Physics Informed Neural Networks towards the real-time calculation of heat fluxes at W7-X

Wendelstein 7-X, the world largest superconducting advanced stellarator, aims to demonstrate high-performance steady-state experiments lasting up to 30 min. To this purpose, high heat flux (HHF) divertors capable of withstanding steady-state heat fluxes up to 10 MW/m2 are being installed on the machine, in preparation for the next experimental campaign (OP2.1). The real-time heat flux estimation is pivotal for controlling the divertor heat loads during the experiments. Currently, the THEODOR (Thermal Energy Onto DivertOR) code computes the heat flux offline by numerically solving the heat equation, but the computation time does not allow the application of this approach to the real-time operation of the device. In this work, a new approach based on Physics Informed Neural Networks (PINNs) is proposed for solving the heat equation and estimating the heat fluxes on the divertor tiles in real time. PINN models are Neural Networks that learn Partial Differential Equations (PDEs) by minimizing the PDE loss. The inputs of a PINN are the independent variables of the PDE, e.g., spatiotemporal coordinates, while the loss of the model is designed to make the neural network satisfy the PDE and related initial and boundary conditions. Hence, the model can be trained without any experimental data. Only the initial and boundary conditions of the PDE are necessary for constructing the model. First intermediate results are discussed considering a normalized tile and starting from a constant thermal diffusivity.