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 freeboundary 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 equilibrium neural network is trained with different combinations of inputs and outputs in order to offer flexibility in use cases. In particular, the NN can use magnetic diagnostics as inputs for equilibrium prediction thus acting as a reconstruction code, or can use profiles and external currents as inputs to act as a traditional free-boundary Grad-Shafranov solver. We report strong performance for both networks indicating that these models could reliably be used within closed-loop simulations. Some limitations regarding generalizability and noise are discussed.

Application of machine learning and artificial intelligence to extend EFIT equilibrium reconstruction

“…The NN training is further constrained by including the equilibrium constraint in the loss function. Another more recent example of equilibrium reconstruction with NNs involves Eqnet, a NN trained to predict the free boundary-plasma equilibria in NSTX-U with several modes of operation based on various set of inputs [39]. Our present MOR approach parallels the KSTAR and NSTX-U efforts in some respects and differs from these cited works in other significant ways, which are highlighted below.…”

“…The estimation of these parameters with a NN, given the magnetic inputs, resembles Ref. [39]'s Eqnet implementation under the reconstruction control mode. Secondly, a separate neural network is applied to learn βN, li, and q95 using the same magnetic inputs as those used in learning 𝜓.…”

“…The first implementation reconstructs ψ (R,Z) on the EFIT rectangular (R,Z) grid given the external magnetic signals and the equilibrium GS constraint. This is similar to both the KSTAR approach and reconstruction mode of Eqnet for NSTX-U [39]. The second implementation uses a separate MLP-NN to directly fit the plasma boundary and various global plasma parameters of interest such as β N , l i , and q 95 .…”

“…Machine learning (ML) and artificial intelligence (AI) techniques have been applied to develop practical and efficient means to compute approximate solutions to various magnetic fusion research problems [29][30][31][32][33][34][35][36][37][38][39]. These include early work to solve the equilibrium GS Eq.…”

“…Machine learning (ML) and artificial intelligence (AI) techniques have been applied to develop practical and efficient means to compute approximate solutions to various magnetic fusion research problems [29][30][31][32][33][34][35][36][37][38][39]. These include early work to solve the equilibrium GS equation (1) based on neural network [29] and more recent work to apply deep neural network to solve the equilibrium GS equation with measured external magnetic signals in the KSTAR tokamak based on the offline EFIT equilibrium reconstruction results [36].…”