Surrogate Modeling for Neutron Transport: A Neural Operator Approach
arXiv:2602.15890v1 Announce Type: cross Abstract: This work introduces a neural operator based surrogate modeling framework for neutron transport computation. Two architectures, the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), were trained for fixed source problems to learn the mapping from anisotropic neutron sources, Q(x,{\mu}), to the corresponding angular fluxes, {\psi}(x,{\mu}), in a one-dimensional slab geometry. Three distinct models were trained for each neural operator, corresponding to different scattering ratios (c = 0.1, 0.5, & 1.0), providing insight into their performance across distinct transport regimes (absorption-dominated, moderate, and scattering-dominated). The models were subsequently evaluated on a wide range of previously unseen source configurations, demonstrating that FNO generally achieves higher predictive accuracy, while DeepONet offers greater computational efficiency. Both models offered significant speedups that become increas
arXiv:2602.15890v1 Announce Type: cross Abstract: This work introduces a neural operator based surrogate modeling framework for neutron transport computation. Two architectures, the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), were trained for fixed source problems to learn the mapping from anisotropic neutron sources, Q(x,{\mu}), to the corresponding angular fluxes, {\psi}(x,{\mu}), in a one-dimensional slab geometry. Three distinct models were trained for each neural operator, corresponding to different scattering ratios (c = 0.1, 0.5, & 1.0), providing insight into their performance across distinct transport regimes (absorption-dominated, moderate, and scattering-dominated). The models were subsequently evaluated on a wide range of previously unseen source configurations, demonstrating that FNO generally achieves higher predictive accuracy, while DeepONet offers greater computational efficiency. Both models offered significant speedups that become increasingly pronounced as the scattering ratio increases, requiring <0.3% of the runtime of a conventional S_N solver. The surrogate models were further incorporated into the S_N k-eigenvalue solver, replacing the computationally intensive transport sweep loop with a single forward pass. Across varying fission cross sections and spatial-angular grids, both neural operator solvers reproduced reference eigenvalues with deviations up to 135 pcm for DeepONet and 112 pcm for FNO, while reducing runtime to <0.1% of that of the S_N solver on relatively fine grids. These results demonstrate the strong potential of neural operator frameworks as accurate, efficient, and generalizable surrogates for neutron transport, paving the way for real-time digital twin applications and repeated evaluations, such as in design optimization.
Executive Summary
This article presents a neural operator-based surrogate modeling framework for neutron transport computation. The authors employ two architectures, Deep Operator Network (DeepONet) and Fourier Neural Operator (FNO), to learn the mapping from anisotropic neutron sources to angular fluxes in a one-dimensional slab geometry. The models are trained for different scattering ratios and evaluated on a wide range of previously unseen source configurations, demonstrating significant speedups and high predictive accuracy. The surrogate models are then incorporated into the S_N k-eigenvalue solver, reproducing reference eigenvalues with deviations up to 135 pcm, while reducing runtime to <0.1% of that of the S_N solver. This work demonstrates the potential of neural operator frameworks as accurate and efficient surrogates for neutron transport, paving the way for real-time digital twin applications and repeated evaluations.
Key Points
- ▸ Neural operator-based surrogate modeling framework for neutron transport computation
- ▸ Deep Operator Network (DeepONet) and Fourier Neural Operator (FNO) architectures employed
- ▸ Significant speedups achieved, with FNO generally achieving higher predictive accuracy
- ▸ Surrogate models incorporated into the S_N k-eigenvalue solver, reducing runtime to <0.1% of S_N solver
Merits
Strength in predictive accuracy
The models demonstrated high predictive accuracy, with FNO achieving higher accuracy than DeepONet in many cases.
Significant computational efficiency
The surrogate models achieved significant speedups, reducing runtime to <0.1% of that of the S_N solver.
Generalizability across different transport regimes
The models were trained for different scattering ratios and evaluated on a wide range of previously unseen source configurations.
Demerits
Limited to one-dimensional slab geometry
The models were trained and evaluated in a one-dimensional slab geometry, limiting their applicability to more complex geometries.
Requires large datasets for training
The models require large datasets for training, which can be time-consuming and computationally expensive to generate.
Expert Commentary
This article presents a significant advance in the application of machine learning techniques to nuclear engineering problems. The use of neural operator-based surrogate modeling frameworks has the potential to enable real-time digital twin applications and repeated evaluations, which can significantly accelerate the design and safety analysis of nuclear reactors. However, the models are limited to one-dimensional slab geometry and require large datasets for training, which can be time-consuming and computationally expensive to generate. Further research is needed to extend the applicability of these models to more complex geometries and to develop more efficient training methods.
Recommendations
- ✓ Further research should be conducted to extend the applicability of the surrogate models to more complex geometries.
- ✓ Efficient training methods should be developed to reduce the computational cost of generating large datasets for training.
