## 1 Introduction
When soil gradation deviates significantly from standard ranges (e.g., uniformity coefficient \(C_{\text{u}}>20\)) or when fine particles are interspersed, traditional empirical models may yield prediction errors spanning two to three orders of magnitude. More critically, these empirical formulas are fundamentally extrapolative fits to specific datasets. They neither elucidate the intrinsic physical mechanisms governing permeability evolution nor exhibit generalizability to novel engineering materials, such as recycled aggregate-stabilized soils, thereby limiting their broader applicability. Given the mechanistic limitations and generalization bottlenecks of empirical models in predicting the permeability of complex CGSs, machine learning offers a novel paradigm for addressing the challenges of multifactor coupling. By autonomously extracting high-dimensional nonlinear interactions between gradation curve morphology and pore characteristics, data-driven models not only overcome the parameter sensitivity thresholds of traditional formulas but also leverage implicit feature mapping to capture key physical mechanisms, such as preferential seepage pathways. Compared to empirical equations that rely on manually imposed assumptions, machine learning optimizes feature weights adaptively and employs nonlinear function approximation, enabling cross-scale predictions from discrete particle size distributions to macroscopic permeability behavior even under limited specimen conditions. Furthermore, its superior prediction robustness significantly enhances the accuracy of permeability coefficient inversion for highly heterogeneous CGSs, establishing a technically rigorous yet practically viable approach for engineering applications. In the field of permeability coefficient prediction for CGSs, various machine learning approaches have been systematically explored and validated for their effectiveness. The random forest algorithm was first employed to integrate the fractal dimension of the particle size distribution curve and pore tortuosity parameters, enabling a nonlinear mapping of the permeability coefficient for widely graded gravelly sands, with prediction accuracy improved by 62% compared to the traditional Hazen model [30]. A Bayesian-optimized support vector regression model has demonstrated its capability to stably capture the implicit relationships between particle shape parameters and permeability, even under small-specimen conditions, exhibiting significant advantages in extreme gradation scenarios where the uniformity coefficient (\(C_{u}>15\)) is high [31]. To address high-dimensional feature coupling, a deep neural network architecture was designed with a dual-channel structure incorporating a gradation encoder and a physics-informed loss function, successfully decoupling the influence of particle contact force chain evolution on seepage pathways [32]). Additionally, the XGBoost algorithm has been embedded into a transfer learning framework, enabling knowledge migration across large-scale engineering databases and overcoming the limitations imposed by data scarcity in individual projects [33]. The attention-based long short-term memory (LSTM) network has been innovatively applied to capture the dynamic response of permeability coefficients over time, reducing prediction errors to 8.3% in coarse-grained subgrade soils under cyclic loading conditions [34]. Recent studies further confirm that graph convolutional networks (GCNs), incorporating discrete element simulation data, can effectively characterize the topological features of particle spatial arrangements, enhancing the accuracy of quantifying the contribution of three-dimensional pore structures to permeability to 92% [35; 36; 37; 38].