Identifying Structural Controls on Nonlinear Flow and Transport in Network Representations of Heterogeneous and Karst-Like Media Using Interpretable Machine Learning

Identifying Structural Controls on Nonlinear Flow and Transport in Network Representations of Heterogeneous and Karst-Like Media Using Interpretable Machine Learning

Understanding how structural heterogeneity and connectivity control flow and transport remains a central challenge in fractured-porous media and karst systems, where strong velocity contrasts, preferential pathways, and non-Fickian transport are commonly observed across scales. Conceptual network representations provide a physically grounded framework to investigate these processes, but isolating the combined effects of geometry, topology, and finite connectivity on flow and transport behavior remains difficult.

In this work, we use pore network models as generic network representations of heterogeneous and karst-like media and combine them with interpretable machine learning to systematically identify the structural characteristics that govern flow and transport responses. Large ensembles of synthetic networks are generated with controlled variations in coordination number, throat size distributions, throat lengths, and connectivity. For each network, single-phase flow and advective-diffusive transport are simulated, and metrics characterizing flow heterogeneity and transport nonlinearity, such as velocity and flow-rate distributions, dispersion coefficients, spatial moments, and breakthrough curve scaling, are extracted.

Interpretable machine learning is used as a diagnostic tool, rather than a surrogate model, to quantify the influence of geometric and topological descriptors on flow localization, preferential channeling, and anomalous transport behavior. Feature importance and sensitivity analyses identify dominant structural controls and interactions, highlighting how connectivity, heterogeneity, and finite network structure shape nonlinear flow and transport. The results provide insight into the mechanisms controlling transport in strongly heterogeneous systems and illustrate how data-driven analysis can support physics-based modeling of fractured and karst environments.