Application of Deep Operator Networks for Data Reduction in Deterministic Neutron Calculations

Abstract

High-fidelity neutron transport simulations require large memory footprints which can become a limiting factor. A significant portion of this memory footprint comes from the large scattering matrices, which are needed for every material, enrichment level, scattering moment, and temperature. Deep operator networks (DeepONets) can replace the scattering term in the criticality neutron transport problem by predicting the matrix-vector product using a machine learning model. These models eliminate the need for scattering matrices in the multigroup source iteration. DeepONets are generalizable, as the trunk network can encode the composition of different materials without having to retrain the model. One example model uses the weight percentages of eight elements found in stainless steel (iron, chromium, carbon, silicon, manganese, molybdenum, nickel, and copper) as inputs to the trunk network. A second example models a mixed oxide (MOX)fissionable material with varying percentages of uranium-235 and plutonium dioxide. Both models are shown to be accurate for different one-dimensional spherical k-eigenvalue criticality problems that vary in material layout and composition. This was accomplished while simultaneously reducing memory requirements by a factor of 70 and accelerating source iteration convergence by a factor of approximately 7 to 16. Future work involves adding more materials to the trunk network, incorporating anisotropic scattering, and including temperature-dependent scattering cross section matrices.