Inverse modeling of capillary imbibition using machine learning

The inverse problem of capillary imbibition involves determining the capillary geometry from imbibition kinematics. Solving this inverse problem is essential for nondestructive characterization of the internal geometry of nanoporous materials, as well as for the design of microfluidic and porous media channels. Previous research works have shown that this problem may have multiple solutions, often requiring time-varying meniscus position in both forward and reverse directions to ensure accuracy. This study introduces a machine learning approach to address the inverse problem. A training dataset is constructed using numerical simulation data, and an optimized neural network model is used to capture the nonlinear relationship between imbibition kinematics in two directions and the capillary radius. The approach is validated through two examples using numerical simulations and experimental data. In both cases, the capillary radius predicted by the neural network model closely matches the true capillary radius. Compared to previous iterative and analytical methods, this approach is computationally efficient, faster, less dependent on data quality and quantity, and exhibits strong robustness.