Neural ordinary differential equations for solving nonlinear system of ethanol fermentation in bioreactor

• Main Authors: Azimi, Ahmad Izul Fakhruddin, Jamil, Norazaliza Mohd, Rahim, Mohd Hasbi Ab
• Format: Conference Proceeding
• Language: English
• Subjects: Bioreactors; Differential equations; Error analysis; Ethanol; Fermentation; Nonlinear systems; Numerical methods; Ordinary differential equations; Runge-Kutta method; Substrates; Training
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0192503

Differential equations are used in many sectors of science and engineering to describe real-world issues. Unfortunately, sometimes it is difficult to solve using analytical methods and researchers have developed numerous approaches to solve these differential equations. The purpose of this paper is to emphasise the study of Neural Ordinary Differential Equations (Neural ODE) in solving differential equations linked to ethanol production via fermentation. Two analyses were conducted in order to compare the most effective approaches for solving these mathematical equations. The first comparison is between the conventional numerical method and Neural ODE. The data from experimental data were utilised to determine which approach had the least error in this analysis. Neural ODE performed well when compared to Runge-Kutta, the fourth and eighth orders. Following that, Neural ODE was compared to a recently created technique, Hypersolver, with the goal of enhancing Neural ODE performance. A study on the number of epochs and batches were performed in order to determine which hyperparameters gave the best and fastest results. The analysis of the number of epochs reveals that as the number of epochs rises, the error decreases, but the wall clock increases. For the analysis of batches in Hypersolver, increasing the batch size reduces the wall-clock during training, but no fixed error trend between microbe, ethanol and substrate can be identified, and these errors remain minimal when compared to Neural ODE. From these studies, it can be concluded that Neural ODE is capable of solving the presented model in the same way as the conventional numerical technique does, and the addition of training in Hypersolver does not show significant impact because the difference between Hypersolver and Neural ODE is very small.