Title: Accelerating Advanced Nuclear Validation: Inverse Critical Experiment Design Using Gradient Optimization and Multigroup Attention Neural Networks

Abstract:

To validate emerging nuclear reactor designs and fuel technologies, it is essential to conduct critical experiments that exhibit high neutronic similarity to the intended application. This similarity is measured by the correlation coefficient $c_k$, a metric that reflects the shared bias in $k_\text{eff}$ resulting from nuclear data uncertainties. Typically, a threshold of $c_k\geq0.9$ is required to ensure an experiment is sufficiently representative of the target technology.

This study introduces a novel methodology for the inverse design of such critical experiments. By leveraging deep neural network surrogate models alongside nonparametric gradient optimization, we generate experiment geometries specifically tailored to maximize $c_k$. The surrogate model was trained using OpenMC-calculated sensitivity vectors derived from grid-based critical experiment configurations. The proposed architecture integrates a U-Net convolutional encoder-decoder with a newly developed multigroup attention pooling layer, designed to account for the varying spatial dependencies inherent in sensitivity data. Our results indicate that this multigroup attention pooling mechanism outperforms conventional pooling techniques, offering both superior performance and greater interpretability of internal model behavior.

Because the surrogate model is differentiable, it facilitates gradient-based optimization across the entire combinatorial design space. This allows for the direct maximization of $c_k$ by adjusting the material assignment at each position within the geometry grid. We applied this method to address the limited existing critical experiment coverage for validating the TN-Americas TN-LC transportation cask utilizing HALEU fuel. The optimization process successfully yielded experiment geometries achieving $c_k$ scores of 0.97757, 0.81324, and 0.93276 for three distinct configurations of interest. These findings highlight the potential of combining deep learning with gradient optimization to expedite the development and validation of advanced nuclear technologies.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC