Machine learning-based prediction of pervaporation permeation using physicochemical properties of permeant-membrane and process conditions

It is well accepted that the pervaporation (PV) permeation was affected by the physicochemical properties of permeant-membrane materials and process conditions. Given many experimental data of PV, a predictive model on PV permeation based on their physicochemical properties and process conditions can be constructed. This study proposes a machine learning approach in terms of artificial neural network (ANN) to predict the permeation flux of PV, as a function of physicochemical properties of permeant-membrane material and process conditions. A large dataset was assembled from the literature and was divided into a training subset and a testing subset. The output variable was the PV flux, while the input variables were the physicochemical properties of permeant-membrane and the process conditions which were considered to affect the PV flux. Two types of inputs were evaluated: regular variables (Type I) and dimensionless groups derived from these regular variables (Type II). Several neural network architectures were evaluated. The best predictive performance for Type I inputs was achieved with a deep neural network consisting of two layers, each with 7 neurons. For Type II inputs, the optimal architecture was a shallow neural network with a single layer containing 6 neurons. The correlation coefficients (<i>R</i>) during model training for Type I and Type II were 0.93674 and 0.88332, respectively, while the root mean square errors (RMSE) were 42.2558 and 38.0766, respectively. The extent of dependency of output on input variables was determined using Garson's equation. It was found that the most affecting physicochemical properties on the PV permeation flux were glass transition temperature (<i>T</i> _<i>gm</i> ), solubility difference of two different permeants <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo> <mml:mrow><mml:mo>Δ</mml:mo> <mml:mi>S</mml:mi> <mml:mi>o</mml:mi> <mml:msub><mml:mi>l</mml:mi> <mml:mrow><mml:mi>i</mml:mi> <mml:mi>j</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> , and molar volume of permeant (<i>v</i> _<i>i</i> ), consecutively. Whereas the operating condition that dominantly affects the PV permeation flux was permeate pressure (<i>P</i> _<i>p</i> ).