Surrogate Modeling for Neutron Transport: A Neural Operator Approach

This work introduces a neural operator–based surrogate modeling framework for neutron transport computation. Two architectures, the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), were trained for fixed source problems to learn the neutron transport governing equation to predict angular fluxes based on anisotropic neutron sources, in a one-dimensional slab geometry. Three distinct models were trained for each neural operator, corresponding to different scattering ratios (c= 0.1, 0.5, and 1.0), providing insight into their performance across distinct transport regimes (absorption-dominated, moderate, and scattering-dominated). The models were subsequently evaluated on a wide range of previously unseen source configurations, demonstrating that FNO generally achieves higher predictive accuracy, while DeepONet offers greater computational efficiency. Both models offered significant speedups that become increasingly pronounced as the scattering ratio increases, requiring <0.3% of the runtime of a conventional SN solver. The surrogate models were further incorporated into the SN k-eigenvalue solver, replacing the computationally intensive transport sweep loop with a single forward pass. Across varying fission cross sections and spatial-angular grids, both neural operator solvers reproduced reference eigenvalues with deviations up to 135 pcm for DeepONet and 112 pcm for FNO, while reducing runtime to <0.1% of that of the SN solver on relatively fine grids. These results demonstrate the strong potential of neural operator frameworks as accurate, efficient, and generalizable surrogates for neutron transport within well-defined training regimes, establishing a foundation toward future applications such as real-time digital twin framework and repeated evaluations, such as in design optimization, contingent on further generalization across cross section parameter spaces and geometric configurations.