Neural network approximation of Bayesian models for the inference of ion and electron temperature profiles at W7-X

In this paper, we describe a method for training a neural network (NN) to approximate the full model Bayesian inference of plasma profiles from x-ray imaging diagnostic measurements. The modeling is carried out within the Minerva Bayesian modeling framework where models are defined as a set of assumptions, prior beliefs on parameter values and physics knowledge. The goal is to use NNs for fast ion and electron temperature profile inversion from measured image data. The NN is trained solely on artificial data generated by sampling from the joint distribution of the free parameters and model predictions. The training is carried out in such a way that the mapping learned by the network constitutes an approximation of the full model Bayesian inference. The analysis is carried out on images constituted of 20 x 195 pixels corresponding to binned lines of sight and spectral channels, respectively. Through the full model inference, it is possible to infer electron and ion temperature profiles as well as impurity density profiles. When the network is used for the inference of the temperature profiles, the analysis time can be reduced down to a few tens of microseconds for a single time point, which is a drastic improvement if compared to the approximate to 4 h long Bayesian inference. The procedure developed for the generation of the training set does not rely on diagnostic-specific features, and therefore it is in principle applicable to any other model developed within the Minerva framework. The trained NN has been tested on data collected during the first operational campaign at W7-X, and compared to the full model Bayesian inference results.