Fourier Neural Operators Speed Up 2D Neutron Flux Estimation

In this work, researchers from the University of Arizona and Los Alamos National Laboratory apply neural operators to two-dimensional neutron transport problems with isotropic scattering. They build on prior one-dimensional results by training Fourier Neural Operators (FNOs) and U-shaped Neural Operators (UNOs) as surrogates to approximate the scalar neutron flux. Three distinct mapping strategies are tested: a direct FNO that maps material and source fields to flux, a direct UNO doing the same, and an FNO that additionally receives the scalar flux after one source iteration (the single-sweep approximation) as an additional input. The surrogates are trained over three random seeds to assess variability, and their accuracy is measured by average relative L2 error norms against a verified discrete-ordinates solver.

The study addresses two key questions: whether including the single-sweep approximation improves accuracy over direct mappings, and whether training on the logarithm of the flux yields better performance in strongly attenuated regions relevant for nuclear shielding. Preliminary findings suggest that the single-sweep input can enhance surrogate accuracy, while log-transformed training may reduce error in low-flux areas. This work paves the way for rapid, high-fidelity neutron flux estimation, potentially accelerating simulations in reactor design, radiation shielding, and nuclear safety without requiring full transport solves every time.