Fusion energy through toroidal magnetic confinement offers the potential to supply large-scale sustainable electricity and industrial heat to power civilisation, without the “chain-reaction” risks of nuclear fission or the generation of long lived radio-isotopes. The magnetic configuration of the toroidal plasma determines stability, confinement, transport and performance. In a tokamak, which is an axis-symmetric toroidal plasma with a large internal current, the magnetic field is heavily shaped by the internal current and pressure distribution, which is only weakly (and indirectly) constrained. Inference of the magnetic confinement configuration from a combination of an array of diagnostics and physics models is a crucial key step in understanding and controlling fusion plasma experiments. To date, this “equilibrium reconstruction” has been accomplished by a combination of lest squares fitting, constrained to a mathematics force-balance model. Over the last decade there has been an increased utilisation of machine learning techniques, comprising Bayesian inference and more recently Physics Inspired Neural Networks and Fourier Neural Operators. Model bounded checking has also been used to verify whether a PINN or FNO trained on a mathematical model conforms to that model. In this project we take the concept one step further, and use a PINN or real experimental data to extract a PDE governing the system.
PDE Discovery of Force Balance in Toroidal Magnetic Confinement
Deep learning of mathematics in fusion energy science