Physics-informed gaussian process regression for reproducible and uncertainty-aware CO2 injectivity prediction

Reliable prediction of CO2 injectivity decline is essential for safe geological carbon storage, yet existing machine learning models often provide deterministic point predictions that lack uncertainty quantification. This paper presents a physics-informed Gaussian process regression (PC-GPR) framework for Relative Injectivity Change (RIC) prediction, embedding constraints derived from two independently grounded physical laws: the Derjaguin-Landau-Verwey-Overbeek (DLVO) colloidal monotonicity condition and the Civan-Kozeny-Carman permeability impairment model. Four GP variants are developed and benchmarked on a curated laboratory dataset (n = 44) under a three-tier validation protocol combining Leave-One-Out cross-validation, repeated k-fold cross-validation, and non-parametric bootstrap confidence intervals. Two complementary uncertainty quantification mechanisms are employed: GP posterior calibration via the Expected Calibration Error (ECE) and split-conformal prediction intervals. The GP-Base model achieves strong predictive performance (LOO R2 = 0.9401, 95% CI: [0.882, 0.978]) with well-calibrated uncertainty (ECE = 0.026) and reliable coverage (97.7% at the nominal 95% level). The PC-GPR-M variant reduces DLVO monotonicity violations to 1.5% across the input domain, demonstrating effective soft constraint enforcement. Operationally, the proposed framework translates predictive uncertainty into actionable injection scheduling guidance, identifying high-risk regions at salinity >30,000 ppm and jamming ratio >0.04. These results provide an uncertainty-aware baseline for future PIML research in subsurface carbon storage.