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

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Erik Jansson, Magnus Röding
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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.

可解释性与基于分析和神经网络的渗透率预测模型的性能:探索可分离性、单调性和维度一致性。
多孔材料的有效传质性能,如渗透率,在很大程度上受其三维微观结构的影响。从微观结构特征预测渗透率的模型有很多,从简单的分析关系到基于神经网络的高性能机器学习模型。在预测性能和可解释性之间存在固有的权衡;分析模型不能提供最好的预测性能,但相对容易理解。另一方面,神经网络提供了更好的预测性能,但更难解释。在本文中,我们研究了许多关于性能与可解释性谱的模型。具体来说,我们使用了在其他地方开发的90000个微观结构的数据集,并考虑使用微观结构描述符孔隙度、比表面积和测地线扭曲度来预测渗透率。在频谱的两端,我们分别研究了解析型、幂律型模型和全连接神经网络。在这两者之间,我们研究的神经网络要么是可分离的,单调的,要么是可分离的和单调的。考虑到利用基于梯度的方法解决微观结构逆设计问题的潜力,建立单调关系是特别有趣的。此外,我们还研究了这些模型在物理维度上一致和不一致的版本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
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.
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