Gaussian Process Surrogate Model with Uncertainty Quantification for PWR Pin-Cell Criticality Prediction

Surrogate models for nuclear reactor calculations typically provide point predictions without quantifying uncertainty, limiting their use in risk-informed applications. While several studies have applied machine learning to reactor physics, systematic evaluation of prediction interval calibration against Monte Carlo statistical uncertainty remains underexplored. This study develops a Gaussian Process regression (GPR) surrogate model that provides both accurate predictions and calibrated uncertainty estimates for the infinite multiplication factor (k∞) of a pressurized water reactor pin-cell. A dataset of 400 OpenMC Monte Carlo simulations was generated using Latin Hypercube Sampling across boron concentration (0–2000 ppm), fuel temperature (600–1200 K), and moderator temperature (500–600 K). The GPR model achieves R2=0.9971 with prediction errors below the Monte Carlo statistical uncertainty (MAE/σMC=0.75), indicating that model accuracy is limited only by inherent training data noise. The key contribution is demonstrating that GPR prediction intervals are well-calibrated, achieving 92.5% coverage for 95% confidence bounds (bootstrap 95% CI: [87.5%, 97.5%], containing the nominal level; binomial test p = 0.297), with mean prediction uncertainty closely matching the Monte Carlo statistical uncertainty (σGPR=0.00192 vs. σMC=0.00200). This near-perfect match suggests the surrogate has captured essentially all deterministic variation, with residual uncertainty attributable to Monte Carlo noise alone. Variance-based sensitivity analysis confirms boron concentration accounts for 99% of output variance. The surrogate preserves physically meaningful reactivity coefficients (Doppler: −2.1 pcm/K; boron worth: −6.1 pcm/ppm) while providing 105-fold computational speedup. The framework is restricted to fresh fuel with fixed enrichment; extension to burnup-dependent scenarios is left for future work.