Predicting Effective Diffusivity of Porous Media from Images by Deep Learning

Abstract

We report the application of machine learning methods for predicting the effective diffusivity (De) of two-dimensional porous media from images of their structures. Pore structures are built using reconstruction methods and represented as images, and their effective diffusivity is computed by lattice Boltzmann (LBM) simulations. The datasets thus generated are used to train convolutional neural network (CNN) models and evaluate their performance. The trained model predicts the effective diffusivity of porous structures with computational cost orders of magnitude lower than LBM simulations. The optimized model performs well on porous media with realistic topology, large variation of porosity (0.28–0.98), and effective diffusivity spanning more than one order of magnitude (0.1 ≲ De < 1), e.g., >95% of predicted De have truncated relative error of <10% when the true De is larger than 0.2. The CNN model provides better prediction than the empirical Bruggeman equation, especially for porous structure with small diffusivity. The relative error of CNN predictions, however, is rather high for structures with De < 0.1. To address this issue, the porosity of porous structures is encoded directly into the neural network but the performance is enhanced marginally. Further improvement, i.e., 70% of the CNN predictions for structures with true De < 0.1 have relative error <30%, is achieved by removing trapped regions and dead-end pathways using a simple algorithm. These results suggest that deep learning augmented by field knowledge can be a powerful technique for predicting the transport properties of porous media. Directions for future research of machine learning in porous media are discussed based on detailed analysis of the performance of CNN models in the present work.

Prediction and Optimization of Ion Transport Characteristics in Nanoparticle-Based Electrolytes Using Convolutional Neural Networks

“…In the studies pertaining to the former, the hand-crafted features representing the microstructure are linked to an associated property using a regression-based model [24][25][26][27][28][29][30] or artificial neural network. 31,32 For the latter case, convolutional neural networks (CNNs) 33 are employed to extract important features from the digitized images of composite microstructures, generated by stochastic growth of grains [34][35][36][37][38] or by random assignment of numbers in the uniformly voxelized grids, [39][40][41] in order to predict the effective property of interest. Motivated by the above advances, we hypothesize that machine learning techniques can be similarly applied to correlate the properties of nanocomposites reinforced with spherical nanoparticles to their microstructure.…”

Predicting permeability via statistical learning on higher-order microstructural information

“…Barman et al 46 studied effective diffusivity prediction in 36 virtual porous polymer films using tortuosity and constrictivity. In a different direction, there are several attempts to use 2D and 3D convolutional neural networks (CNNs) to extract information directly from the binary image data describing the structure [47][48][49][51][52][53] in order to predict effective properties. However, these models are usually difficult to interpret and hard to rescale.…”

Towards the digitalisation of porous energy materials: evolution of digital approaches for microstructural design

“…Young's modulus and Poisson's ratio), 198 effective thermal conductivity of porous carbon nanotubes 199 and effective diffusivity of general porous materials. 200 As is well known, the key for DNNs in predicting the structure-property linkage is the availability of large training datasets. In the above works, digital images of microstructures can be from either experimental data like X-ray CT and SEM or mathematical reconstruction models.…”