arXiv subjects

William Hornsby

Publications and source records attributed to William Hornsby.

14 recordsLinked to original sources

arXiv2026

GyroSwin: 5D Surrogates for Gyrokinetic Plasma Turbulence Simulations

Nuclear fusion plays a pivotal role in the quest for reliable and sustainable energy production. A major roadblock to viable fusion power is understanding plasma turbulence, which significantly impairs plasma confinement, and is vital for next-generation reactor design. Plasma turbulence is governed by the nonlinear gyrokinetic equation, which evolves a 5D distribution function over time. Due to its high computational cost, reduced-order models are often employed in practice to approximate turbulent transport of energy. However, they omit nonlinear effects unique to the full 5D dynamics. To tackle this, we introduce GyroSwin, the first scalable 5D neural surrogate that can model 5D nonlinear gyrokinetic simulations, thereby capturing the physical phenomena neglected by reduced models, while providing accurate estimates of turbulent heat transport. GyroSwin (i) extends hierarchical Vision Transformers to 5D, (ii) introduces cross-attention and integration modules for latent 3D$\leftrightarrow$5D interactions between electrostatic potential fields and the distribution function, and (iii) performs channelwise mode separation inspired by nonlinear physics. We demonstrate that GyroSwin outperforms widely used reduced numerics on heat flux prediction, captures the turbulent energy cascade, and reduces the cost of fully resolved nonlinear gyrokinetics by three orders of magnitude while remaining physically verifiable. GyroSwin shows promising scaling laws, tested up to one billion parameters, paving the way for scalable neural surrogates for gyrokinetic simulations of plasma turbulence.

physics.plasm-ph↗

arXiv2026

A Shortcut to Statistically Steady-State Turbulence with Flow Matching

Many nonlinear physical systems exhibit an initial transient phase in which perturbations grow before nonlinear interactions lead to a statistically steady state. While this saturated regime is of primary interest, direct numerical simulations must resolve the full transient dynamics before reaching it, incurring significant computational cost. In Computational Fluid Dynamics, reduced-order approaches such as Large Eddy Simulation mitigate computational cost by modeling small-scale dynamics, enabling tractable approximations of turbulent flows. In contrast, for systems such as gyrokinetics, comparably effective closures for the full dynamics are not generally available, and high-fidelity simulations remain necessary. Existing surrogate modeling approaches for these systems are autoregressive, hence they suffer from accumulating error. We instead propose to bypass explicit time evolution by directly modeling the distribution of saturated states under an ergodicity assumption, stating that ensemble averages over samples are equivalent to time averages of a single long simulation. We introduce GyroFlow, a latent generative model that directly estimates steady-state statistics of gyrokinetic turbulence in 5D phase space, without resolving the transient phase. GyroFlow generates saturated snapshots from noise, conditioned on dimensionless operating parameters and outperforms autoregressive, reduced-order, and other generative approaches, while providing substantial speedup. To evaluate generation quality we propose FGyD, a distributional metric computed in the latent space of a pretrained gyrokinetic model, and show that it correlates with downstream flux accuracy and solver convergence. Finally, GyroFlow can be used to warm-start the numerical code used to produce the data.

physics.plasm-ph↗

arXiv2026

Physics-Informed Neural Compression of High-Dimensional Plasma Data

High-fidelity scientific simulations are now producing unprecedented amounts of data, creating a storage and analysis bottleneck. A single simulation can generate tremendous data volumes, often forcing researchers to discard valuable information. A prime example of this is plasma turbulence described by the gyrokinetic equations: nonlinear, multiscale, and 5D in phase space. It constitutes one of the most computationally demanding frontiers of modern science, with runs taking weeks and yielding tens of terabytes of data dumps. The increasing storage demands underscore the importance of compression. However, reconstructed snapshots do not necessarily preserve essential physical quantities. We present a spatiotemporal evaluation pipeline, accounting for structural phenomena and multi-scale transient fluctuations to assess the degree of physical fidelity. Indeed, we find that various compression techniques lack preservation of both spatial mode structure and temporal turbulence characteristics. Therefore, we explore Physics-Informed Neural Compression (PINC), which incorporates physics-informed losses tailored to gyrokinetics and enables extreme compressions ratios of over 70,000x. Entropy coding on top of PINC further pushes it to 120,000x. This direction provides a viable and scalable solution to the prohibitive storage demands of gyrokinetics, enabling post-hoc analyses that were previously infeasible.

physics.plasm-ph↗

arXiv2025

A Performance Analysis of Task Scheduling for UQ Workflows on HPC Systems

Uncertainty Quantification (UQ) workloads are becoming increasingly common in science and engineering. They involve the submission of thousands or even millions of similar tasks with potentially unpredictable runtimes, where the total number is usually not known a priori. A static one-size-fits-all batch script would likely lead to suboptimal scheduling, and native schedulers installed on High Performance Computing (HPC) systems such as SLURM often struggle to efficiently handle such workloads. In this paper, we introduce a new load balancing approach suitable for UQ workflows. To demonstrate its efficiency in a real-world setting, we focus on the GS2 gyrokinetic plasma turbulence simulator. Individual simulations can be computationally demanding, with runtimes varying significantly-from minutes to hours-depending on the high-dimensional input parameters. Our approach uses UQ and Modelling Bridge, which offers a language-agnostic interface to a simulation model, combined with HyperQueue which works alongside the native scheduler. In particular, deploying this framework on HPC systems does not require system-level changes. We benchmark our proposed framework against a standalone SLURM approach using GS2 and a Gaussian Process surrogate thereof. Our results demonstrate a reduction in scheduling overhead by up to three orders of magnitude and a maximum reduction of 38% in CPU time for long-running simulations compared to the naive SLURM approach, while making no assumptions about the job submission patterns inherent to UQ workflows.

cs.DC↗

arXiv2025

5D Neural Surrogates for Nonlinear Gyrokinetic Simulations of Plasma Turbulence

Nuclear fusion plays a pivotal role in the quest for reliable and sustainable energy production. A major roadblock to achieving commercially viable fusion power is understanding plasma turbulence, which can significantly degrade plasma confinement. Modelling turbulence is crucial to design performing plasma scenarios for next-generation reactor-class devices and current experimental machines. The nonlinear gyrokinetic equation underpinning turbulence modelling evolves a 5D distribution function over time. Solving this equation numerically is extremely expensive, requiring up to weeks for a single run to converge, making it unfeasible for iterative optimisation and control studies. In this work, we propose a method for training neural surrogates for 5D gyrokinetic simulations. Our method extends a hierarchical vision transformer to five dimensions and is trained on the 5D distribution function for the adiabatic electron approximation. We demonstrate that our model can accurately infer downstream physical quantities such as heat flux time trace and electrostatic potentials for single-step predictions two orders of magnitude faster than numerical codes. Our work paves the way towards neural surrogates for plasma turbulence simulations to accelerate deployment of commercial energy production via nuclear fusion.

physics.plasm-ph↗

arXiv2024

Gaussian process surrogate models for the properties of micro-tearing modes in spherical tokamaks

Spherical tokamaks (STs) have many desirable features that make them a suitable choice for fusion power plants. To understand their confinement properties, accurate calculation of turbulent micro-instabilities is necessary for tokamak design. Presented is a novel surrogate model for Micro-tearing modes (MTMs), the micro-instability thought to be dominant in high beta STs. Direct numerical calculation of micro-instabilities is computationally expensive and is a significant bottleneck in integrated plasma modelling. The considerable number of geometric and thermodynamic parameters, the interactions that influence these coefficients and the resolutions needed to accurately resolve these modes, makes direct numerical simulation for parameter space exploration computationally extremely challenging. However, this and the dearth of accurate reduced physics models for MTMs makes it suitable for surrogate modelling using Gaussian Process Regression, a modern machine learning technique. This paper outlines the further development of a data-driven reduced-order model across a spherical tokamak reactor-relevant parameter space utilising Gaussian Process Regression (GPR) and classification; techniques from machine learning. To build the original simple GP model these two components were used in an active learning loop to maximise the efficiency of data acquisition thus minimising computational cost. The `simple' GP was seen to show a plateau of fidelity with more data and to be under-confident, particular in areas of parameter space close to marginal stability. It is postulated that the presence of multiple sub-types of MTM could be the root cause, with the underlying function being less smooth than expected. An expansion of the model using clustering algorithms to find optimal sub models using a mixture of experts approach is shown to greatly improve the variances in the outputs of the GP model.

physics.plasm-ph↗

arXiv2024

ReMKiT1D -- A framework for building reactive multi-fluid models of the tokamak Scrape-Off Layer with coupled electron kinetics in 1D

In this manuscript we present the recently developed flexible framework for building both fluid and electron kinetic models of the tokamak Scrape-Off Layer in 1D - ReMKiT1D (Reactive Multi-fluid and Kinetic Transport in 1D). The framework can handle systems of non-linear ODEs, various 1D PDEs arising in fluid modelling, as well as PDEs arising from the treatment of the electron kinetic equation. As such, the framework allows for flexibility in fluid models of the Scrape-Off Layer while allowing the easy addition of kinetic electron effects. We focus on presenting both the high-level design decisions that allow for model flexibility, as well as the most important implementation aspects. A significant number of verification and performance tests are presented, as well as a step-by-step walkthrough of a simple example for setting up models using the Python interface.

physics.plasm-ph↗

arXiv2023

Gaussian Process Regression models for the properties of micro-tearing modes in spherical tokamak

Spherical tokamaks (STs) have many desirable features that make them an attractive choice for a future fusion power plant. Power plant viability is intrinsically related to plasma heat and particle confinement and this is often determined by the level of micro-instability driven turbulence. Accurate calculation of the properties of turbulent micro-instabilities is therefore critical for tokamak design, however, the evaluation of these properties is computationally expensive. The considerable number of geometric and thermodynamic parameters and the high resolutions required to accurately resolve these instabilities makes repeated use of direct numerical simulations in integrated modelling workflows extremely computationally challenging and creates the need for fast, accurate, reduced-order models. This paper outlines the development of a data-driven reduced-order model, often termed a {\it surrogate model} for the properties of micro-tearing modes (MTMs) across a spherical tokamak reactor-relevant parameter space utilising Gaussian Process Regression (GPR) and classification; techniques from machine learning. These two components are used in an active learning loop to maximise the efficiency of data acquisition thus minimising computational cost. The high-fidelity gyrokinetic code GS2 is used to calculate the linear properties of the MTMs: the mode growth rate, frequency and normalised electron heat flux; core components of a quasi-linear transport model. Five-fold cross-validation and direct validation on unseen data is used to ascertain the performance of the resulting surrogate models.

physics.plasm-ph↗

arXiv2014

On seed island generation and the non-linear self-consistent interaction of the tearing mode with electromagnetic gyro-kinetic turbulence

The multi-scale interaction of self-consistently driven magnetic islands with electromagnetic turbulence is studied within the three dimensional, toroidal gyro-kinetic framework. It can be seen that, even in the presence of electromagnetic turbulence the linear structure of the mode is retained. Turbulent fluctuations do not destroy the growing island early in its development, which then maintains a coherent form as it grows. The island is seeded by the electromagnetic turbulence fluctuations, which provide an initial island structure through nonlinear interactions and which grows at a rate significantly faster than the linear tearing growth rate. These island structures saturate at a width that is approximately $ρ_{i}$ in size. In the presence of turbulence the island then grows at the linear rate even though the island is significantly wider than the resonant layer width, a regime where the island is expected to grow at a significantly reduced non-linear rate. A large degree of stochastisation around the separatrix, and an almost complete break down of the X-point is seen. This significantly reduces the effective island width.

physics.plasm-ph↗

arXiv2014

The linear tearing instability in three dimensional, toroidal gyrokinetic simulations

Linear gyro-kinetic simulations of the classical tearing mode in three-dimensional toroidal geometry were performed using the global gyro kinetic turbulence code, GKW . The results were benchmarked against a cylindrical ideal MHD and analytical theory calculations. The stability, growth rate and frequency of the mode were investigated by varying the current profile, collisionality and the pressure gradients. Both collision-less and semi-collisional tearing modes were found with a smooth transition between the two. A residual, finite, rotation frequency of the mode even in the absense of a pressure gradient is observed which is attributed to toroidal finite Larmor-radius effects. When a pressure gradient is present at low collisionality, the mode rotates at the expected electron diamagnetic frequency. However the island rotation reverses direction at high collisionality. The growth rate is found to follow a $η^{1/7}$ scaling with collisional resistivity in the semi-collisional regime, closely following the semi-collisional scaling found by Fitzpatrick. The stability of the mode closely follows the stability using resistive MHD theory, however a modification due to toroidal coupling and pressure effects is seen.

physics.plasm-ph↗

arXiv2014

Nonlinear seed island generation by three-dimensional electromagnetic, gyrokinetic turbulence

Turbulence is shown to be critical to the onset and evolution of the neoclassical tearing mode, affecting both its growth and rotation. The interaction is here studied for the first time in the three dimensional, toroidal gyrokinetic framework. Turbulent fluctuations do not destroy the growing island early in its development, which maintains a coherent form as it grows, in fact the island is seeded and its rotation frequency determined, by nonlinear interaction. This process provides an initial structure that is of the order of an ion gyro-radius wide, allowing the island to rapidly reach a large size. A large degree of stochastisation around the seperatrix, and a complete breakdown of the X-point is seen, which significantly reduces the effective island width. A turbulent modification of the electrostatic field in and around the island greatly affects the size of the resonant layer width, and the island is seen to grow at the linear rate even though the island is significantly wider than the singular layer width.

physics.plasm-ph↗

arXiv2013

Toroidal momentum transport in a tokamak caused by symmetry breaking parallel derivatives

A new mechanism for toroidal momentum transport in a tokamak is investigated using the gyro-kinetic model. First, an analytic model is developed through the use of the ballooning transform. The terms that generate the momentum transport are then connected with the poloidal derivative of the ballooning envelope, which are one order smaller in the normalised Larmor radius, compared with the derivative of the eikonal. The mechanism, therefore, does not introduce an inhomogeneity in the radial direction, in contrast with the effect of profile shearing. Numerical simulations of the linear ion temperature gradient mode with adiabatic electrons, retaining the finite rho* effects in the ExB velocity, the drift, and the gyro-average, are presented. The momentum flux is found to be linear in the normalised Larmor radius (ρ*) but is, nevertheless, generating a sizeable counter-current rotation. The total momentum flux scales linear with the aspect ratio of the considered magnetic surface, and increases with increasing magnetic shear, safety factor, and density and temperature gradients.

physics.plasm-ph↗

arXiv2012

Ion temperature gradient instability at sub-Larmor radius scales with non-zero ballooning angle

Linear gyro-kinetic stability calculations predict unstable toroidal Ion Temperature Gradient modes with normalised poloidal wave vectors well above one ($k_θρ_i > 1$) for standard parameters and with adiabatic electrons. These modes have a maximum amplitude at a poloidal angle $θ$ that is shifted away from the low field side ($θ\ne 0$). The physical mechanism is clarified through the use of a fluid model. It is shown that the shift of the mode away from the low field side ($θ\ne 0$) reduces the effective drift frequency, and allows for the instability to develop. Numerical tests using the gyro-kinetic model confirm this physical mechanism. It is furthermore shown that modes with $θ\ne 0$ can be important also for $k_θρ_i < 1$ close to the threshold of the ITG. In fact, modes with $θ\ne 0$ can exist for normalised temperature gradient lengths below the threshold of the ITG obtained for $θ= 0$.

physics.plasm-ph↗

arXiv2012

On the dynamics of vortex modes within magnetic islands

Recent work investigating the interaction of magnetic islands with micro-turbulence has uncovered the striking observation of large scale vortex modes forming within the island structure [W.A. Hornsby {\it et al.}, Phys. Plasmas {\bf 17} 092301 (2010)]. These electrostatic vortices are found to be the size of the island and are oscillatory. It is this oscillatory behaviour and the presence of turbulence that leads us to believe that the dynamics are related to the Geodesic Acoustic Mode (GAM), and it is this link that is investigated in this paper. Here we derive an equation for the GAM in the MHD limit, in the presence of a magnetic island modified three-dimensional axisymmetric geometry. The eigenvalues and eigenfunctions are calculated numerically and then utilised to analyse the dynamics of oscillatory large-scale electrostatic potential structures seen in both linear and non-linear gyro-kinetic simulations.

physics.plasm-ph↗