Neural net modeling of equilibria in NSTX-U

Abstract

Neural networks (NNs) offer a path towards synthesizing and interpreting data on faster timescales than traditional physics-informed computational models. In this work we develop two neural networks relevant to equilibrium and shape control modeling, which are part of a suite of tools being developed for the National Spherical Torus Experiment-Upgrade (NSTX-U) for fast prediction, optimization, and visualization of plasma scenarios. The networks include Eqnet, a free-boundary equilibrium solver trained on the EFIT01 reconstruction algorithm, and Pertnet, which is trained on the Gspert code and predicts the non-rigid plasma response, a nonlinear term that arises in shape control modeling. The NNs are trained with different combinations of inputs and outputs in order to offer flexibility in use cases. In particular, Eqnet can use magnetic diagnostics as inputs and act as an EFIT-like reconstruction algorithm, or, by using pressure and current profile information the NN can act as a forward Grad-Shafranov equilibrium solver. This forward-mode version is envisioned to be implemented in the suite of tools for simulation of plasma scenarios. The reconstruction-mode version gives some performance improvements compared to the online reconstruction code real-time EFIT (RTEFIT), especially when vessel eddy currents are significant. We report strong performance for all NNs indicating that the models could reliably be used within closed-loop simulations or other applications. Some limitations are discussed.

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

“…Throughout the course of developing our NN model and training on various iterations of the processed data, we investigated many variations in the architecture. In general, we found that as long as the activation functions capture the range of the outputs, the number of nodes is sufficiently large, and we trained for a sufficient number of epochs, we obtained accurate inferences of the ψ (R, Z), global parameters, EFIT pressure profile, and EFIT current profile (consistent with the conclusions in [24,43,44]).…”

“…The choice for this particular MLP design was partially motivated by previous experience that investigated the performance of simple MLP NNs when inferring EFIT solutions. The architecture decisions of such an MLP NN are based on initial studies throughout the development of this work and others (see, for example, [24,43,44]) that produced outputs with sufficient accuracy (i.e. high R 2 values and profiles or contours that visually agreed with the solution) to capture the features of the EFIT solution 7 .…”

On the potential of physics-informed neural networks to solve inverse problems in tokamaks

“…In tokamaks the accurate measurement and control of the magnetic configuration is essential to achieve the required performances [37]. This aspect has become increasingly important in the last years, due to the continuous increase of the scenarios' sophistication and several new methodologies, also based on artificial intelligence, have been developed [38][39][40][41]. From the hybrid scenario to various small or free edge localised modes (ELMs) regimes, fine tuning of the fields is indispensable for both the quality and the stability of the plasmas.…”

Deep learning approaches to recover the plasma current density profile from the safety factor based on Grad–Shafranov solutions across multiple tokamaks

“…We achieve this by utilizing machine learning (ML) techniques based on a numerically generated equilibrium database. Machine learning has been widely used in fusion research, for example in plasma instability and disruption predictions [3][4][5][6][7][8][9][10][11][12][13][14], magnetic control [15], non-powerlaw scaling [16], turbulent transport [17][18][19] and plasma profile predictions [20,21], as well as fast magnetic equilibrium reconstruction [22][23][24][25][26][27].…”