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

Abstract

Reliable prediction of CO 2 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 R 2  = 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.