Neural Operators Enhance Two-Dimensional Neutron Flux Estimation

Japan K. Patel, Barry D. Ganapol, Anthony Magliari, Matthew C. Schmidt, Todd A. Wareing· July 23, 2026 View original

Summary

This study extends neural operator applications to two-dimensional neutron flux estimation, comparing Fourier Neural Operators (FNOs) and U-shaped Neural Operators (UNOs). It investigates whether a single-sweep approximation input improves accuracy and if training on the logarithm of the flux enhances results in strongly attenuated regions.

The estimation of neutron flux is critical in nuclear engineering, and this research explores the use of neural operators as surrogates for two-dimensional neutron flux calculations. Building on previous one-dimensional studies, the work evaluates both Fourier Neural Operators (FNOs) and U-shaped Neural Operators (UNOs) for approximating high-fidelity scalar flux. Three distinct surrogate models were developed: two direct mappings from material and source fields to flux (one FNO, one UNO), and a third FNO that additionally incorporates the scalar flux from a single-sweep approximation. Each model was trained and evaluated against a high-fidelity discrete-ordinates solver. The study specifically addresses two key questions: whether providing the single-sweep approximation as an input enhances accuracy, and if training the models on the logarithm of the flux improves performance in regions with strong attenuation, which are particularly relevant for shielding applications. The results aim to guide the development of more efficient and accurate neutron transport simulations.

Why it matters

Professionals in nuclear energy, materials science, and defense can benefit from faster and more accurate neutron flux estimations, leading to improved reactor design, safety analysis, and radiation shielding optimization.

How to implement this in your domain

  1. 1Evaluate the FNO and UNO models for specific neutronics simulation tasks within nuclear engineering projects.
  2. 2Experiment with incorporating single-sweep approximations as inputs to neural operator models for potential accuracy gains.
  3. 3Investigate training neural operators on logarithmic flux values to improve accuracy in critical shielding regions.
  4. 4Collaborate with AI/ML specialists to integrate these neural operator surrogates into existing high-fidelity solvers.

Who benefits

Nuclear EnergyDefenseMaterials ScienceScientific Computing

Key takeaways

  • Neural operators (FNOs, UNOs) are being explored for two-dimensional neutron flux estimation.
  • The study examines the impact of single-sweep approximations on model accuracy.
  • Training on logarithmic flux values is investigated for improved performance in attenuated regions.
  • This research aims to enhance the efficiency and accuracy of neutron transport simulations.

Original post by Japan K. Patel, Barry D. Ganapol, Anthony Magliari, Matthew C. Schmidt, Todd A. Wareing

"arXiv:2607.19388v1 Announce Type: new Abstract: This work extends our one-dimensional single-sweep neural-operator studies to two dimensions. We consider one-group transport with isotropic scattering. As in the one-dimensional work, we use Fourier neural operators (FNOs) to appro…"

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Originally posted by Japan K. Patel, Barry D. Ganapol, Anthony Magliari, Matthew C. Schmidt, Todd A. Wareing on X · view source

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