Abstract
Despite the impressive progress made in the modeling of tokamak disruptions, several limitations remain. These limitations emerge both due to gaps in our understanding of disruption physics along with the difficulty of integrating the diverse range of physical processes present during a tokamak disruption. Data based deep learning methods offer a promising path through which the latter challenge may be alleviated. The application of deep learning methods to the modeling of tokamak disruptions is, however, hindered by the often sparse experimental data sets that are available, along with the computational cost of generating simulation data. As a result, data based models are often sharply limited with regard to the range of plasma regimes over which they can be applied. Physics-informed deep learning methods, which seek to impose physical constraints into the training of a deep neural network offer the potential for greater generalizability. In this approach, physical constraints are imposed in the training of a neural network thus enabling the neural network to make predictions outside the available data set, or even in the absence of experimental or simulation data.
In the present work, we employ a physics-informed neural network (PINN) to identify solutions to the relativistic Fokker-Planck equation, in the absence of experimental or simulation data. As a first application, we employ a PINN to evaluate the runaway electron hot tail seed for the case of an idealized axisymmetric thermal quench. It is shown that the PINN is able to accurately predict the hot tail seed across a range of parameters including the thermal quench time scale, initial plasma temperature, and local current density. While the offline training of the PINN is computationally intensive, once trained, the PINN is able to make predictions at a fraction of the cost of a conventional Fokker-Planck solver and thus provides an efficient surrogate model for predicting RE seeding during the thermal quench.