## 1 Introduction  
Machine learning methods (ML) and neural networks (ANN) are increasingly being applied in engineering, particularly in the field of wastewater treatment [1, 2, 3, 4, 5]. The primary objectives addressed by these techniques include the development of regression models for predicting water quality [6], minimizing energy consumption [7], and implementing classification models for anomaly detection and preventive maintenance [8]. Machine learning algorithms demonstrate a high level of predictive accuracy when supported by effective data preprocessing, robust validation, and model evaluation practices [9]. In addition to the practical application and fine-tuning of established models, there is growing interest in neural networks whose architectures have been tailored for specific tasks. This includes modifications to the number of neuron layers, the total number of neurons,and their distribution across layers. The architecture of this model, including the number of input and output neurons, is determined by the structure of the input and output data. In many instances, the internal structure of the network is determined using [PERSON]'s theory, which employs a hypothetical continuous transformation function. It is essential to conduct experimental validation of the constructed network to verify its parameters. In some cases, algorithms such as the Mezard-Nadal, Marchand, or Lee-Taft methods are suggested for expanding and enhancing the network, while in other situations, techniques for network reduction may be applied. [PERSON] [10] developed various neural network configurations to predict biogas production during the anaerobic digestion of wastewater sludge. A total of 18 neural network configurations were examined, including linear networks, multilayer perceptrons (MLP), radial basis function networks (RBF), and general regression neural networks (GRNN). These neural network structures were trained using several algorithms: backpropagation (BP); conjugate gradient (CG); K-means (a training algorithm for radial basis neurons); K-nearest neighbors (KN) for deviation radius determination, pseudoinversion (PI) for linear optimization of least squares errors, and subsample (SS) training algorithms. The linear networks were specifically trained using the PI algorithm. This study identified the operational parameters of the anaerobic digestion unit that significantly influenced the model's performance, primarily focusing on the technological parameters of the equipment. In contrast, the characteristics of the incoming wastewater had the least impact and were considered uncontrolled parameters. Consequently, a model was developed that enables the optimization of the process through the adjustment of technological parameters. [PERSON] [11] investigates the applicability of various neural network architectures in membrane wastewater treatment and seawater desalination. That study highlights the most common neural network architectures, including multilayer perceptrons (MLP), radial basis function networks (RBF), recurrent neural networks (RNN), bootstrap aggregated neural networks (BANN), radial basis function neural networks (RBFNN), Elman neural networks (ENN), and deep neural networks (DNN). The applicability of these neural networks is classified according to the type of primary technological processes: microfiltration; ultrafiltration; nanofiltration; and reverse osmosis. Among these, the MLP architecture remains the most widely used, demonstrating stable performance while still leaving room for improvement in prediction accuracy. [PERSON] [12] utilized a neural network to predict the efficacy of advanced oxidation processes (AOP), specifically Fenton and SPF technologies. The neural network produced multiple outputs, allowing for a comprehensive assessment of the technology's cost with high forecasting accuracy metrics. That study employed a multilayer perceptron (MLP) architecture.