Machine learning surrogates of Bayesian models of nuclear fusion experiments*

The diagnosis of large nuclear fusion experiments involves several different measurement devices relying on the observation of different plasma physics processes and leading to the collection of a vast amount of heterogeneous measurements. Bayesian inference provides a framework to integrate such data sources to infer a relatively small number of plasma parameters together with their uncertainties. It is performed by positing a predictive model of the observable plasma physics processes. The complexity of the models makes Bayesian inference computationally demanding: the inference of plasma profiles from a single measurement record can take tens of minutes. Here we show that artificial neural networks (ANN) can be trained as fast surrogates of Bayesian inference. The training data are generated with Bayesian models implemented within the Bayesian modeling framework Minerva: the data sampled from the joint probability distribution of the models can be used to teach ANN to reconstruct the model free parameters and joint probability values within hundreds of microseconds, making real time application possible. Such combination of Bayesian inference, modeling and ANN allows us to tackle different challenges at once: integrated modeling, uncertainty propagation and scalable inference. Our implementation is general and not bound to a specific experimental device: we show promising results with tests on different kinds of measurements from the W7-X and JET experiments. Future works can lead to an entirely automatic procedure for training machine-learning models as approximate inference algorithms for any Bayesian model implemented within a common framework.