A physics-informed deep learning description of relativistic electron formation and evolution

Deep learning methods offer the promise of drastically reducing the computational cost of evaluating a diverse range of plasma physics models. The application of deep learning methods to several plasma applications is, however, hindered by the often sparse experimental and computational data sets available. Physics-informed machine learning methods, whereby physical constraints are embedded in the training of a neural network (NN), offer a path through which the quantity of data required to train a NN can be drastically reduced. The present work, employs a physics-informed neural network (PINN) to predict runaway electron (RE) formation during a tokamak disruption. Two distinct PINN implementations are pursued. In the first, a PINN is developed to predict the runaway probability function from the adjoint relativistic Fokker-Planck equation in the presence of a rapid quench of the plasma's thermal energy, in the absence of experimental or simulation data. This `hot tail' PINN enables the evaluation of the hot tail RE seed across a broad range of thermal quench scenarios. In the second, a PINN is developed to directly infer the time evolution of the electron distribution function from the relativistic Fokker-Planck (FP) equation. This FP PINN is subsequently utilized to evaluate the Dreicer seed as a function of the background plasma parameters, as well as the form of the saturated primary distribution of REs.