arXiv subjects

Kamran Pentland

Publications and source records attributed to Kamran Pentland.

8 recordsLinked to original sources

arXiv2026

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

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.

physics.plasm-ph↗

arXiv2026

Real-time virtual circuits for plasma shape control via neural network emulators: integration and testing in the MAST-U PCS

The deployment of advanced, AI-enabled control algorithms in tokamak experiments requires robust integration with existing plasma control system (PCS) architectures and extensive pre-experimental validation. In this contribution, we describe the integration and testing of neural-network-emulated virtual circuits for plasma shape control within the MAST Upgrade (MAST-U) PCS environment. The neural network models predict the plasma shape using the plasma current, poloidal field coil currents, and plasma profile parameters. In this paper, we explain how they are deployed via a real-time C++ inference server that interfaces with the PCS, returning the shape prediction and its Jacobian, and how, from the latter, virtual circuit matrices and updated coil current requests are computed for real-time actuation. Emphasis is placed on the validation workflow and best practices adopted to ensure confidence in the proposed control framework prior to experimental deployment. This work demonstrates practical AI-based shape control components for fusion control systems, with direct relevance for upcoming MAST-U experiments and future devices.

physics.plasm-ph↗

arXiv2026

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

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 \textit{virtual 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.

physics.plasm-ph↗

arXiv2025

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

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.

physics.plasm-ph↗

arXiv2025

Bayesian optimisation of poloidal field coil positions in tokamaks

The tokamak is a world-leading concept for producing sustainable energy via magnetically-confined nuclear fusion. Identifying where to position the magnets within a tokamak, specifically the poloidal field (PF) coils, is a design problem which requires balancing a number of competing economic, physical, and engineering objectives and constraints. In this paper, we show that multi-objective Bayesian optimisation (BO), an iterative optimisation technique utilising probabilistic machine learning models, can effectively explore this complex design space and return several optimal PF coil sets. These solutions span the Pareto front, a subset of the objective space that optimally satisfies the specified objective functions. We outline an easy-to-use BO framework and demonstrate that it outperforms alternative optimisation techniques while using significantly fewer computational resources. Our results show that BO is a promising technique for fusion design problems that rely on computationally demanding high-fidelity simulations.

physics.plasm-ph↗

arXiv2023

Error bound analysis of the stochastic parareal algorithm

Stochastic parareal (SParareal) is a probabilistic variant of the popular parallel-in-time algorithm known as parareal. Similarly to parareal, it combines fine- and coarse-grained solutions to an ordinary differential equation (ODE) using a predictor-corrector (PC) scheme. The key difference is that carefully chosen random perturbations are added to the PC to try to accelerate the location of a stochastic solution to the ODE. In this paper, we derive superlinear and linear mean-square error bounds for SParareal applied to nonlinear systems of ODEs using different types of perturbations. We illustrate these bounds numerically on a linear system of ODEs and a scalar nonlinear ODE, showing a good match between theory and numerics.

math.NA↗

arXiv2022

GParareal: A time-parallel ODE solver using Gaussian process emulation

Sequential numerical methods for integrating initial value problems (IVPs) can be prohibitively expensive when high numerical accuracy is required over the entire interval of integration. One remedy is to integrate in a parallel fashion, "predicting" the solution serially using a cheap (coarse) solver and "correcting" these values using an expensive (fine) solver that runs in parallel on a number of temporal subintervals. In this work, we propose a time-parallel algorithm (GParareal) that solves IVPs by modelling the correction term, i.e. the difference between fine and coarse solutions, using a Gaussian process emulator. This approach compares favourably with the classic parareal algorithm and we demonstrate, on a number of IVPs, that GParareal can converge in fewer iterations than parareal, leading to an increase in parallel speed-up. GParareal also manages to locate solutions to certain IVPs where parareal fails and has the additional advantage of being able to use archives of legacy solutions, e.g. solutions from prior runs of the IVP for different initial conditions, to further accelerate convergence of the method -- something that existing time-parallel methods do not do.

math.NA↗

arXiv2022

Stochastic parareal: an application of probabilistic methods to time-parallelisation

Parareal is a well-studied algorithm for numerically integrating systems of time-dependent differential equations by parallelising the temporal domain. Given approximate initial values at each temporal sub-interval, the algorithm locates a solution in a fixed number of iterations using a predictor-corrector, stopping once a tolerance is met. This iterative process combines solutions located by inexpensive (coarse resolution) and expensive (fine resolution) numerical integrators. In this paper, we introduce a stochastic parareal algorithm aimed at accelerating the convergence of the deterministic parareal algorithm. Instead of providing the predictor-corrector with a deterministically located set of initial values, the stochastic algorithm samples initial values from dynamically varying probability distributions in each temporal sub-interval. All samples are then propagated in parallel using the expensive integrator. The set of sampled initial values yielding the most continuous (smoothest) trajectory across consecutive sub-intervals are fed into the predictor-corrector, converging in fewer iterations than the deterministic algorithm with a given probability. The performance of the stochastic algorithm, implemented using various probability distributions, is illustrated on low-dimensional systems of ordinary differential equations (ODEs). We provide numerical evidence that when the number of sampled initial values is large enough, stochastic parareal converges almost certainly in fewer iterations than the deterministic algorithm, maintaining solution accuracy. Given its stochastic nature, we also highlight that multiple simulations of stochastic parareal return a distribution of solutions that can represent a measure of uncertainty over the ODE solution.

math.NA↗