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Gradient Harmony Optimization-Driven Hybrid Physics-Informed Neural Network for Solving Neutron Diffusion Problems
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DOI：10.1109/TNS.2026.3655477.png)
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Abstract
En 中文
Physics-informed neural networks (PINNs) provide a flexible framework for solving neutron diffusion equations (NDEs), yet their accuracy and stability are often hindered by limited spatial sensitivity and conflicting gradients among multiple loss components. To address these challenges, we propose a gradient harmony optimization (GHO) hybrid PINN that integrates a spatial localization module (SLM) for enhanced positional awareness, a ResNet-based backbone for improved feature representation, and a GHO strategy to mitigate multi-objective gradient conflicts. The proposed method is systematically validated on a hierarchy of benchmark problems, including 1-D cylindrical and spherical reactors, 2-D bare and cylindrical geometries, a fully 3-D homogeneous cube, and the standard IAEA 2-D two-group benchmark. Comprehensive experiments demonstrate that each component-SLM, hybrid architecture, and GHO-provides measurable accuracy improvements, while their combination yields significant reductions in flux-field errors and faster convergence compared with conventional PINN baselines and multi-objective optimizers such as PCGrad. Although classical deterministic solvers remain more efficient for single forward calculations, the trained GHO hybrid PINN serves as a fast and differentiable surrogate with strong generalization across different geometries, offering clear advantages for parametric studies, inverse analysis, and real-time reactor-physics applications. The results highlight the potential of harmonized optimization and hybrid network design to advance PINN-based modeling in nuclear engineering.
Keywords:
Neural networks
Optimization
Training
Sensitivity
Neutrons
Mathematical models
Inductors
Convergence
Accuracy
Numerical stability
Gradient harmony optimization (GHO)
hybrid neural network (Hybrid_PINN) architecture
neutron diffusion equation (NDE)
physics-informed neural network (PINN)
reactor core physics
Journal
I
IF:
1.9
Papers:
324
Citations:
1.4W