Differentiable Neutron Transport

Neutron transport simulation plays a central role in nuclear engineering, yet its inverse problems—such as shielding design and sensitivity analysis—remain extremely challenging. The governing transport equation shares a common mathematical foundation with the volume rendering equation used for participating media in computer graphics. Recent advances in differentiable rendering have demonstrated that inverse problems—such as recovering scene properties from observations—can be efficiently solved through gradient-based optimization, where the gradients are estimated through Monte Carlo methods. Inspired by these developments, we extend differentiable rendering techniques to neutron transport problems, enabling inverse design and sensitivity analysis in nuclear systems. To adapt these methods to the neutron transport problem, we generalize the automatic differentiation of Monte Carlo light transport simulation to multi-energy neutron transport; propose a new simplified way to handle moving geometric discontinuities; and propose new estimators for derivatives of volume integrals. We demonstrate the effectiveness of the proposed framework on several model inverse problems, including gradient-based optimization of multi-group neutron moderation, sensitivity analysis of material properties, and diagnostic sensor shape optimization. These results show that differentiable Monte Carlo neutron transport can support optimization and analysis tasks, opening new opportunities for inverse design in nuclear shielding and related applications.