Nathan Andrew Gibson

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.

The optimization of energy group structures is integral to ensure the accuracy of multigroup neutron transport calculations. This works introduces the use of reinforcement learning (RL) with surrogate modeling to optimize the group structure for one-dimensional spherical k-criticality problems. The proximal policy optimization (PPO) RL algorithm is modified to be used with energy grid structures, rewarding accurate group structures while favoring fewer energy groups. This method starts from a high-fidelity energy grid and remove energy bounds until reaching a target energy structure. The RL agent identify which bounds are important for the final group structure, which prevent it being stuck in local minima without limiting the initial group structure. Neural network surrogate models that incorporate energy, material, and spatial information are used for evaluating energy grid structures without requiring full transport simulations. This alleviates the computational constraint commonly used in other group structure optimization problems in addition to accelerating the RL training process. Applied to Godiva and BeRP ball problems, the RL constructed group structures outperform commonly used group structures. The RL group structure optimization method is also shown to perform similar to the hierarchical agglomeration approach but offers more flexibility.

This work describes a blueprint for a process that accelerates progress in science by quantitatively answering the following question: What is the optimal combination of fundamental-science and application-driven experiments to maximally reduce pertinent data uncertainties? Answering this question entails solving a high-dimensional and complex optimization problem that is best solved with advanced statistic techniques often classified as machine learning. We apply this process within the framework of nuclear data with the aim to select an experiment combination that will reduce uncertainties in Pu 239 nuclear data for neutron energies between 1 and 600 keV. In this field, fundamental-physics driven data, called , look at one nuclear physics observable at a time. They are contrasted to application-driven, , data where one or few resulting values inform a broad set of nuclear data across several nuclides and energies. The candidates for integral experiments are criticality measurements that were refined by a genetic algorithm to be maximally sensitive to Pu 239 fission cross sections in the desired energy range. Twenty-three candidate differential experiments were investigated and span multiple nuclear physics observables (e.g., total, capture cross sections) for isotopes appearing in the integral experiments. The optimal combination among these candidate experiments was investigated via generalized least squares fitting, augmented with Gaussian processes to ameliorate statistical irregularities in data, and the D-optimality criterion. The latter evaluates for each pair of candidates the joint reduction in uncertainties of all 12200 nuclear data appearing in the integral experiments compared to the knowledge we have from 168 past experiments, theory, and nuclear data. We chose as differential measurements those that investigate Cu 63 and Pu 239 total cross sections, based on D-optimality rank and feasibility constraints. Two integral (criticality) experiments were selected: An experiment with Al 2 O 3 and graphite interleaved with Pu and a thick Cu reflector explores 1–30 keV, while we target the 30–600 keV range with an experiment that swaps boron in place of graphite with a different geometry. Published by the American Physical Society 2025