A Gaussian-Process Surrogate for Control Rod Worth with Calibrated Uncertainty: Application to VERA Core Physics Benchmark Problem 4

Abstract

Differential and integral control rod worth are usually obtained by differencing eigenvalue calculations at discrete rod positions, which resolves the derivative poorly and gives it no uncertainty. We build a Gaussian-process (GP) surrogate for reactivity as a function of rod position on VERA Core Physics Benchmark Problem 4, a $3\times3$ assembly cluster with a hybrid AIC/B$_4$C rod cluster control assembly, modelled in OpenMC with ENDF/B-VIII.0. A parametric sigmoidal mean carries the dynamic range, a Matern-5/2 GP carries the residual, and the reported Monte Carlo uncertainty of each run enters as known observation noise. Because differentiation is linear, the differential rod worth and its variance follow in closed form from the kernel derivatives. Trained on 43 runs at three particle counts and tested on 11 independent runs, the surrogate meets a fixed 10 pcm accuracy target above the test-run noise, and its intervals are calibrated: the standardized leave-one-out residuals over 129 independent runs have variance 1.07 with 95% interval [0.85, 1.39]. The total worth agrees with the direct OpenMC end-point difference within combined uncertainty, and the differential worth peak is located to within one step. Three mean functions of very different fit quality give the same differential worth to within 0.1 pcm/step, while the width of its band depends on the kernel smoothness by a factor of four. The number of runs required and the remaining approximations are reported, and the extension to rod position and soluble boron is outlined.