I am a computational scientist working in the plasma simulation group at the United Kingdom Atomic Energy Authority.
I am interested in all sorts of mathematical modelling problems (regardless of the application) and often find myself working at the interface between applied and computational mathematics. I have particular interests in:
- Numerical integration for ODEs/PDEs.
- MHD equilibrium modelling.
- Surrogate modelling (e.g. Gaussian processes).
- Bayesian methods (e.g. data assimilation, optimisation, UQ).
- Parallel-in-Time (PinT) methods.
- High performance computing.
- Multiscale/hybrid modelling problems.
Do get in contact if you'd like to discuss any of my research or are interested in collaboration!
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University of WarwickPh.D. in Mathematics of Real-World SystemsSep. 2020 - Sep. 2023 -
University of WarwickMSc in Mathematics of Real-World SystemsSep. 2019 - Sep. 2020
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University College LondonMSc in Mathematical ModellingSep. 2018 - Sep. 2019 -
University of BathBSc in Mathematics with Industrial Placement YearSep. 2013 - Jul. 2017
Experience
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United Kingdom Atomic Energy Authority (UKAEA)Computational ScientistOct. 2023 - Present -
University of WarwickGraduate Teaching AssistantOct. 2020 - Sep. 2023
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Kings College LondonGraduate Mathematics TutorOct. 2020 - Apr. 2021 -
UK Mathematics TrustMarking VolunteerSep. 2017 - Sep. 2020 -
University of BathSummer Research InternJun. 2017 - Sep. 2017
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University of BathMathematics TutorSep. 2016 - Apr. 2017
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ConocoPhillips Ltd.Quantitative Market Risk AnalystJul. 2015 - Jul. 2016
Selected Research
Real-time applicability of emulated virtual circuits for tokamak plasma shape control
P. Cavestany, A. Ross, A. Agnello, A. Garrod, N. Amorisco, G. K. Holt, K. Pentland, J. Buchanan
2025 IEEE Conference on Control Technology and Applications
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 (≈5-10%) can be achieved on a selection of geometric targets using combinations of neural network emulators with ≈1e5 parameters. A sample of ≈1e5−1e6 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.
Plasma shape control Virtual circuits Neural network emulation MHD equilibria MAST-U
Real-time applicability of emulated virtual circuits for tokamak plasma shape control
P. Cavestany, A. Ross, A. Agnello, A. Garrod, N. Amorisco, G. K. Holt, K. Pentland, J. Buchanan
2025 IEEE Conference on Control Technology and Applications
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 (≈5-10%) can be achieved on a selection of geometric targets using combinations of neural network emulators with ≈1e5 parameters. A sample of ≈1e5−1e6 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.
Plasma shape control Virtual circuits Neural network emulation MHD equilibria MAST-U
Bayesian optimisation of poloidal field coil positions in tokamaks
T. Nunn, K. Pentland, V. Gopakumar, J. Buchanan
Physics of Plasmas
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.
Bayesian optimisation Poloidal field coils Spherical tokamak MHD equilibria FreeGS
Bayesian optimisation of poloidal field coil positions in tokamaks
T. Nunn, K. Pentland, V. Gopakumar, J. Buchanan
Physics of Plasmas
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.
Bayesian optimisation Poloidal field coils Spherical tokamak MHD equilibria FreeGS
Multiple solutions to the static forward free-boundary Grad-Shafranov problem on MAST-U
K. Pentland, N. C. Amorisco, P. E. Farrell, C. J. Ham
Nuclear Fusion
The Grad-Shafranov (GS) equation is a nonlinear elliptic partial differential equation that governs the ideal magnetohydrodynamic equilibrium of a tokamak plasma. Previous studies have demonstrated the existence of multiple solutions to the GS equation when solved in idealistic geometries with simplified plasma current density profiles and boundary conditions. Until now, the question of whether multiple equilibria might exist in real-world tokamak geometries with more complex current density profiles and integral free-boundary conditions (commonly used in production-level equilibrium codes) has remained unanswered. In this work, we discover multiple solutions to the static forward free-boundary GS problem in the MAST-U tokamak geometry using the validated evolutive equilibrium solver FreeGSNKE and the deflated continuation algorithm. By varying the plasma current, current density profile coefficients, or coil currents in the GS equation, we identify and characterise distinct equilibrium solutions, including both deeply and more shallowly confined plasma states. We suggest that the existence of even more equilibria is likely prohibited by the restrictive nature of the integral free-boundary condition, which globally couples poloidal fluxes on the computational boundary with those on the interior. We conclude by discussing the implications of these findings for wider equilibrium modelling and emphasise the need to explore whether multiple solutions are present in other equilibrium codes and tokamaks, as well as their potential impact on downstream simulations that rely on GS equilibria.
Multiple solutions Grad-Shafranov MHD equilibria FreeGSNKE Deflated continuation MAST-U
Multiple solutions to the static forward free-boundary Grad-Shafranov problem on MAST-U
K. Pentland, N. C. Amorisco, P. E. Farrell, C. J. Ham
Nuclear Fusion
The Grad-Shafranov (GS) equation is a nonlinear elliptic partial differential equation that governs the ideal magnetohydrodynamic equilibrium of a tokamak plasma. Previous studies have demonstrated the existence of multiple solutions to the GS equation when solved in idealistic geometries with simplified plasma current density profiles and boundary conditions. Until now, the question of whether multiple equilibria might exist in real-world tokamak geometries with more complex current density profiles and integral free-boundary conditions (commonly used in production-level equilibrium codes) has remained unanswered. In this work, we discover multiple solutions to the static forward free-boundary GS problem in the MAST-U tokamak geometry using the validated evolutive equilibrium solver FreeGSNKE and the deflated continuation algorithm. By varying the plasma current, current density profile coefficients, or coil currents in the GS equation, we identify and characterise distinct equilibrium solutions, including both deeply and more shallowly confined plasma states. We suggest that the existence of even more equilibria is likely prohibited by the restrictive nature of the integral free-boundary condition, which globally couples poloidal fluxes on the computational boundary with those on the interior. We conclude by discussing the implications of these findings for wider equilibrium modelling and emphasise the need to explore whether multiple solutions are present in other equilibrium codes and tokamaks, as well as their potential impact on downstream simulations that rely on GS equilibria.
Multiple solutions Grad-Shafranov MHD equilibria FreeGSNKE Deflated continuation MAST-U
Validation of the static forward Grad-Shafranov equilibrium solvers in FreeGSNKE and Fiesta using EFIT++ reconstructions from MAST-U
K. Pentland, N. C. Amorisco, O. El-Zobaidi, S. Etches, A. Agnello, G. K. Holt, A. Ross, C. Vincent, J. Buchanan, S. J. P. Pamela, G. McArdle, L. Kogan, G. Cunningham
Physica Scripta
In this paper, we are interested in solving the static forward Grad-Shafranov (GS) problem for free-boundary MHD equilibria. Our focus is on the validation of the static forward solver in the Python-based equilibrium code FreeGSNKE by solving equilibria from magnetics-only EFIT++ reconstructions of MAST-U shots. In addition, we also validate FreeGSNKE against equilibria simulated using the well-established MATLAB-based equilibrium code Fiesta. To do this, we develop a computational pipeline that allows one to load the same (a)symmetric MAST-U machine description into each solver, specify the required inputs (active/passive conductor currents, plasma profiles and coefficients, etc.) from EFIT++, and solve the GS equation for all available time slices across a shot. For a number of different MAST-U shots, we demonstrate that both FreeGSNKE and Fiesta can successfully reproduce various poloidal flux quantities and shape targets (e.g. midplane radii, magnetic axes, separatrices, X-points, and strikepoints) in agreement with EFIT++ calculations to a very high degree of accuracy.
[Publication] [arXiv] [Code] [Poster] [Talk]
MHD equilibria Grad-Shafranov FreeGSNKE Fiesta EFIT++ MAST-U
Validation of the static forward Grad-Shafranov equilibrium solvers in FreeGSNKE and Fiesta using EFIT++ reconstructions from MAST-U
K. Pentland, N. C. Amorisco, O. El-Zobaidi, S. Etches, A. Agnello, G. K. Holt, A. Ross, C. Vincent, J. Buchanan, S. J. P. Pamela, G. McArdle, L. Kogan, G. Cunningham
Physica Scripta
In this paper, we are interested in solving the static forward Grad-Shafranov (GS) problem for free-boundary MHD equilibria. Our focus is on the validation of the static forward solver in the Python-based equilibrium code FreeGSNKE by solving equilibria from magnetics-only EFIT++ reconstructions of MAST-U shots. In addition, we also validate FreeGSNKE against equilibria simulated using the well-established MATLAB-based equilibrium code Fiesta. To do this, we develop a computational pipeline that allows one to load the same (a)symmetric MAST-U machine description into each solver, specify the required inputs (active/passive conductor currents, plasma profiles and coefficients, etc.) from EFIT++, and solve the GS equation for all available time slices across a shot. For a number of different MAST-U shots, we demonstrate that both FreeGSNKE and Fiesta can successfully reproduce various poloidal flux quantities and shape targets (e.g. midplane radii, magnetic axes, separatrices, X-points, and strikepoints) in agreement with EFIT++ calculations to a very high degree of accuracy.
[Publication] [arXiv] [Code] [Poster] [Talk]
MHD equilibria Grad-Shafranov FreeGSNKE Fiesta EFIT++ MAST-U
Neural-Parareal: dynamically training neural operators as coarse solvers for time-parallelisation of fusion MHD simulations
S. J. P. Pamela, N. Carey, J. Brandstetter, R. Akers, L. Zanisi, J. Buchanan, V. Gopakumar, M. Hoelzl, G. Huijsmans, K. Pentland, T. James, G. Antonucci, The JOREK Team
Computer Physics Communications
In this paper, we developed the Neural-Parareal framework to enhance the efficiency of time-parallel simulations for fusion research by integrating neural operators that dynamically train as new data becomes available. This approach replaces traditional coarse-solvers with neural network surrogates, leading to progressively more accurate predictions and significant speed-ups in the parareal simulations. Our findings demonstrate the effective convergence of high-performance computing and artificial intelligence, advocating for their common use in digital engineering design.
Fourier neural operators Parallel-in-time Parareal High performance computing
Neural-Parareal: dynamically training neural operators as coarse solvers for time-parallelisation of fusion MHD simulations
S. J. P. Pamela, N. Carey, J. Brandstetter, R. Akers, L. Zanisi, J. Buchanan, V. Gopakumar, M. Hoelzl, G. Huijsmans, K. Pentland, T. James, G. Antonucci, The JOREK Team
Computer Physics Communications
In this paper, we developed the Neural-Parareal framework to enhance the efficiency of time-parallel simulations for fusion research by integrating neural operators that dynamically train as new data becomes available. This approach replaces traditional coarse-solvers with neural network surrogates, leading to progressively more accurate predictions and significant speed-ups in the parareal simulations. Our findings demonstrate the effective convergence of high-performance computing and artificial intelligence, advocating for their common use in digital engineering design.
Fourier neural operators Parallel-in-time Parareal High performance computing
GParareal: a time-parallel ODE solver using Gaussian process emulation
K. Pentland, M. Tamborrino, T. J. Sullivan, J. Buchanan, L. C. Appel
Statistics and Computing
In this paper, we introduced GParareal, a time-parallel algorithm for solving initial value problems (IVPs) by employing a Gaussian process emulator to model the correction term between coarse and fine solutions. Our results demonstrate that GParareal converges in fewer iterations than the traditional parareal method, improving computational speed and enabling the use of legacy solution archives to further enhance convergence. This approach addresses limitations in existing time-parallel methods and offers a significant advancement in solving IVPs with high numerical accuracy.
[Publication] [arXiv] [Code] [Poster] [Talk]
Parallel-in-time Parareal Gaussian processes
GParareal: a time-parallel ODE solver using Gaussian process emulation
K. Pentland, M. Tamborrino, T. J. Sullivan, J. Buchanan, L. C. Appel
Statistics and Computing
In this paper, we introduced GParareal, a time-parallel algorithm for solving initial value problems (IVPs) by employing a Gaussian process emulator to model the correction term between coarse and fine solutions. Our results demonstrate that GParareal converges in fewer iterations than the traditional parareal method, improving computational speed and enabling the use of legacy solution archives to further enhance convergence. This approach addresses limitations in existing time-parallel methods and offers a significant advancement in solving IVPs with high numerical accuracy.
[Publication] [arXiv] [Code] [Poster] [Talk]
Parallel-in-time Parareal Gaussian processes