A Physics-Informed Neural Network for BNCT Neutron Flux Modeling
Abstract
Purpose
Monte Carlo (MC) particle transport methods which with high computational cost of MC simulations severely limits their efficiency of BNCT dose calculations. We developed a physics-informed neural network (PINN) framework for efficient and physically consistent neutron flux modeling.
Methods
Our framework adopts a modular, multi-stage training work flow. First, a conditional Fourier-feature neural network is trained to represent the neutron flux field across multiple beam radium between 3.0 to 6.0 cm using MC(PHITS) case as references . Second, an effective volumetric source term is learned using a dedicated source network and subsequently frozen to stabilize downstream optimization. Third, diffusion and absorption coefficients are inferred via a parameter network, enabling continuous interpolation across beam configurations. Finally, a joint fine-tuning stage integrates data loss and physics residual loss, augmented with a source-region–aware regularization strategy that explicitly penalizes residual violations in source-dominated regions for unseen intermediate beam radium. The trained PINN is evaluated by comparing the predicted neutron flux with PHITS reference data while simultaneously assessing the PDE residual.
Results
Unlike per-case fitting, the parameter network learns a continuous physical trend rather than memorizing discrete cases.For all training beam radium r0 between 3.0 to 6.0 cm, the proposed PINN achieves low global PDE residuals, with RMS residual values on the order of 10−3 and10−2. The physics residuals remain well controlled in the source-dominated regions. For interpolated beam radium(r0=3.25,4.25,5.75 cm), the residuals increase moderately, however, the residuals remain bounded and continuous, with no evidence of numerical instability or unphysical divergence.
Conclusion
The results demonstrates that the model preserves physical consistency under parameter interpolation rather than relying on memorization of discrete cases, which demonstrate the feasibility of incorporating physics-informed learning for parametric neutron flux modeling in BNCT.