Physics-Informed Sparse Dictionary Learning (PISDL) for Accurate Rock Strength Prediction and Extrapolation from Sparse Measurements

Abstract Accurate extrapolation of rock strength from sparse triaxial data is difficult because conventional criteria (e.g., Hoek–Brown) become unstable when calibrated with limited datasets. This study proposes a physics-informed sparse dictionary learning (PISDL) framework that embeds the Hoek–Brown equation inside a sparse representation and Bayesian inference scheme to improve prediction using limited datasets. The proposed method constructs a physics-informed dictionary by discretizing the parameter space of the Hoek–Brown criterion and employs sparse regression techniques together with physical filter to identify important dictionary atoms from limited experimental data. Bayesian inference with Markov Chain Monte Carlo (MCMC) sampling is utilized for uncertainty quantification, providing posterior distributions of the model parameters. The proposed framework is validated using experimental datasets of dolomite, sandstone, and coal. Compared with Hoek–Brown fitted to the same sparse data, PISDL raises R 2 from 65.07% to 90.90% for dolomite, 91.09% to 96.22% for sandstone, and 68.75% to 89.73% for coal, and lowers RMSE (e.g., decreasing from 155.89 to 79.34 MPa for dolomite). Results show that embedding domain physics into sparse dictionary structures with Bayesian uncertainty quantification yields accurate, interpretable, and extrapolative rock strength predictions from limited measurements with uncertainty quantification. The proposed PISDL framework offers a robust tool for rock engineering applications where data scarcity is a common challenge.