## 1 Introduction
Additionally, an ANN can solve multi-dimensional issues and multi-task [21]-it creates a neural structure with processing units linked by coefficients (weights). With each iteration, the algorithm fluctuates the values of the importance and the biases such that the values generated by the algorithm are closer to the actual values. The neurons of the neural structure add up the product of weights and inputs to create a linear combination of the information delivered to an activation function. With back-propagation of mistakes during training iterations, the output is produced via feed-forward data flow. Above all, ANN models offer the advantage of forecasting the behavior of highly complex systems when traditional adsorption isotherms may be incorrect [22]. Owing to its capacity to simulate highly nonlinear systems, its application in complicated procedures such as multi-component adsorption has been effectively applied [23; 24; 25; 26; 27]. The Levenberg-Marquardt algorithm (LMA)-based ANN is recommended for nonlinear training because it combines gradient descent and quasi-Newton techniques to produce fast convergence and performance. Additionally, including LMA with second-order error optimization into ANN aids in overcoming the drawbacks of the back-propagation technique and delivers consistent and rapid results [28; 29]. [PERSON] et al. (2021) [27] performed the adsorption modeling of Ni, Cu, and Pb ions using different types of solutions. This was achieved using biochar derived from date seed and depicted that LMAwas a fast algorithm, albeit not the best selection when the dataset in use is relatively more minor [30]. However, the study also featured another algorithm to compensate for this drawback--Bayesian regularization (BR), a slower algorithm but much more suitable for smaller datasets [27]. It is used to process a nonlinear regression as well-defined ridge regression, and the Bayesian models can be used to avoid overtraining and overfitting data. This is achieved by providing an objective Bayesian criterion for stopping training using evidence procedures [31]. It is proposed in this research to use human fecal ash as an adsorbent to adsorb urea from human urine, thus creating a self-sustaining sanitation loop. Wastes produced in this closed-loop system will be recycled and repurposed instead of being discharged into the environment, allowing us to manage resources more effectively while minimizing environmental externalities. The experimental results obtained are used to build an ANN model which is highly capable of predicting the recovery of urea from human urine. Different second-order methods are employed to train our network. The prediction accuracy and convergence time are then compared: Bayesian regularization techniques such as ANN, quasi-Newton, Levenberg-Marquardt, and conjugate gradient are considered, and the one that is the best match for our task is chosen. The following objectives were assessed in our study: (i) the adsorption capacity of urea (sorbate) from synthetic urine was determined, (ii) the effect of different process parameters were evaluated, (iii) the data obtained were fitted with known isotherm models (Langmuir, Freundlich, Temkin) to understand the adsorption mechanism, (iv) an ANN model was developed using the data samples generated in our study, (v) possible end uses for fecal ash (sorbent) were identified and incorporated as a part of a closed nutrient loop.