## 1 Introduction
Components of LSTM include a Memory Cell, the fundamental unit responsible for storing information and managing its retention, updating, and deletion; an Input Block, which determines which portions of new information will be added to the memory; a Forget Gate, which regulates what information will be discarded from the memory; and an Output Block, which specifies which part of the stored information will be utilized for the current output. [PERSON] [19] trained an LSTM model using data from a laboratory A/O bioreactor and compared its performance with that of a multifactorial linear regression model. The mean absolute percentage error (MAPE) was used as the target metric. On average, the LSTM model demonstrated significantly higher forecasting accuracy across three indicators, with a difference of up to 30%. [PERSON] [20] explored a model that predicted anomalous levels of ammonia and nitrates in treated wastewater during seasonal temperature fluctuations. An LSTM Auto-Encoder was employed in this study. This model is trained on normal data, where the input sequence is fed into the LSTM encoder, compressed into a latent space, and then reconstructed by a decoder. The objective is to minimize the reconstruction error. When processing new sequences, anomalous data generate a higher reconstruction error, allowing for the detection of deviations from normal patterns. The inclusion of the encoder led to improved performance compared to traditional LSTM models, potentially due to the application of various time-processing techniques, such as different window aggregations, steps, and sizes. The effectiveness of using autoencoders in conjunction with LSTM models is supported by several contemporary studies [21; 22; 23]. Another widely used neural network architecture for working with time series data is the Multi-Attention Gated Recurrent Unit (MAGRU). This architecture combines an attention mechanism with a modified version of the Gated Recurrent Unit (GRU), making it suitable for tasks that require sequential data processing. [PERSON] [24] utilized networks of this architecture to monitor wastewater treatment parameters at a facility in South Korea, achieving greater accuracy compared to other neural networks as evaluated by the Mean Absolute Error (MAE). On average, MAGRU demonstrated accuracy metrics that were 15-20% higher than those of other models employed in this study. These findings are corroborated by additional sources [25; 26; 27]. Overall, it can be observed that hybrid models tend to be the most effective in comparative studies, providing a flexible approach to data handling. Notable examples include the Complete Sliding Window LSTM Gaussian Process Regression (CSWLSTM-GPR) [28], AutoRegressive Integrated Moving Average-LSTM (ARIMA-LSTM) [29], and LSTM with Genetic Algorithm (GA-LSTM) [30], among others. The study by [PERSON] [31] addresses critical challenges in multivariate time series regression by proposing a novel nonlinear function-on-function model. Unlike conventional approaches, such as multivariate regression models and Seq2 Seq architectures, which are limited by their inability to handle irregular time series and temporal dependencies, the proposed method leverages fully connected neural networks to capture complex correlations. This model integrates and extends the function-on-function linear model, addressing issues of bias, inefficiency, and underfitting commonly associated with traditional methods. The effectiveness of this approach is validated through applications to real-world datasets, demonstrating its potential to significantly enhance predictive accuracy in time series analysis. This contribution represents a significant advancement in functional data analysis and time series modeling, offering robust solutions for diverse applications. This study investigates the performance of neural networks, specifically MAGRU, LSTM, ARIMA-LSTM, and Prophet, for forecasting the operation of the oxidation ditch (OD) under the simultaneous nitrification and denitrification (SND) technology.