RSFNO: A Fourier Neural Operator–Based Solver for High-Dimensional Neutron Transport Equations

Abstract: This work establishes the theoretical foundations and practical implementation of a Fourier Neural Operator-based solver for high-dimensional neutron transport equations. We leverage the operator-learning framework to approximate the solution operator of the Boltzmann equation, allowing for efficient representations of reactor-scale neutron flux. RSFNO integrates stochastic geometric parameterization with frequency-domain learning to establish a direct end-to-end mapping from shielding configurations to flux distributions. Evaluated on a reactor shielding benchmark, the model demonstrates remarkable efficiency: despite being trained on just 800 samples, it reduces the full-domain mean squared error by 58.95\% compared to a strong Unet3D baseline. In deep-penetration regions, its accuracy rivals or exceeds that of a $10^{6}$-particle Monte Carlo (MC) simulation. Crucially, RSFNO completes a full-domain prediction in 11.79~s on a single NVIDIA RTX~4090, achieving an effective $\sim 2795\times$ speedup over the MC baseline. While not yet a replacement for high-fidelity safety analysis, RSFNO offers a reliable, ultra-fast surrogate for the computationally expensive deterministic steps in hybrid variance-reduction workflows (e.g., CADIS). These results highlight the promise of Fourier-operator-based solvers in accelerating large-scale transport analysis and enabling scalable, data-driven reactor shielding design.