Interpretability versus performance of analytical and neural-network-based permeability prediction models: Exploring separability, monotonicity, and dimensional consistency

Effective mass transport properties of porous materials, such as permeability, are heavily influenced by their three-dimensional microstructure. There are numerous models developed for the prediction of permeability from microstructural characteristics, ranging from straightforward analytical relationships to high-performing machine learning models based on neural networks. There is an inherent tradeoff between predictive performance and interpretability; analytical models do not provide the best predictive performance but are relatively simple to understand. Neural networks, on the other hand, provide better predictive performance but are harder to interpret. In this paper, we investigate a multitude of models on the performance-versus-interpretability spectrum. Specifically, we use a dataset of 90000 microstructures developed elsewhere and consider the prediction of permeability using the microstructural descriptors porosity, specific surface area, and geodesic tortuosity. At the respective ends of the spectrum, we study analytical, power-law-type models and fully connected neural networks. In between, we study neural networks that are either separable, monotonic, or both separable and monotonic. Establishing monotonic relationships is particularly interesting considering the potential for solving the inverse microstructure design problem using gradient-based methods. In addition, we study versions of these models that are consistent and inconsistent in terms of physical dimension.