Joel Aftreth: Neural network models of ion temperature measurements in the Wendelstein 7-X stellarator

BCCN Berlin / Technische Universität Berlin

Abstract

 

Stellarators are starting to demonstrate their potential to generate the high plasma temperatures and confinement times needed for an efficient generation of fusion power. While it is possible to calculate plasma temperatures post-hoc from recorded diagnostic measurements, it would be highly desirable to be able to calculate the internal temperature in near real-time, in order to control the plasma more precisely. Traditionally, three methods are used at the Wendelstein 7-X (W7-X) stellarator in Greifswald, Germany to reconstruct the temperature profile. These methods rely on physics assumptions and are not fast enough for real time evaluation. This project is an effort to calculate the near real-time temperature inside the W7-X, meaning sub-100ms calculations in order to be relevant to plasma control purposes, by training a neural network in two forms to be a faster surrogate of such physics methods. In the first case, to train the model, the x-ray images produced by ions in the plasma are used as input, and the corresponding temperature profiles obtained with the physics based algorithm are used as output. The neural network model uses a convolutional neural network architecture and is able to achieve a mean squared error of 0.0038 keV and a mean relative error of 8.4% compared to the physics model ground truth, with a calculation time of 0.3 ms per image, compared to 100 seconds for the physics model.

A second method for calculating the temperature profile has been developed using Bayesian inference which allows estimating uncertainties accurately. This method relies on a more accurate physics forward model that simulates x-ray images from ion temperature profiles, (the inverse of the first method above), but it is even more computationally expensive due to the many repetitions of the simulation step required. A second neural network is trained here as a substitute for the physics simulator/forward model, with best results coming from a transposed convolutional network. This neural network generates x-ray images from ion temperature profiles that match the simulated images to a reasonable degree with a calculation time of 0.2 ms per simulation (compared to 500 ms per simulation for the physics model), but still most likely needs further refinement since it achieves 4.7% relative error predicting spectral line widths, but 50% relative error predicting spectral amplitudes compared to the physics model. In future fine-tuned works, this network can be used to perform Bayesian inference and deliver the uncertainty information in unprecedented short time scales. These results suggest that, going forward, machine learning methods can be a potential first approximation substitute for these physics models, and the speed boost they provide may make near real-time plasma temperature control a possibility.

 

Additional Information

Master Thesis Defense

 

Organized by

Prof. Dr. Robert Wolf (Max-Planck-Institute for Plasma Physics & TU)   & Prof. Dr. Klaus Obermayer (TU)  / Lisa Velenosi