Encoder-decoder neural network for solving the nonlinear Fokker-Planck-Landau collision operator in XGC

An encoder-decoder neural network has been used to accelerate the numerical solving of a partial integro-differential equation, the Fokker-Planck-Landau collision operator. This is part of the governing equation in the massively parallel particle-in-cell code, XGC, which is used to study turbulence in fusion energy devices. The neural network emphasizes physics-inspired learning, where it is taught to respect physical conservation constraints of the collision operator by including them in the training loss, along with the L2 loss. The run time for the current Picard iterative solver of the operator is $O(n^2)$, where n is the number of plasma species. As the XGC1 code begins to attack problems including a larger number of species, the collision operator will become expensive computationally, making the neural network solver even more important, especially since the training only scales as $O(n)$. A wide enough range of collisionality has been considered in the training data to ensure the full domain of collision physics is captured. Eventual work will include expansion of the network to include multiple plasma species.