Prediction of coal permeability evolution under true triaxial stress conditions based on optimized deep learning algorithms

Coal seam permeability is significantly influenced by tectonic and mining-induced stresses. Accurate permeability prediction is therefore crucial for ensuring safe gas extraction, efficient CO2 sequestration, and effective unconventional energy development. However, traditional permeability models have notable limitations: exponential models typically exhibit substantial errors under complex stress conditions, while purely data-driven models lack physical interpretability and are highly sensitive to sample size. In this study, a stress–permeability database was established based on true triaxial seepage experiments conducted on coal samples. Two advanced predictive approaches—an optimized genetic programming (GP) method and physics-informed neural networks (PINNs)—were proposed and developed. For the optimized GP algorithm, the introduction of dynamic complexity penalties and multi-threaded parallel evaluations significantly mitigated code bloat, enhancing computational efficiency by approximately 23% and markedly improving prediction accuracy (with evaluation metric a20 exceeding 0.9). The PINNs approach incorporated Darcy's law and permeability equations into the neural network by explicitly formulating Darcy residuals and elastic model residuals. Adaptive weighting was employed to balance data-driven errors and physics-based residuals, enabling simultaneous convergence of both residual types. Ultimately, the model reached a balanced state between data loss and physics loss, achieving an exceptional prediction accuracy with an R2 value greater than 0.99. A comprehensive comparative assessment revealed that PINNs delivered the highest predictive accuracy, while the optimized GP algorithm provided superior computational efficiency. Both approaches represent effective alternatives to traditional permeability models, offering efficient solutions for permeability prediction in engineering practice.