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We investigate the physics-constrained training of an encoder-decoder neuralnetwork for approximating the Fokker-Planck-Landau collision operator in the5-dimensional kinetic fusion simulation in XGC. To train this network, wepropose a stochastic augmented Lagrangian approach that utilizes pyTorch'snative stochastic gradient descent method to solve the inner unconstrainedminimization subproblem, paired with a heuristic update for the penalty factorand Lagrange multipliers in the outer augmented Lagrangian loop. Our trainingresults for a single ion species case, with self-collisions and collisionagainst electrons, show that the proposed stochastic augmented Lagrangianapproach can achieve higher model prediction accuracy than training with afixed penalty method for our application problem, with the accuracy high enoughfor practical applications in kinetic simulations.

Training neural networks under physical constraints using a stochastic augmented Lagrangian approach