Reconstruction of the reversed field pinch magnetic perturbations in toroidal geometry by means of Deep Learning for real-time plasma control - proof of concept for real-time toroidal reconstruction

Aug 6, 2026

Aiming at the upcoming operation of RFX-mod2 in reversed field pinch configuration, the work targets a major upgrade to the experiment’s real-time control by replacing the conventional simplified cylindrical approximation with a correct toroidal reconstruction. The toroidal reconstruction from experimental measurements currently involves lengthy computations that are not feasible in real time. Because the underlying solution space is well behaved, the solving algorithm is replaced with a deep learning model integrated into a real-time FPGA-based system. The thesis focuses on computing toroidal equilibrium and demonstrates feasibility through training, validation, and FPGA-oriented optimizations such as pruning and heterogeneous quantization.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages106

Reading Time4 h 27 min

AccessFree to download

Introduction

Magnetic confinement fusion and RFP context

RFX-mod machine and MHD instabilities

Toroidal reconstruction and machine learning in fusion plasmas

Neural Networks

Core concepts, training, and model selection

Equilibrium Model

Dataset and polynomial-Gaussian window model

Fixed cubic spline and cubic spline models

FPGA Implementation

FPGA basics, hls4ml, and optimization/deployment

Deployed model performance

Conclusions and future work

Appendix

Cubic Splines

UNIVERSIT `A DEGLI STUDI DI PADOVA Dipartimento di Fisica e Astronomia “Galileo Galilei” Master Degree in Physics of Data Final Dissertation Reconstruction of the reversed field pinch magnetic perturbations in toroidal geometry by means of Deep Learning for real-time plasma control Thesis supervisor Prof. Jacopo Pazzini Thesis co-supervisor Dr . Andrea Rigoni Garola Candidate Lorenzo Saccaro Academic Year 2023/2024 Abstract In view of the forthcoming operation of RFX-mod2 in reversed field pinch configuration, a significant enhancement for the experiment’s real-time control system is transitioning from the conventional simplified cylindrical approximation to the correct toroidal reconstruction. Presently the toroidal reconstruction starting from the experimental measurements, requires lengthy calculations that are impractical in real-time. Given that the solution space is reasonably well-behaved, the solving algorithm can be substituted with a Deep Learning (DL) network that can be integrated into the real-time system. This thesis tackles the first step of these complex calculations, which is the computation of the equilibrium in toroidal geometry. To achieve this, different neural networks have been trained and validated leveraging the existing toroidal reconstruction code. The most promising model has been selected anda series of optimizations, including pruning and heterogeneous quantization, have been performed in order to adapt the network to a real-time environment built in FPGA components. This work serves as a proof of concept for the feasibility of the real-time toroidal reconstruction using DL methods. iv Contents Introduction 1 1 Theoretical Perspective 3 1.1 Magnetic confinement fusion ................................ 3 1.1.1 Tokamak configuration ................................ 4 1.1.2 RFP configuration .................................. 5 1.2 RFX-mod machine ...................................... 5 1.3 MHD instabilities ....................................... 7 1.3.1 Dynamo mechanism in RFP ............................. 10 1.3.2 MH and QSH magnetic topologies ......................... 11 1.4 Toroidal reconstruction of magnetic perturbations .................... 12 1.5 Machine learning in fusion plasmas ............................. 14 2 Neural Networks 17 2.1 Basic concepts ........................................ 17 2.1.1 Neurons and layers .................................. 18 2.1.2 Activation functions ................................. 18 2.1.3 Loss function ..................................... 20 2.2 Training neural networks ................................... 22 2.2.1 Backpropagation ................................... 23 2.2.2 Stochastic Gradient Descent ............................. 24 2.2.3 Momentum and advanced optimizers ........................ 25 2.3 Universal approximation theorems ............................. 26 2.3.1 Arbitrary width ................................... 26 2.3.2 Arbitrary depth ................................... 27 2.3.3 Bounded depth and bounded width ........................ 27 2.4 Overfitting and model selection ............................... 28 2.4.1 Regularization and dropout ............................. 28 2.4.2 Hyperparameters tuning ............................... 30 3 Equilibrium Model 33 3.1 Dataset ............................................ 33 3.2 Polynomial-Gaussian window model ............................ 34 3.2.1 Hyperparameters tuning ............................... 37 3.2.2 Results ........................................ 37 3.3 Fixed Cubic Spline model .................................. 47 3.3.1 Hyperparameters tuning ............................... 47 3.3.2 Results ........................................ 47 3.4 Cubic Spline model ...................................... 55 3.4.1 Performance analysis ................................. 57 4 FPGA Implementatio

FAQs

Why is toroidal reconstruction needed for RFX-mod2 real-time control?

RFX-mod2 will operate in a reversed field pinch configuration, where real-time control requires toroidal reconstruction rather than the simplified cylindrical approximation.

What challenge prevents current toroidal reconstruction from being used in real time?

Starting from experimental measurements, toroidal reconstruction requires lengthy calculations that cannot be executed fast enough for a real-time system.

How does deep learning change the computation workflow?

Deep learning replaces the solving algorithm by using trained neural networks to compute equilibrium in toroidal geometry, enabling integration into a real-time pipeline.

Which FPGA-oriented optimizations were applied to deploy the selected model?

The work performs pruning and heterogeneous quantization and includes tuning steps to meet FPGA resource and latency constraints using an FPGA deployment flow.

Aug 6, 2026

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