Optimization of Gompertz model with machine learning towards applicable and accurate simulation of anaerobic digestion

Yadong Ge, Rui Zhang, Zhi Wang, Beibei Yan, Junyu Tao, Yinjin Song, Lan Mu, Hong Su, Guanyi Chen,
Optimization of Gompertz model with machine learning towards applicable and accurate simulation of anaerobic digestion,
Energy,
Volume 333,
2025,
137395,
ISSN 0360-5442,
https://doi.org/10.1016/j.energy.2025.137395.
(https://www.sciencedirect.com/science/article/pii/S0360544225030373)
Abstract: This study optimized the Gompertz model with machine learning. The vital parameters of Gompertz were obtained by machine learning instead of experiment, and the accuracy and interpretability of the new model were compared to the traditional Gompertz model. The results showed that the prediction accuracy of the three machine learning algorithms was superior, with the maximum average R2 and Root Mean Square Error (RMSE) reaching 0.95 and 1.448, respectively. For all machine learning inputs, the inoculum and feedstock had significant impact on the output, with an average contribution rate of 36.5 % and 42.5 %, respectively. Compared to traditional Gompertz model, the accuracy of the machine learning model improved by 23.1 %. Furthermore, when a small amount of experimental data was incorporated into the machine learning model, the accuracy was further improved by 42.3 %. The Theil Inequality Coefficient (TIC) values of the four feedstocks in the new model reached 0.019, 0.011, 0.012, and 0.020 respectively. This study confirms the hypothesis that accurately predicting crucial intermediate parameters using machine learning models can enhance the performance of the Gompertz model.
Keywords: Anaerobic digestion; Gompertz model; Machine learning; Biomass