## 1 Introduction
In a separate investigation, [PERSON] [13] combined a neural network with a support vector machine (SVM) to optimize the operation of a novel membrane-rotating biological contactor (MRBC). This research implemented a neural network utilizing a backpropagation training algorithm based on the Levenberg-Marquardt model, which employs a Gauss-Newton approach. Backpropagation is a standard method for training neural networks in which neuron weights are adjusted in the reverse direction based on the error between the expected and actual outputs of the network. This process is a crucial component of the training algorithm, aimed at minimizing error through gradient descent techniques. The Levenberg-Marquardt model is a numerical method employed for solving optimization problems, particularly in nonlinear regression [14]. This method combines two approaches: the gradient descent method, which is applied when the optimization surface deviates significantly from a quadratic form, and the Gauss-Newton method, which is effective for problems where the optimization surface is close to quadratic. The Levenberg-Marquardt model adapts its optimization steps by combining both methods: gradient descent is employed when the gradients vary significantly, while the Gauss-Newton method is used when the error is approximately linear (nearly quadratic) [15]. In the course of this study, a model was developed to optimize key technological parameters, including the rotation speed of the disk, hydraulic retention time (HRT), and the solid retention time (SRT) of activated sludge in the reactor. The coefficient of determination exceeded 0.9 on the test data, indicating a strong correlation between this model and real operating conditions. [PERSON] [16] trained a similar model to refine the characteristics of sludge pretreatment, achieving an R\({}^{2}\) value exceeding 0.99. Models utilizing backpropagation have also been explored by researchers under the guidance of [PERSON] [17]. They developed a model with one hidden layer containing 20 neurons and an output layer with 4 neurons to predict the efficiency of wastewater treatment in rice farming. The model's performance was assessed using the coefficient of determination, which yielded a value of 0.9935. Similarly, [PERSON] [18] obtained comparable results with a similarly structured model for predicting the efficiency of advanced wastewater treatment using coagulants, flocculants, and magnetic powder. In the previously discussed studies, the modeling approach was based on the premise that the datasets did not represent ordered time series. Consequently, the developed neural networks were applied to datasets without considering trend analysis. However, there is considerable interest in the application of neural networks, specifically to time series data. These networks enable the effective implementation of \"soft sensors\" that provide information on water quality at various treatment facility nodes, predicted based on incoming wastewater data while accounting for daily and seasonal variability. Several classes of specialized neural networks are suitable for these purposes. One notable example is the long short-term memory artificial neural network (LSTM). LSTM is a type of artificial neural network that belongs to the class of recurrent neural networks (RNNs) and is specifically designed for processing and analyzing sequential data. LSTMs are particularly useful for working with data that exhibit temporal dependencies, such as time series, text, or sequential events. The primary advantage of LSTM networks lies in their ability to retain critical information over extended periods while disregarding less significant data.