## 3 Results and Discussion
### Comparison of the Best Model with Literature and Implications of the Study  
The performance analysis of the various models used in this study, as summarized in Table 2, revealed that MLPNN configured using the hyperbolic tangent in the hidden layer and sigmoid at the outer layer with a gradient descent optimization algorithm producing the best prediction of biohydrogen from the biodiesel waste. This is evidenced by the highest R\({}^{2}\) value of 0.978 and the lowest RMSE value of 9.91 mL H\({}_{2}\)/L of biodiesel waste. The robust performance of the model in modeling the prediction of biohydrogen production could be attributed to the unique characteristics of the hyperbolic tangent as well as the activation at the hidden layer [35]. The hyperbolic activation function enables rapid network convergence at the hidden layer, thereby complementing the sigmoid activation function and facilitating a robust prediction [36]. The sigma activation function's primary goal is to keep the predicted or output value inside a certain bound, which contributes to the model's effectiveness and precision [37]. Besides, it is generally accepted that the best method for optimizing neural networks and other machine-learning algorithms is using gradient descent. Gradient descent as an iterative optimization algorithm has the advantage of reducing the cost function to obtain a model that can accurately predict a targetted output [38]. The difference between the model's anticipated output and the actual output was measured by the cost function (C) or the loss function.  
The performance of the best model in this study is comparable with similar MLP-neural network configurations that have been successfully employed to model geothermal power generation [39], hydrogen solubility in hydrocarbon fuels [40], prediction of corrosion inhibition performances of ionic liquids [41], the interfacial tension of the hydrogen-brine system [42], and lignin extraction from oil palm biomass [43] (Table 4). Various models have displayed robust performance in modeling the target model output, as indicated by high R\({}^{2}\) and low RMSE values. The slight variation in the performance indicator of the best model in this study and those reported in the literature can be attributed to the peculiarity of the datasets, the differences in training algorithms, and the nature of activation functions.  
Since the MLPNN can recognize all conceivable interactions between predictor variables, numerous training methods, and the capacity to implicitly detect complicated nonlinear connections between dependent and independent variables, model algorithms can be employed to determine the most important parameters that influence biohydrogen production from biodiesel waste such as glycerol, considering all possible input parameters. Besides, using the existing data to model the prediction of biohydrogen could help optimize the process, thereby preventing material loss, enhancing process safety, and eventually saving costs. However, the study is limited since all the available hyperparameters in the model configurations have not been fully exhausted. Hence, future research could consider  
Figure 7: Analysis of the relative importance of input variables on predicted biohydrogen production.  
the effect of various layers and perhaps varying the number of artificial neurons in the hidden layer as well as employing the possibility of more training algorithms.