  We investigate the physics-constrained training of an encoder-decoder neural
network for approximating the Fokker-Planck-Landau collision operator in the
5-dimensional kinetic fusion simulation in XGC. To train this network, we
propose a stochastic augmented Lagrangian approach that utilizes pyTorch's
native stochastic gradient descent method to solve the inner unconstrained
minimization subproblem, paired with a heuristic update for the penalty factor
and Lagrange multipliers in the outer augmented Lagrangian loop. Our training
results for a single ion species case, with self-collisions and collision
against electrons, show that the proposed stochastic augmented Lagrangian
approach can achieve higher model prediction accuracy than training with a
fixed penalty method for our application problem, with the accuracy high enough
for practical applications in kinetic simulations.
