GS-DeepNet: mastering tokamak plasma equilibria with deep neural networks and the Grad–Shafranov equation

Abstract

The force-balanced state of magnetically confined plasmas heated up to 100 million degrees Celsius must be sustained long enough to achieve a burning-plasma state, such as in the case of ITER, a fusion reactor that promises a net energy gain. This force balance between the Lorentz force and the pressure gradient force, known as a plasma equilibrium, can be theoretically portrayed together with Maxwell’s equations as plasmas are collections of charged particles. Nevertheless, identifying the plasma equilibrium in real time is challenging owing to its free-boundary and ill-posed conditions, which conventionally involves iterative numerical approach with a certain degree of subjective human decisions such as including or excluding certain magnetic measurements to achieve numerical convergence on the solution as well as to avoid unphysical solutions. Here, we introduce GS-DeepNet, which learns plasma equilibria through solely unsupervised learning, without using traditional numerical algorithms. GS-DeepNet includes two neural networks and teaches itself. One neural network generates a possible candidate of an equilibrium following Maxwell’s equations and is taught by the other network satisfying the force balance under the equilibrium. Measurements constrain both networks. Our GS-DeepNet achieves reliable equilibria with uncertainties in contrast with existing methods, leading to possible better control of fusion-grade plasmas.

Tokamak edge localized mode onset prediction with deep neural network and pedestal turbulence

“…Interestingly, our neural network is able to predict ELM onsets whose precursors are less visible in the cross-power spectrogram from two poloidally adjacent BES channels. As we presented that the neural network taking the turbulent structures evolving in time is possible to generate proper outcomes, developing a physics-based neural network [71,72] for analyzing plasma turbulent characteristics measured by the BES system with a differential equation such as a force-balance equation [2] can be considered as a future work to generate two-dimensional velocimetry and turbulent flow shear profile [59,60] in real time.…”

Impact of various DIII-D diagnostics on the accuracy of neural network surrogates for kinetic EFIT reconstructions

“…This work builds a multi-layer perceptron (MLP) NN surrogate for kinetic equilibrium reconstructions and aims to demonstrate the impacts of different available plasma diagnostics on the accuracy of equilibrium reconstructions and internal kinetic profile predictions using a database of kinetic EFITs. We highlight that several research groups have already made progress in the field of NN surrogates of nonkinetic equilibrium reconstructions and associated applications: reconstructing magnetic flux contours on KSTAR [21,22], predicting the time evolution of global state parameters on EAST [23,24], integrating preliminary plasma control using machine learning (ML) models on DIII-D [20,25], amongst other studies 5 . This work focuses on the types of equilibrium reconstruction that are determined by the diagnostic inputs aspect of the equilibrium reconstruction and investigates the accuracy of the NN surrogates' inference of the EFIT solution.…”

Solving real-world optimization tasks using physics-informed neural computing

“…By incorporating physics laws into the learning process, PINN can efficiently predict complex physical phenomena from sparse or absent data. It is rapidly emerging as an alternative scheme to traditional computational simulation techniques [15][16][17][18][19] . The rise of PINN is attributed to its ability to operate without the use of a mesh and to easily implement arbitrary constraints beyond initial or boundary conditions.…”