Mathematical formulation of the machine learning backpropagation network and regression modelling of the chemical stability and thermal properties of PLA/HKUST-1 fabricated porous membranes

As part of the ongoing quest to optimize the application and operational performance of biodegradable polymer materials, mathematical models have been developed to predict the chemical stability and thermal properties of PLA/HKUST-1 mixed matrix biopolymer composites, utilizing machine learning deep neural networks and regression modelling. These models were constructed by integrating a single-entry input that encompasses the percentage mass composition of PLA and HKUST-1, immersion time, casting thickness, and immersion temperature into a test function designed to predict behavior characterized by the chemical stability and thermal properties of these materials. Leveraging experimental datasets available in the literature, the models were trained to derive arbitrary constants and empirical constants that are instrumental in forecasting the chemical stability and thermal properties of the materials. With error estimates ranging from 0.01 to 2.16%, the formulated models accurately represented most output signals, including thermal stability at 5.0 and 50.0% mass loss, glass transition temperature, crystallization temperature, and melting point temperature of mixed matrix biopolymer materials. The application of this methodology may prove beneficial for the design and fabrication of novel polymer/composite materials with diverse engineering applications.

Graphical abstract

Plots of experimental and (a) DNN predictive values of reduced Chemical stability at 5 °C against reduced values of X and (b) linear and quadratic regression model predictive values of chemical stability at 5% [^oC] against X = (x₃*x₄*x₅)/(x_a-x_b).