Ex-Core Neutron-Flux Reconstruction Using Machine-Learned Green’s Kernels and Flux-Gradient Measurements

Accurate reconstruction of the neutron-flux distribution in a reactor core is essential for power-shape monitoring, diagnostics, control, and irradiation experiments, but dense in-core instrumentation is often impractical in advanced reactors (high temperature, corrosive coolants, and irradiation constraints) and microreactors (limited penetrations and access). This work presents GRACE (Green’s-kernel Reconstruction from ACcessible Ex-core measurements), a physics-directed framework for reconstructing three-dimensional neutron-flux fields from boundary measurements by embedding a Green’s-function representation of one-group diffusion into a neural parameterization of the kernel. By recasting flux estimation as an inverse boundary-value problem, GRACE identifies an effective Green’s kernel that can be reused as a boundary-to-interior propagator across operating configurations, reducing reliance on scenario-specific surrogates trained on large simulation libraries. Numerical validation using an OpenMC model of the Purdue University Reactor (PUR-1) demonstrates accurate reconstruction, with mean fractional errors below 5%, for previously unseen control-rod configurations using only simulated boundary data. To provide the boundary-gradient input required by the reconstruction, we introduce and demonstrate a quadrupole sensor for measuring the neutron-flux gradient at the core boundary. An activation-based prototype using gold wires was deployed at PUR-1, yielding reproducible gradient signatures and agreement with OpenMC predictions at the few-percent level. These results demonstrate that flux-gradient information can be obtained experimentally, establishing a path toward core-monitoring strategies based entirely on ex-core measurements.