Inverse Critical Experiment Design via Gradient Optimization and a Multigroup Attention-Based Neural Network Architecture
This paper presents a methodology for inverse design of critical experiments using deep neural network surrogate modeling and nonparametric gradient optimization to maximize neutronic similarity (c_k). The model combines a U-Net encoder-decoder with a novel multigroup attention pooling layer, enabling gradient-based optimization of material assignments in a geometry grid. Applied to a TN-LC transportation cask with HALEU fuel, the method achieves c_k scores of 0.97757, 0.81324, and 0.93276 for three configurations, demonstrating the potential of deep learning in accelerating nuclear technology validation.
[2606.04033] Inverse Critical Experiment Design via Gradient Optimization and a Multigroup Attention-Based Neural Network Architecture
[Submitted on 1 Jun 2026]
Title:Inverse Critical Experiment Design via Gradient Optimization and a Multigroup Attention-Based Neural Network Architecture
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Abstract:The validation of advanced nuclear reactor designs and fuel concepts requires critical experiments with high neutronic similarity to the target technology. Neutronic similarity is quantified by the correlation coefficient $c_k$, which captures the shared bias in $k_\text{eff}$ induced by uncertainties in nuclear data. Generally, a $c_k\geq0.9$ is needed for an experiment to be sufficiently similar to a target technology. This work presents a methodology for the inverse design of critical experiments. Deep neural network surrogate modeling and nonparametric gradient optimization are used to generate experiment geometries that maximize $c_k$.
A deep neural network is trained on OpenMC-calculated sensitivity vectors for grid-based critical experiment geometries. The model architecture combines a U-Net convolutional encoder-decoder with a novel multigroup attention pooling layer, introduced to capture the differing spatial dependencies of sensitivities. Multigroup attention pooling is shown to achieve better performance than traditional pooling, as well as interpretable internal behavior. The differentiability of the surrogate enables gradient-based optimization of the full combinatorial design space, allowing $c_k$ to be maximized by directly changing the material assignment of each position in the geometry grid.
The method is applied to the validation of the TN-Americas TN-LC transportation cask with HALEU fuel, for which existing critical experiment coverage is limited. The optimization procedure is shown to produce experiment geometries achieving $c_k$ scores of 0.97757, 0.81324, and 0.93276 for three configurations of interest. This approach demonstrates the potential of deep learning and gradient optimization to accelerate the development of advanced nuclear technology.
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2606.04033 [cs.LG]
(or arXiv:2606.04033v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.04033
arXiv-issued DOI via DataCite
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From: Dean Price [view email] [v1] Mon, 1 Jun 2026 21:19:18 UTC (3,057 KB)
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