Interpretability versus performance of analytical and neural-network-based permeability prediction models: Exploring separability, monotonicity, and dimensional consistency.
{"title":"Interpretability versus performance of analytical and neural-network-based permeability prediction models: Exploring separability, monotonicity, and dimensional consistency.","authors":"Erik Jansson, Magnus Röding","doi":"10.1103/PhysRevE.111.045509","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":20085,"journal":{"name":"Physical review. E","volume":"111 4-2","pages":"045509"},"PeriodicalIF":2.4000,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical review. E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/PhysRevE.111.045509","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.