Modeling the anaerobic digestion of palm oil mill effluent via physics-informed deep learning

The modeling of anaerobic digestion (AD) plays a significant role in process monitoring and prediction. Typically, mechanistic models or machine learning are used to model the AD process, where the former relies on the first-principle knowledge, while the latter learns the trend in data. In this study, models of AD were developed using data obtained from two palm oil mill effluent (POME) AD industrial plants, here they are denoted as plant A and plant B. The mechanistic model ADM1-R4 was first used to simulate POME AD to predict 3 AD outputs – methane, carbon dioxide, and effluent concentration. However, moderate prediction accuracy was observed, this could be due to highly dynamic environments in industrial plants and the incomplete knowledge of the mechanistic model where only 3 input features were considered. Then, artificial neural networks (ANNs) were trained using simulated data from the variational autoencoder for training and making the same predictions on the test data. ANNs were more inclusive as they included 6 or 7 input features and were found to make predictions with higher accuracy. Moreover, different ANN architectures were also investigated. Nevertheless, ANNs were time-consuming to train. Hence, physics-informed neural networks, namely ADM1-R4-NN, were further developed by embedding the information of mechanistic equations into the loss function of ANN. Overall, ADM1-R4-NN outperformed ANN and ADM1-R4, showing higher training efficiency (vs ANN) and testing accuracy (vs ANN and ADM1-R4). For plant A, the best prediction of ADM1-R4-NN resulted in R² values of 0.87–0.95, while for plant B, the R² was 0.81–0.88. Finally, feature importance analysis was conducted, where hydraulic retention time and mass loading were found to be the top influencing factors, while pretreatment temperature was a significant factor as well. The developed ADM1-R4-NN is a promising model for POME AD, and this method has the potential to be applied to other wastewater AD processes.