Introduction

Accurate and efficient prediction of plasma equilibria and instabilities is essential for the design, operation, and optimization of magnetic confinement fusion devices. Next-generation experiments require modelling and control tools that are both fast and physically faithful, capable of handling multiple parameters and constraints. Traditional solvers, such as Grad–Shafranov-based codes for equilibrium and extended-MHD simulations for tearing instabilities, often become computationally prohibitive when extended physics, high resolution, or multiple parameter scans (i.e., repeated runs under varying conditions) are required.

Core idea

Phimicon addresses the aforementioned challenges through a machine learning (ML) framework based on novel Hybrid Fourier–Kolmogorov–Arnold Network (HyFourKAN) architectures. These networks combine Kolmogorov–Arnold Networks (KANs), which capture local, nonlinear features such as pedestals, shear layers, and discontinuities, with Fourier-based branches designed to learn oscillatory structures and topological distortions near X-points. By connecting the branches in parallel or in series, HyFourKANs efficiently represent the coexistence of large-scale structures and fine scale features.

The project consists of two components. The first focuses on plasma equilibrium modelling, enabling rapid prediction of tokamak equilibrium states, including macroscopic flows, pressure anisotropy, and kinetic effects from fast particles, under varying profiles, boundary conditions, and plasma parameters. The second component addresses magnetic reconnection and tearing-mode simulations, providing fast and physically faithful predictions of magnetic island formation and evolution using nonlinear extended-MHD models.

A key innovation is the use of meta-learning, which combines families of pretrained HyFourKAN experts into lightweight meta-networks, allowing fast generalization to previously unseen equilibria and reconnection scenarios. Physics-informed training ensures consistency with governing PDEs, boundary conditions, and experimental constraints.

By exploring extended equilibrium modelling and magnetic reconnection/tearing-mode simulations, Phimicon aims to deliver a compact, generalizable ML toolkit for fusion research. This will enable rapid scenario exploration, accelerate parametric scans, and pave the way for integration into advanced plasma control workflows in devices such as ITER.

Objectives

Ultimately the Phimicon project aims to enhance computational efficiency and accuracy in unsupervised and semi-supervised ML computations in magnetic confinement. The goal is to create a computational ML environment that serves as an alternative or enhancement to current conventional numerical methods and solvers in plasma and fusion physics. This environment will be used to construct tokamak equilibrium states with macroscopic flows in connection with advanced confinement regimes, pressure anisotropy and kinetic effects stemming from the presence of fast-particle populations. This research also investigates fast magnetic reconnection processes in tokamaks using nonlinear 2D and potentially 3D models incorporating electron inertial effects, thermal effects, and possibly kinetic contributions.