Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Diffusion Analysis With High and Low Concentration Regions by Finite Difference Method, Adaptive Network-Based Fuzzy Inference System, and Bilayered Neural Network Method

Version 1 : Received: 7 September 2021 / Approved: 9 September 2021 / Online: 9 September 2021 (10:50:57 CEST)

How to cite: Shao, Q.; Faizollahzadeh Ardabili, S.; Mafarja, M.; Turabieh, H.; Zhang, Q.; Band, S.S.; Chau, K.; Mosavi, A. Diffusion Analysis With High and Low Concentration Regions by Finite Difference Method, Adaptive Network-Based Fuzzy Inference System, and Bilayered Neural Network Method. Preprints 2021, 2021090173 (doi: 10.20944/preprints202109.0173.v1). Shao, Q.; Faizollahzadeh Ardabili, S.; Mafarja, M.; Turabieh, H.; Zhang, Q.; Band, S.S.; Chau, K.; Mosavi, A. Diffusion Analysis With High and Low Concentration Regions by Finite Difference Method, Adaptive Network-Based Fuzzy Inference System, and Bilayered Neural Network Method. Preprints 2021, 2021090173 (doi: 10.20944/preprints202109.0173.v1).

Abstract

The diffusion of molecules in aqueous solutions in the domain of membrane technology is very critical in the efficiency of chemical engineering and purification processes. In this study, the diffusion in high and low concentration regions is simulated with finite difference method (FDM), and then the results of numerical computations are coupled with adaptive network-based fuzzy inference system (ANFIS) and bilayered neural network method (BNNM). Machine learning approach can individually predict diffusion phenomena across the domain based on understanding of the machine instead of the discretization of an ordinary differential equation (ODE). The findings of the machine learning method are in good agreement with those of FDM at different times of the simulation. In addition to numerical computation, the error of the system is computed for different iterations. The results show that by increasing the number of iterations and training datasets, all errors reduce significantly for both training and testing. BNN method is also used to train the prediction process of diffusion for a more accurate comparison. This technique is similar to ANFIS method in terms of prediction capability. According to the findings, ANFIS approach predicts diffusion slightly better than BNN method. In this regard, ANFIS technique produces R>0.99 while BNN method produces R around 0.98. Both machine learning methods are accurate enough to predict diffusion throughout the domain for different time steps. The computational time for both algorithms is less than that of FDM method to predict low and high concentrations in the domain. Besides, based on the results, artificial intelligence (AI) can find the relationship between inputs and outputs and determine which input has the main influence on the output in this study to optimize the process. As such, future studies can be focused on AI and other methods for faster prediction and optimization processes.

Keywords

ANFIS; Bilayered neural network; diffusion phenomena; diffusion of molecules; machine learning

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