Analysis of a Generative Adversarial Network and a Denoising Diffusion Probabilistic Model for the Design of Nuclear Reactor Loading Patterns
Resumo
At the end of each operation cycle in a nuclear power plant, a portion of the spent nuclear fuel must be replaced, while the remaining fuel is rear-ranged within the core, forming a Loading Pattern (LP), an NP-hard combinatorial problem subject to safety constraints. Although LP design is still predominantly supported by optimization metaheuristics, the application of deep generative models to this problem lacks comparative evidence. This work compares StyleGAN2-ADA and a Denoising Diffusion Probabilistic Model (DDPM) for LP generation, representing LP configurations as images. DDPM required less hyperparameter tuning and trained substantially faster than StyleGAN2-ADA. Statistically significant differences were found between the models, with DDPM achieving better structural compliance and generating markedly more configurations outside the training set, suggesting broader exploration of the feasible LP space. Overall, the findings support DDPM as a favorable option for LP generation under the conditions tested.
Palavras-chave:
Generative Artificial Intelligence, Diffusion Models, Generative Adversarial Networks, Nuclear Energy, Galerkin Finite Element Method
Referências
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Ho, J., Jain, A., and Abbeel, P. (2020). Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems, 33:6840–6851.
Karras, T., Aittala, M., Hellsten, J., Laine, S., Lehtinen, J., and Aila, T. (2020a). Training generative adversarial networks with limited data. Advances in Neural Information Processing Systems, 33:12104–12114.
Karras, T., Laine, S., and Aila, T. (2019). A style-based generator architecture for generative adversarial networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4401–4410.
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Meneses, A. A. M., Araujo, L. M., and Schirru, R. (2024). A GPU-accelerated linear system solution for the Galerkin finite element method applied to neutron diffusion equation. Nuclear Engineering and Design, 421:113103.
Meneses, A. A. M., Machado, M. D., and Schirru, R. (2009). Particle swarm optimization applied to the nuclear reload problem of a pressurized water reactor. Progress in Nuclear Energy, 51(2):319–326.
Meneses, A. A. M., Silva, P. V., Nast, F. N., Araujo, L. M., and Schirru, R. (2020). Application of cuckoo search algorithm to loading pattern optimization problems. Annals of Nuclear Energy, 139:107214.
Nichol, A. and Dhariwal, P. (2021). Improved denoising diffusion probabilistic models. In Proceedings of the 38th International Conference on Machine Learning, volume 139 of Proceedings of Machine Learning Research, pages 8162–8171.
Rombach, R., Blattmann, A., Lorenz, D., Esser, P., and Ommer, B. (2022). High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10684–10695.
Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric Statistical Procedures, Fifth Edition. CRC Press.
von Platen, P., Patil, S., Lozhkov, A., Cuenca, P., Lambert, N., Rasul, K., Davaadorj, M., Nair, D., Paul, S., Berman, W., Xu, Y., Liu, S., and Wolf, T. (2022). Diffusers: State-of-the-art diffusion models. GitHub repository.
Chapot, J. L. C., da Silva, F. C., and Schirru, R. (1999). A new approach to the use of genetic algorithms to solve the pressurized water reactor’s fuel management optimization problem. Annals of Nuclear Energy, 26:641–655.
Dhariwal, P. and Nichol, A. (2021). Diffusion models beat GANs on image synthesis. Advances in Neural Information Processing Systems, 34:8780–8794.
Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep Learning. MIT Press, Cambridge, MA.
Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., and Hochreiter, S. (2017). GANs trained by a two time-scale update rule converge to a local Nash equilibrium. In Advances in Neural Information Processing Systems, volume 30.
Ho, J., Jain, A., and Abbeel, P. (2020). Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems, 33:6840–6851.
Karras, T., Aittala, M., Hellsten, J., Laine, S., Lehtinen, J., and Aila, T. (2020a). Training generative adversarial networks with limited data. Advances in Neural Information Processing Systems, 33:12104–12114.
Karras, T., Laine, S., and Aila, T. (2019). A style-based generator architecture for generative adversarial networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4401–4410.
Karras, T., Laine, S., Aittala, M., Hellsten, J., Lehtinen, J., and Aila, T. (2020b). Analyzing and improving the image quality of StyleGAN. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8110–8119.
Levine, S. (1986). In-core fuel management of four reactor types. In Ronen, Y., editor, Handbook of Nuclear Reactors Calculations, volume II. CRC Press.
LNCC SERED (2025). Manual SDumont: 02 - caracteristicas. GitHub Wiki. Accessed: 2026-04-07.
Meneses, A. A. M. and Araujo, L. M. (2026). Design of nuclear fuel loading patterns for a PWR with Wasserstein generative adversarial networks. Nuclear Engineering and Design, 449:114765.
Meneses, A. A. M., Araujo, L. M., and Schirru, R. (2024). A GPU-accelerated linear system solution for the Galerkin finite element method applied to neutron diffusion equation. Nuclear Engineering and Design, 421:113103.
Meneses, A. A. M., Machado, M. D., and Schirru, R. (2009). Particle swarm optimization applied to the nuclear reload problem of a pressurized water reactor. Progress in Nuclear Energy, 51(2):319–326.
Meneses, A. A. M., Silva, P. V., Nast, F. N., Araujo, L. M., and Schirru, R. (2020). Application of cuckoo search algorithm to loading pattern optimization problems. Annals of Nuclear Energy, 139:107214.
Nichol, A. and Dhariwal, P. (2021). Improved denoising diffusion probabilistic models. In Proceedings of the 38th International Conference on Machine Learning, volume 139 of Proceedings of Machine Learning Research, pages 8162–8171.
Rombach, R., Blattmann, A., Lorenz, D., Esser, P., and Ommer, B. (2022). High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10684–10695.
Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric Statistical Procedures, Fifth Edition. CRC Press.
von Platen, P., Patil, S., Lozhkov, A., Cuenca, P., Lambert, N., Rasul, K., Davaadorj, M., Nair, D., Paul, S., Berman, W., Xu, Y., Liu, S., and Wolf, T. (2022). Diffusers: State-of-the-art diffusion models. GitHub repository.
Publicado
19/10/2026
Como Citar
COELHO, Gabriel Pereira; ARAUJO, Lenilson Moreira; MENESES, Anderson Alvarenga de Moura.
Analysis of a Generative Adversarial Network and a Denoising Diffusion Probabilistic Model for the Design of Nuclear Reactor Loading Patterns. In: ENCONTRO NACIONAL DE INTELIGÊNCIA ARTIFICIAL E COMPUTACIONAL (ENIAC), 23. , 2026, Cuiabá/MT.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2026
.
p. 1580-1591.
ISSN 2763-9061.
DOI: https://doi.org/10.5753/eniac.2026.31246.
