasma shape from a reduced description of its instantaneous state. The reduced plasma state comprises the currents in the twelve active poloidal-field (PF) coils of MAST-U, the total plasma current, and a small number of parameters describing the plasma current-density profile. From these inputs, the emulators predict seven shape parameters routinely used in MASTU control: the inner and outer midplane radii (Rin , Rout ); the lower X-point position (RX , ZX ); the “squareness gap” Sgap , defined between the plasma core and a specified point on the main-chamber wall; the lower outboard strike-point position Rs ; and Rnose , the radial position at which the lower divertor leg intersects a virtual line across the divertor entrance. Local shape-response matrices are obtained by differentiating the emulator predictions with respect to the active PF coil currents, using either finite differences or automatic differentiation, and the corresponding VCs are then constructed from these matrices. Further details and definitions are provided by Ross et al. (2026). While the plasma and PF coil currents are provided in real time by the plasma control system (PCS), in this experimental deployment the profile parameters are prescribed. We use reconstructed profile parameters from prior representative discharges. Also, the implementation of RTVC presented here does not account for the currents induced in the passive structures within the emulator state.

charge playback, and comparison with the TensorFlow emulator implementation in the FPDT. It was then operated in non-actuating “piggyback” mode during MAST-U discharges, during which the conventional controller continued to actuate the plasma, while RTVC recorded the PF coil requests it would have issued from the same measurements (Marshall et al., 2026). This validation allows the experiments in Section 3 to focus on the closed-loop plasma response to the real-time VCs. The MAST-U shape controller runs at 10 kHz using the latest available VC, with RTVC supplying an updated matrix every 5 ms to 5.6 ms.

3 Experimental demonstration We designed experiments to validate complementary aspects of the proposed RTVC framework, progressing from compatibility with plasma scenarios routinely run on MAST-U to more dynamic plasma shape evolution for which RTVCs are principally intended. These experiments are not intended to demonstrate superior control performance relative to conventional VCs. Such a comparison would require a dedicated campaign of discharges specifically aimed at a systematic comparison, which was not possible within the available machine time. Instead, the purpose of these experiments has been to assess whether RTVCs could reliably realise plasma shape control tasks of increasing complexity while preserving the existing controller architecture. Table 3.1 and Figure 3.1 provide an overview of the RTVCcontrolled discharges. A green background in Figure 3.1 indicates that the shape parameter is feedback controlled by RTVC: the corresponding feedback reference is displayed with a black dashed line, while the measured shape evolution as reconstructed in real time by the LEMUR algorithm (Kochan et al., 2023) is shown in orange. Shape parameters controlled using RTVC-provided VCs are also listed in the middle column of Table 3.1. Together with the real time shape measurements, Fig. 3.1 also displays the pre-shot simulation results obtained for the same discharges using the emulators within the FPDT.

2.2 Integration into the MAST-U plasma control system

3.1 Routine plasma control

The NN emulators are deployed through a dedicated realtime inference server integrated with the MAST-U PCS; implementation details are given in Marshall et al. (2026). At each VC update, the server receives the plasma current, PF coil currents, and plasma profile parameters, evaluates the emulators, and returns the local shape response Jacobian. The PCS computes its pseudoinverse and uses the result to replace selected entries of the conventional VC matrix. The downstream controller, gains, and machine protection handling remain unchanged, allowing conventional and realtime VCs to be selected by shape parameter and pulse phase, as illustrated in Figure 1.1. Because the real-time inference engine does not yet support automatic differentiation, the Jacobian is evaluated by finite differences of the emulator outputs. Ross et al. (2026) showed that this produces VCs of comparable accuracy to those obtained using automatic differentiation. Before active plasma control, the complete deployed workflow was validated through software-level tests, offline dis-

Shot 53996 was designed to conservatively test compatibility of the RTVC framework with routine MAST-U shape control, and was based on reference discharge 53320 – a 750 kA double-null, conventional-divertor scenario, heated with two neutral beams and with no plasma shape evolution. In this shot, Rout , Rin , ZX and Rnose are actively controlled. RTVC takes control of the core shape (Rout , Rin , ZX ) at t=185 ms, while Rnose control is performed using a conventional VC schedule (as highlighted by the lilac shading), the same used in the reference shot. The real-time VCs derived by RTVC are obtained as pseudoinverse of the Jacobian including all of Rout , Rin , ZX , Sgap , Rnose . Although Sgap is not actively controlled in this shot, including it in the pseudoinversion discourages the RTVC control actions from producing unintended changes in this parameter. The discharge reached its programmed duration and the RTVC-controlled shape parameters remained close to the requested waveforms throughout the controlled phase, demon3

N. C. Amorisco et al.

Table 3.1 Overview of the experimental validation objectives, RTVC controlled shape parameters, and shape parameters used in the matrix inversion. Shot

Objective

RTVC controlled shape pars.

Included in inverse matrix

53996

Constant shape control

(Rout , Rin , ZX )

(Rout , Rin , ZX , Sgap , Rnose )

54000

Minor core shape perturbations and sweep divertor-leg

(Rout , Rin , ZX , Rs )

(Rout , Rin , ZX , Sgap , Rnose , Rs )

54002

Increase elongation and sweep divertorleg

(Rout , Rin , ZX , RX , Sgap , Rs )

(Rout , Rin , ZX , RX , Sgap , Rs )

54168

Simultaneous control of all seven shape parameters and shape perturbations

(Rout , Rin , ZX , RX , Sgap , Rnose , Rs )

(Rout , Rin , ZX , RX , Sgap , Rnose , Rs )

Figure 3.1 Evolution of the shape parameters in each RTVC-controlled MAST-U shot. Shown are the experimentally observed values recorded in real-time by the LEMUR algorithm (orange), the FPDT simulations made prior to the discharge (dashed-dot purple), and the pre-programmed feedback reference waveforms (dashed black). The shading indicates periods where feedback control was switched on (green with RTVC, lilac with Conventional VCs). Vertical dashed red lines indicate when the plasma went into ramp-down.

strating the use of both real-time and conventional VCs together.

inverse but not actively controlled by the RTVC.

3.2 Prescribed shape perturbations and divertor-leg motion

The measured evolution, shown in Figure 3.1, demonstrates successful tracking of the imposed trapezoidal shape perturbations in both Rout and ZX , and accurate enacted motion of the divertor leg. In particular, the Rs evolution follows the requested outward sweep until the discharge terminates at 563 ms following a Langmuir probe protection trip. The termination was not attributed to RTVC operation, but was consistent with an operational limitation encountered during Super-X attempts in the same experimental session, thought to be associated with a possible bias in the real-time LEMUR estimate of Rs near the outer divertor tiles. Prior to the termination, RTVC successfully enacted the requested changes in both the core shape and divertor-leg geometry.

Shot 54000 tested whether RTVC could enact deliberate shape changes. The scenario was constructed from the successful 53996 configuration, but introduced prescribed trapezoidal perturbations to the core shape through Rout and ZX , and a partly simultaneous feedback-driven divertor-leg sweep, aiming for the Super-X configuration (Morris et al., 2014, 2018; Valanju et al., 2009). The Rs reference was designed to sweep the leg, using RTVC, from approximately 0.8 m to 1.4 m between 400 ms and 600 ms. As in shot 53996, Rnose was retained under the same pre-set VC schedule as the original reference shot, while Sgap was included in the 4

Deployment of real-time virtual circuits on MAST-U

3.4 Simultaneous control of seven shape parameters Shot 54168 was an exploratory stress test of simultaneous feedback control of all seven shape parameters available to RTVC. Such operation is not routinely attempted on MASTU because the shape responses are strongly cross-coupled and the resulting pseudoinversion can be poorly conditioned. Unlike the preceding experiments, all seven parameters were included in the RTVC inverse and assigned active feedback control. RTVC was enabled at 150 ms, and the discharge reached its programmed ramp-down at 1 s. As shown in Figure 3.1, transient departures from the requested shape occurred around 0.50 s and 0.77 s. The shape parameters subsequently returned towards their references, but tracking was markedly less smooth than in the preceding experiments. This result motivates the analysis of the VC inversion presented in Section 4.

Figure 3.2 Poloidal magnetic flux evolution in shot 54002 during the RTVC-controlled phase, generated using EFIT++. Snapshots are shown at RTVC activation, 140 ms after activation, and 220 ms after activation, illustrating the evolution from a conventional configuration towards the higher elongation with near-super-X configuration.

4 Discussion and outlook This work demonstrates that real-time, emulator-derived local plasma linearisations can be deployed in closed-loop control of MAST-U plasmas. Across discharges involving a constant shape, prescribed perturbations, feedback-driven divertor leg motion, and a strongly evolving configuration, the same RTVC implementation and emulators were used without scenario-specific retraining and without replacing the established MAST-U shape control architecture. Shot 54168 extended this test to the simultaneous control of all seven available shape parameters. The campaign therefore establishes the experimental feasibility of RTVC across distinct control tasks. The experiments also clarify the consequences of the approximations made in the present emulator configuration. Currents induced in the passive conducting structures are not included, and the plasma current density profile is represented by prescribed parameters rather than real-time estimates. The successful discharges show that these approximations did not preclude shape control in the states tested, consistent with the preceding simulations (Pentland et al., 2026b). They do not imply that passive currents or profile evolution are negligible in general, particularly during rapidly evolving phases. Including estimates of the passive current state and real-time plasma profiles would provide a more complete description of the instantaneous equilibrium and is a priority for future development. The present RTVC implementation also retained the Moore–Penrose pseudoinverse S + used in the conventional VC workflow. This choice isolated the effect of replacing preset linearisations with real-time ones, and was adequate for the preceding control tasks. Shot 54168 deliberately departed from normal MAST-U practice by assigning active feedback control to all seven RTVC shape parameters simultaneously. This mode is normally avoided because several shape parameters have strongly correlated PF coil responses. Asking the controller to correct them independently can therefore make the local shape matrix poorly conditioned, causing its pseudoinverse to convert shape corrections into disproportionately large PF coil current requests. The relevant limitation is the rank and conditioning of S = ∂P /∂Iact . This can be

3.3 Dynamic plasma shape evolution Shot 54002 was purposely designed to be more demanding, targeting a dynamic transition towards a plasma shape that has remained difficult to maintain reliably and control robustly on MAST-U: an elongated plasma with a Super-X leg configuration. This is the dynamic scenario that the RTVC paradigm is best posed to address: a highly evolving plasma shape in which the local linearisations change significantly during the discharge, making control design via conventional pre-set VC phases especially challenging. In this shot, all shape control was performed using RTVC, which controlled six out of seven shape parameters. In order to avoid the Langmuir probe protection limit encountered in shot 54000 the Rs sweep was limited to 1.2 m. RTVC control was enabled earlier than in the previous shots, at 150 ms. The core shape parameters were driven towards a higher plasma elongation configuration. Figure 3.1 shows RTVC successfully enacting the controlled ramp towards higher elongation through changes in both Rout and ZX , together with the prescribed adjustment to Sgap . The divertor-leg sweep is also completed successfully, after which the strike-point position Rs is maintained without triggering the real-time protection system. At approximately 380 ms, interaction with the nose results in a loss of shape control. This interaction was not reproduced in the pre-shot FPDT simulation. Although RX was controlled in this shot, unlike in the reference shot Rnose was not directly constrained. A discrepancy between the modelled and realised plasma responses could therefore produce an uncorrected displacement of the plasma nose while the actively controlled parameters remained close to their targets. Nevertheless, the requested shape transition had already been completed during the preceding RTVC-controlled interval. This is independently corroborated by the offline EFIT++ reconstructions of the same shot, shown in Figure 3.2, reproducing the substantial evolution in triangularity, elongation, and leg position inferred in real time by LEMUR and driven by RTVC control. 5

N. C. Amorisco et al. carry out scenario-specific retraining of neural control policies. Routine use of RTVC will require a richer real-time plasma state, a better-conditioned inverse, and validation over a wider operational envelope. The central enabling step has nevertheless been demonstrated: RTVCs can be integrated into an existing PCS and used to control plasmas across substantially different scenarios without changing the underlying control architecture.

Acknowledgements This work was funded by the Fusion Computing Lab collaboration (between UKAEA and STFC Hartree) and part funded by the EPSRC Energy Programme (EP/W006839/1). For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any author accepted manuscript version arising from this submission. To obtain further information, please contact publicationsmanager@ukaea.uk.

Figure 4.1 The VC norm ∥Vact ∥2 of the RTVC-controlled shape parameters in shots 53996 (solid black) and 54168 (solid red). Recall the shape matrix in shot 53996 included Rout , Rin , ZX , Sgap and Rnose , while RTVC feedback was applied to the first three (Rnose being controlled with a static VC) The pseudoinversion with all seven shape parameters in shot 54168 is compared with offline diagnostic inversions omitting either Rnose (dashed blue) or Rs (dashed green), and with the Rnose –Rs pair alone (dotted purple). The diagnostic inversions are shown for comparison and were not used to control the discharge. A vertical dotted line is denoted to mark the local amplification event at approximately 0.5 s.

Data availability The data supporting this work will be made available in accordance with the MAST-U data-access policy.

Declarations The authors have no conflicts of interest to declare.

explicitly observed by comparing the quantity ∥Vact ∥2 in shot 54168 with those in 53996 (see Figure 4.1). Here ∥Vact ∥2 represents the norm of the VC matrix comprising the active control vectors. Shot 53996 demonstrates that norms of order (1–2) × 105 A m−1 are compatible with successful, stable shape control. Shot 54168, however, produces significantly higher VC drives through much of the controlled period. Consequently, shape-control requests of a given magnitude are translated into larger PF coil current requests, increasing sensitivity to cross-coupling, measurement error, and model mismatch. This sustained amplification is consistent with, and may have contributed to, the less smooth shape tracking during shot 54168. Although this comparison does not establish a causal relationship, Figure 4.1 shows that the amplification is particularly pronounced close to the event at 0.50 s, when the Rnose and Rs columns of the local shape matrix S become nearly collinear. This near-degeneracy causes the pseudoinverse to amplify shape corrections into large PF coil current requests. Damped or Tikhonov-regularised inversion could limit this amplification, while state-dependent conditioning could increase the damping when near-degenerate shape directions are detected. RTVC already provides the evolving shape matrix S, so these changes affect only the small downstream inversion and require neither emulator retraining nor changes to the surrounding PCS architecture. They will be included in future RTVC development.

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