Introduction

Fusion energy is widely regarded as one of the most promising pathways toward a clean and virtually inexhaustible energy supply. Among the various fusion reactor concepts, the tokamak stands out as the most mature and promising candidate for future commercial deployment. In a tokamak, plasma at temperatures of hundreds of millions of degrees is confined by carefully engineered, high-intensity magnetic fields.  Accurate and efficient calculation of plasma properties within the reactor is essential for both the design and operation of these devices. One key factor is the fast and reliable computation of magnetic equilibria, i.e. the delicate balance between the plasma’s internal forces and confining magnetic fields. Traditionally, this problem is addressed by solving the Grad-Shafranov equation using numerical solvers. However, such methods are often computationally demanding, making them impractical for real-time control or extensive parametric scans. In addition, their accuracy and performance can degrade when applied to complex geometries or when extended to account for additional physical effects such as flows, pressure anisotropy, and kinetic effects which are important due to the presence of energetic particles generated by the fusion reactions and also by external heating methods.  

KANTEQ core idea

KANTEQ (Kolmogorov-Arnold Networks for Tokamak EQuilibria) addresses a major computational bottleneck in fusion research: the fast and accurate calculation of magnetic equilibria in tokamak reactors. Traditional solvers are slow and often unsuitable for real-time control or large parametric studies. By introducing Physics-Informed Kolmogorov-Arnold Networks (KANs), this project offers a fundamentally new, neural-network-based approach. KANTEQ could significantly speed up equilibrium calculations, support advanced control systems, and help design future reactors, ultimately accelerating the path toward clean fusion energy. Beyond fusion, the method could generalize to other PDE-based systems in physics and engineering. 

Unlike conventional multilayer perceptrons (MLPs), Kolmogorov–Arnold Networks (KANs) employ learnable activation functions rather than fixed ones. This feature allows them to capture nonlinear dependencies more effectively while also providing greater interpretability. Although training can be slower—since the coefficients of the learnable activation functions (often spline-based) must also be optimized—the superior accuracy of KANs makes them attractive as surrogate models. 

To mitigate the training cost, KANTEQ will include a library of pretrained KANs spanning different classes of equilibria, characterized by varying normalized pressure and current profiles as well as diverse geometries. These pretrained networks will be assembled into a meta-network capable of predicting new equilibria in very short times. 

Another novelty of KANTEQ is the incorporation of additional physical effects into the equilibrium calculation. These effects are crucial for understanding and interpreting tokamak phenomenology. Examples include macroscopic sheared flows, which play a role in forming transport barriers; pressure anisotropy, expected from the disparity between parallel and perpendicular pressures; and kinetic effects arising from populations of energetic particles.  

Objectives

•  Development of a modular software tool based on Kolmogorov–Arnold Networks for solving tokamak equilibrium problems. 

• Training KANs on a wide variety of plasma profiles, parameters, and tokamak geometries. 

• Construction of a library of pretrained neural models for equilibrium reconstruction. 

• Formation of meta-networks combining pretrained models for fast inference on new cases. 

•  Benchmarking KANTEQ against existing solvers on speed, accuracy, and scalability. 

• Dissemination results through open webinars, share models/code on GitHub for community use and publish a research paper.

Want to support KANTEQ?

KANTEQ is an independent theoretical and computational research project, funded entirely through personal resources. Its progress could be substantially accelerated with access to additional infrastructure such as a dedicated workstation for local KAN training or cloud computing resources for large-scale experiments. If you are able to provide such infrastructure, it would make a meaningful difference to the project. Please feel free to contact me to discuss possibilities.