Characterization of DeepONet Performance for Neutron Transport Modeling

This paper presents a feasibility and performance study of a Deep Operator Network (DeepONet) surrogate model for solving the neutron transport equation, potentially as a real-time solver to enable digital twin techniques for nuclear reactor autonomous control. In autonomous control, it requires real-time prediction of future system status under varying physical conditions. Conventional model-based methods, such as Monte Carlo and deterministic solvers, and artificial intelligence/machine learning–based partial differential equation solvers, such as physics-informed neural networks, require repeated simulations or retraining for new input boundary/initial conditions, limiting their practicality for real-time deployment. DeepONet addresses this by learning mappings between function spaces, enabling generalization to arbitrary input conditions and providing superfast predictions without retraining. The current study develops three distinct DeepONet models, each designed for isotropic, anisotropic and pure scattering regimes, to evaluate their predictive performance. Models were trained on diverse neutron source distributions generated using Gaussian random fields (GRFs) and tested across diverse scenarios, including GRFs with shifted statistical parameters, combined sources, and sinusoidal profiles. Results demonstrate that DeepONet consistently achieves high R2 score and low average relative error, showing excellent generalization performance and outperforming the developed feedforward neural network across all test cases. More importantly, it delivers substantial computational speedups, up to 80, 71, and 900 times, respectively, highlighting its efficiency and real-time potential. Additionally, a fourth DeepONet model is developed for parametric studies by incorporating scattering cross sections as parameter inputs that also achieves a higher prediction accuracy. The framework’s speed, accuracy, and adaptability make it a strong candidate for deployment in digital twin environments.