Insight mechanism of ANN model for denitrification in spouted bed bioreactor

Abstract

Numerous technologies have been developed to remove nitrate from wastewater due to its significant health and environmental impacts. In the present study, an isolate of Pseudomonas syringae was utilized to investigate the denitrification rate using immobilized granular activated carbon (GAC) in a draft tube spouted bed reactor. Developing a theoretical model for this reactor requires an understanding of multiple interrelated parameters, many of which may vary under different operating conditions. Given the inherent nonlinearities of the system, such modelling can be both complex and resource-intensive. Artificial Neural Networks (ANNs) offer a promising solution for modelling such nonlinear systems due to their flexibility and generalization capabilities. In this work, a feed-forward backpropagation neural network with three layers was constructed, consisting of three input neurons, nine neurons in the hidden layer, and one output neuron. The ANN model effectively predicted the effluent nitrate concentration in the reactor, achieving a correlation coefficient of 98.8%, a root mean square error (RMSE) of 9.25 × 10⁻⁵%, an average absolute error of 0.57%, and a residual sum of squares (RSS) of 30.84. In comparison, the multiple regression analysis (MRA) model produced a lower correlation coefficient of 90%, a higher RMSE of 0.01%, an average absolute error of 1.32%, and an RSS of 166.63. These results demonstrate that the ANN model outperforms the regression model across all evaluated performance metrics, making it a more effective tool for capturing the complex dynamics of the denitrification process in the reactor.

Introduction

Water is a vital resource for sustaining all life forms; however, increasing population pressures, urbanisation, and industrial expansion have significantly strained its availability and quality. The growing demand for safe and high-quality water for domestic, agricultural, and industrial use is escalating exponentially. Consequently, effective wastewater treatment systems that meet the stringent effluent standards prescribed by the Central Pollution Control Board (CPCB) are crucial for ensuring environmental and public health safety^1,2.

In recent years, wastewater treatment facilities have faced dual challenges: rising effluent loads due to industrial expansion and the demand for real-time, high-precision control. Traditional plant operation, heavily reliant on operator expertise, is often too slow and inefficient to respond dynamically to these challenges. To address this, there is an increasing reliance on mathematical modelling tools, particularly those that are data-driven, adaptive, and cost-effective, to evaluate and optimise treatment plant performance in real-time^3–6.

Among the primary pollutants, nitrate (NO₃⁻) is of particular concern due to its high solubility and persistence in aquatic systems. Effluents from fertilizer manufacturing, petrochemical industries, explosives production, and food processing can contain nitrate concentrations exceeding 50–200 ppm, far above the WHO guideline of 10 ppm for safe drinking water^7–9. High nitrate levels are linked to eutrophication, blue baby syndrome, and potential carcinogenic effects. Therefore, efficient and robust denitrification methods are imperative.

This study investigates a novel approach for nitrate removal using a draft tube spouted bed bioreactor coupled with granular activated carbon (GAC) as a bio-carrier. The uniqueness of this system lies in its dual-region (aerobic and anoxic) environment, created by the fluid circulation pattern within the draft tube and annular space, which offers ideal conditions for simultaneous nitrification and denitrification. Previous hydrodynamic and mass transfer studies highlight the complexity and unique flow behaviour of draft tube spouted bed bioreactor, making them particularly challenging for mechanistic modelling^10,11.

To overcome these limitations, the present research employs a data-driven modelling strategy that combines Multiple Regression Analysis (MRA) and Artificial Neural Networks (ANN). ANN has emerged as a powerful tool for learning nonlinear relationships within complex bioreactor systems without requiring detailed mechanistic knowledge^12–14. This study employs a feed-forward backpropagation neural network with three input neurons (representing key process variables), nine hidden neurons, and one output neuron (denitrification efficiency, expressed as a percentage).

This highlights the superiority of the ANN model, especially in capturing the nonlinear interactions between hydrodynamic conditions and biological kinetics in three-phase systems^15,16. The system’s predictive accuracy makes it a strong candidate for integration into real-time control systems, potentially embedded into PLCs or SCADA platforms to automate decision-making and enhance operational efficiency in treatment plants.

Various modelling approaches for bioreactors such as packed bed^17,18stirred tank bioreactor¹⁹bubble column, plated pulsed column²⁰fluidized bed reactors²¹anaerobic baffled reactor²² COD removal efficiency in UASB²³sequential batch reactor²⁴nitrogen removal with sequencing batch reactor and aerobic granular activated sludge process²⁵ and spouted bed reactor for phenol degradation²⁶ are reported in the literature. In general, it is believed that modelling of three-phase bioreactors with an attached growth process is more complex. In such cases, it is essential to clearly understand and consider the issues related to mixing between phases, mass transfer and biokinetics. To use such a model, accurate measurements of parameters such as active biomass weight (81 g/m²) and biofilm thickness (100 μm) are essential^27–30. 27, 28, 29, 30. It is worth noting that the solids immobilised with microorganisms used in such reactors are irregularly shaped (for example, granular activated carbon). Therefore, it becomes increasingly challenging to measure biofilm thickness accurately.

This study presents a comparative analysis of Artificial Neural Network (ANN) and Multiple Regression Analysis (MRA) models for predicting denitrification efficiency in a lab-scale spouted bioreactor system under varying operational conditions. Unlike prior works that primarily relied on linear modelling approaches or applied machine learning without rigorous validation, this study integrates a robust statistical evaluation, including residual analysis, regression coefficients, and error metrics, to highlight where traditional regression methods fail to capture nonlinear interactions between influent nitrate, dilution rate, and GAC loading. Furthermore, the use of Levenberg–Marquardt optimisation for ANN training, along with the provision of optimal weights, biases, and architecture diagnostics (training/validation/test splits), ensures reproducibility and depth not commonly reported in the existing literature^31,32. This comprehensive approach enhances the transparency and predictive reliability of ANN-based modelling in wastewater treatment systems.

This research lies in applying MRA and ANN models to a three-phase draft tube spouted bed bioreactor system, which inherently involves complex mass transfer and biokinetics. It is demonstrating quantitative improvements over conventional statistical modelling. Additionally, it provides a framework that can be extended to other pollutants and reactor types. Future directions include validating the ANN model at pilot or industrial scales, integrating it with sensor networks for real-time data acquisition, and expanding it to hybrid AI-mechanistic models to enhance interpretability and understanding. Additionally, life cycle assessment (LCA) and techno-economic analysis (TEA) will help evaluate the feasibility of large-scale implementation.

Materials and methodology

Experimentation

An isolate of Pseudomonas syringae, obtained from the wastewater treatment facility of a nearby fertiliser industry³³, was used throughout the study. The bacterial strain was sub-cultured every 15 days on nutrient agar slants and preserved at 4 °C for further use. The cell was immobilised using granular activated carbon (GAC) as the support medium. The experimental setup consists of a draft tube spouted bed reactor, including a cylindrical column with a conical copper base having a cone angle of 60°. The central body of the reactor was flanged at both ends, connected at the top to an outlet and at the bottom to the conical section. Two guiding supports were fixed at the top and bottom of the column to stabilize the internal draft tube. Air and synthetic feed solution were introduced at the base of the conical section. Stainless steel mesh screens (< 0.5 mm) were placed at both the inlet and outlet to prevent the escape of GAC particles.

A synthetic influent with nitrate concentrations of 100, 300, 500, 1000, and 1200 mg/L, maintaining a carbon-to-nitrogen ratio of 3:1, was supplied to the reactor via a peristaltic pump, as shown in Fig. 1. The reactor was loaded with varying amounts of GAC (0, 60, 80, 150, 200, and 250 g), each immobilised with P. syringae. Experimental trials were conducted at multiple dilution rates: 0.166, 0.330, 0.500, 0.107, 0.179, and 0.200/ h. The influence of dilution rate on biofilm thickness was investigated under steady-state conditions across different influent nitrate concentrations³⁴. Compressed air was passed through a filtration unit and introduced at a regulated rate to fluidize the GAC bed and ensure proper mixing. Wastewater samples were collected at defined intervals and then centrifuged at 10,000 rpm for 10 min. The supernatant was analyzed for nitrate and nitrite concentrations, while the residual biomass was quantified. The experiment was continued until steady-state conditions were achieved. Finally, the reactor contents were emptied, and the immobilised biomass, along with the biofilm thickness, was measured for each run. The entire setup of the spouted bed bioreactor is fabricated locally, with all accessories, including pumps, rotameters, filters, and compressors, procured locally.

Fig. 1.

Schematic diagram of experimental setup.

Model development

The objective of this study is to assess the predictive performance of a three-phase draft tube spouted bed bioreactor using two modelling approaches: Multiple Regression Analysis (MRA) and Artificial Neural Networks (ANN), to capture the complex dynamics of a bioreactor-based nitrate removal process. Significant independent variables were addressed when creating these models, including influent substrate concentration, dilution rate, solids loading, and one dependent variable, % denitrification. Biological wastewater treatment systems, such as bioreactors, often exhibit nonlinear, interactive, and multifaceted behaviour due to enzyme and microbial kinetics, physicochemical equilibrium effects (e.g., pH, concentration), and sorption-desorption dynamics³⁵. Traditional statistical tools, such as MRA, offer interpretability and ease of use, but they frequently fall short when interactions are nonlinear or highly complex. ANNs, on the other hand, offer greater flexibility in pattern recognition from data, but are frequently criticised for their black-box nature. This research is significant because it explicitly compares different methodologies in a real-world environmental engineering problem, therefore influencing future modelling decisions.

This comparative study validates the view that AI-driven tools, such as ANN, are not only options but also required in environmental process modelling, when system complexity defies conventional analytical assumptions. The insights gained here are not restricted to nitrate removal; they apply to any bioreactor-based or biosorption system where the process involves dynamic, nonlinear, and multivariate behaviour.

Feedforward ANN

A Feedforward Artificial Neural Network is one of the most basic types of artificial neural networks, characterised by connections between nodes that do not form cycles; i.e., data travels only in one direction, from input to output³⁷. The input data is routed through the network layer by layer. Each neuron in a layer receives input, multiplies it by weights, adds a bias, and uses an activation function. There is no feedback from output to input or within layers, resulting in the phrase feedforward. A predictive ANN consists of two or more layers of processing components coupled by weighted connections. The network operates in two distinct phases: training and recall. 22,23 During exercise, a collection of (training) data is regularly fed into the ANN, which processes each data vector according to its architecture, updates its weights, and, in some cases, modifies some processing element parameters following a training rule³⁸. It is easy to construct and train, and it is suitable for static input and output relationships; however, successful modelling requires large datasets.

Training

The training’s purpose is to adjust the network’s weights so that it can process the batch of training data to produce a specific outcome. Training a neural network involves an iterative process in which the network is fed with inputs along with the corresponding correct outputs for those inputs. It will try to alter its weights and produce the correct output. If this succeeds, the network, trained on a set of data, is now ready to make predictions on previously unseen data. Training with as many data points as possible is required to make the ANN more robust³¹. If it cannot create the desired output, it resets independently for the supplied input and attempts to do so again. After the output is produced, the network’s performance can be evaluated using the same weights on previously unidentified data.

This present work supplies the ANN model with input parameters such as influent nitrate concentration, which is a major driver of the denitrification process because it affects reaction kinetics, microbial uptake rates, and adsorption saturation rate; its inclusion in the model captures the rate of reaction and adsorption saturation; dilution rate (flowrate/reactor volume), which is a crucial parameter in biological reactors and is directly related to hydraulic retention time; granular activated carbon loading is included because it functions as an adsorbent and support media for microbes with bio reactive capacity, influencing surface area, biofilm formation, and pore diffusion. The primary outcome of the model was the percentage of denitrification. These inputs were then used to train both the ANN and MRA models, ensuring that the modelling phase was firmly grounded in process science rather than relying solely on data.

The study’s primary goal was to assess how well the two modelling techniques—ANN and MRA—performed when examining the intricate bioreactor used in the denitrification process. These biological wastewater systems, such as bioreactors, often exhibit nonlinear, interacting, and multifactorial behaviours due to factors including adsorption capacity, enzymes, microbial kinetics, and equilibrium investigations. When interactions are nonlinear or highly complex, traditional statistical approaches, such as MRA, frequently fall short despite their interpretability and simplicity of use. ANNs, on the other hand, are sometimes criticised for being black-box systems, although they provide greater flexibility in learning patterns from data³⁹. Because it directly compares different methods in a practical environmental engineering scenario, this work is important because it will help inform future modelling decisions.

A topology of 3:9:1 with a three-layer feed-forward neural network with backpropagation was employed. The input layer consisted of 3 neurons, the one hidden layer had 5 neurons, and the output layer consisted of one neuron. The input and hidden layers employed the “logsig” transfer function, whereas the hidden layer and output layer used the “purelin” function. The training algorithm used was the Levenberg–Marquardt (LM) method. The data was divided into a training set (70%), a validation set (15%), and a test set (15%). According to the universal approximation theory, a network with a single hidden layer and enough neurons may comprehend any input or output structure³². The ‘trainlm’ function was used for training. The ANN model was created using MATLAB (MathWorks, Natick, MA, USA).

Data handling

The 96 data points collected from the reactors were utilised in this modelling work. Among the data inputs, 70% of the total data points were utilised to train the network, and 15% were randomly chosen to validate and test the network. The input variables were initially prepared for the approach and scaled using the maxima technique, where each variable was mapped to a range of 0 to 1. The data was trained by varying the number of neurons in the hidden layer from three to nine to determine the optimal number of hidden neurons. After repeated data training, the correlation coefficients and mean square error were evaluated for each network. The network’s efficiency is evaluated by the mean square error method. Nitrate denitrification (%) was modelled using the feed-forward backpropagation ANN. A trial-and-error approach was employed to determine the optimal network structure, adjusting the number of hidden layers, the number of neurons per layer, and the activation functions. The trial models are presented in Table 1, and M2 was selected as the model with the highest R² value and the lowest MSE value. Three hundred forty epochs and nine neurons were trained often; the mean square error was 0.57, and the correlation coefficient was good. For the hidden layer, nine neurons were chosen as a result.

Table 1.

Trail models.

Model ID	Hidden layers	Neurons per layer	R 2	MSE	Remarks
M1	1	3	0.912	0.0081	Underfitting
M2	1	5	0.987	0.0023	Optimal
M3	2	4,3	0.981	0.0030	Slight overfitting
M4	1	7	0.984	0.0025	Good, but less stable
M5	2	5,5	0.979	0.0036	Overfitting observed

Results and discussion

Multiple regression analysis (MRA) model

The statistical technique optimised process variables, such as influent concentration, dilution rate, and GAC loading, in the reactor while removing nitrate from wastewater in the draft tube spouted bed reactor. The biodenitrification experiments were conducted using a draft tube spouted bed reactor, with influent nitrate concentrations, dilution rates, and GAC loading varied. A total of 96 data points, obtained from two reactors, were used in the modelling study. Initially, the independent variables were pre-processed for the method and scaled between 0 and 1 using the maxima technique. The following second-order empirical model, commonly used for three-factorial experiments, was employed. Y = β₀ + Σ βi Xi + Σ βii Xi² + Σ βijXiXj, where Y is the predicted response (steady state percentage denitrification), Xi is the independent variable (factor), β₀ is the intercept term, βi is the linear coefficient, βii is the quadratic coefficient, and βij is the interaction (cross product) coefficient. Three factors affecting the response are influent nitrate concentration (X1), dilution rate (X2) and GAC loading (X3). Expanding for three factors, equation gives Y = β₀ + β₁ × ₁ + β₂ × ₃ + β₃ × ₃ + β₁₁ × ₁ + β₁₁ × ₁² + β₂₂ X₂² + β33 × ₃² + β₁₂ × ₁ × ₂ + β₂₃ × ₂ × ₃₊ β₁₃ × ₁ × _3I. The ranges of the variables are scaled in the range of 0–1. Figure 2 presents the percentage denitrification values predicted by the MRA model and experimental data. As shown in the figure, the predicted values from the model closely match the experimental values. The sequence of experimental findings is represented by the X-axis, which spans from 10 to 90 points. The output variable being modelled is represented by the Y axis on a logarithmic scale of 0.70 to 1.00. Throughout the range, the model-predicted line closely resembles the experimental data. Both the experimental and forecasted data consistently exhibit slight oscillations, which may be attributed to measurement variability or system noise. Even though there is some variation between the experimental and anticipated values, the general trend is accurately depicted. This graphic confirms that the MRA model accurately depicts the experimental data. Because the LM algorithm successfully reduced the error, a strong link was established between the variables. Figure 3 compares experimental and model-predicted values of percentage denitrification. As shown in the figure, there was approximately a 10% deviation between the experimental and predicted values. These data points were used to fit the model through multiple regression analysis, which utilises the Levenberg-Marquardt (LM) algorithm to determine the parameter values using Polymath software.

Fig. 2.

Profile of comparison of MRA model and experimental output data.

Fig. 3.

Comparison of experimental and model-predicted values of percentage denitrification.

Factor plot

The individual effect of each parameter on the steady-state percentage denitrification was studied using the factor plot. This was investigated by varying one factor from zero to unity while keeping others at optimum conditions. The effect of influent nitrate concentration, dilution rate and GAC loading, as indicated by factors X1, X2 and X3, respectively, is presented in (Fig. 4). It is observed from the factor plot that, with an increase in nitrate concentration and dilution rate, there was a decrease in percentage denitrification. Conversely, with an increase in GAC loading, there was an increase in percentage denitrification.

Fig. 4.

Effect of the individual variable on percentage denitrification.

As shown in Fig. 4, the dilution rate and influent nitrate concentration had a significant impact on the percentage of nitrate removal. This was also reflected in the model as coefficients of X1 and X2. An increase in dilution rate above 0.333/h reduced the percentage of denitrification. The effect of GAC loading on percentage denitrification shows that with an increase in loading, the percentage denitrification increases slowly. The same observations were obtained through experiments. This graph helps identify which process variable(s) significantly reduce nitrate removal efficiency. X1 is critical and needs to be minimised, X2 shows a moderate effect and needs to be adjusted, and X3 is within the optimal range, contributing to effective nitrate reduction.

Artificial neural network (ANN) model

The predicted and investigated values of denitrification percentage are presented in Fig. 5, and it can be seen that the experimental values and predicted values from the ANN model match very closely. The ANN model’s excellent accuracy indicates that it has successfully mastered the intricate nonlinear relationship between denitrification efficiency and input parameters. The % denitrification decreases in both graphs from experiments 20 to 45 and again from 75 to 100, presumably as a result of altered operating circumstances. A small difference between the ANN and experimental results is acceptable, which is likely due to unmodeled or experimental noise⁴⁰. This plot graphically demonstrates that the ANN model provides a dependable, precise, and broadly applicable method for predicting the percentage of denitrification. It records performance extremes, variations, and trends under a range of experimental circumstances. The ANN model may generalize effectively for unknown data and does not require any prior assumptions about the data structure. This plot graphically demonstrates that the ANN model provides a dependable, precise, and broadly applicable method for predicting % denitrification. It records performance extremes, variations, and trends under a range of experimental circumstances. The regression coefficients for testing, training, validating, and overall data are presented in (Fig. 6). Each plot compares the actual (target) values of the denitrification percentage with the predicted outputs of the ANN model. The training data shows the fit of the ANN model, with a high R value of 0.99, indicating excellent learning from the dataset with minimal errors. The validation data with R = 0.98723 reflects how the model generalises to unseen data, and the slightly slower slope and intercept indicate a small deviation compared to the training data. The test data with R = 0.9895 represents the model’s predictive performance on completely new, unseen data. The complete set of data indicates that the model performs uniformly well across all datasets. The correlation coefficient was 0.987 for the overall data, indicating the suitability of the ANN model for the spouted bed reactor used in the present study. The model training and testing correlation coefficients were found to be 0.99387 and 0.9918, respectively. When the correlation coefficient is closer to one, the model fits well and gives better predictions⁴¹. Within the series of experimental conditions adopted, the ANN model developed in this study predicts the performance of the complex bioreactor system, such as a spouted bed with a draft tube. Hence, this model can be applied to such complex bioreactors. All things considered, the slopes and intercepts demonstrate little bias and excellent model calibration. The ANN does a fairly good job of capturing the link between inputs and outputs, as evidenced by the regression lines almost matching the Y = T line. The robustness of the model is confirmed by the lack of overfitting in the variation between training, validation, and testing⁴².

Fig. 5.

Profile of comparison of the ANN Model and experimental output data.

Fig. 6.

Profiles of regression analysis.

Comparison of ANN and regression model

The percentage denitrification gained in each experiment was related to those two models using the regression model and the ANN model. These were compared based on statistical parametric values, including the correlation coefficient, average absolute error (%), root mean square error (%), and residual sum of squares (RSS). The lower the calculated values of RMSE, AAE, and RSS, the improved the ability of the model to signify the percentage denitrification was observed⁴³. The comparison of the ANN with the regression model is presented in (Table 2), and it can be seen from Table 2 that the overall correlation coefficient for the ANN model is higher (0.988) than the MRA model (0.9) and MSE, RMSE and RSS values are significantly less as compared to MRA model. The results in Table 2 indicate that the ANN model predicts the denitrification efficiency of the draft tube-spouted bed reactor better than the MRA model.

Table 2.

Comparison between ANN and MRA.

Model	R 2	MSE	RMSE	RSS
MRA	0.934	0.0089	1.32	166.63
ANN	0.987	0.0023	0.57	30.84
Observations	ANN provides a closer fit to actual data and remains superior even with complexity	Lower MSE indicates better ANN accuracy	ANN offers higher precision	Indicates better generalization by ANN

ANN captured nonlinear patterns and consistently outperformed MRA across the sample. MRA assumes a fixed form of the connection (quadratic or linear), which overlooks saturation, declining returns, and threshold behaviours⁴⁴. ANN significantly outperformed MRA (R2 = 0.934, RMSE = 1.32) with an R2 of 0.987 and RMSE of 0.057. For all three parameters, when MRA consistently under- or over-estimated, ANN was able to capture the system’s thresholds and nonlinear saturations. Any bioreactor-based or biosorption system that incorporates dynamic, nonlinear, and multivariate behaviour (e.g., COD/BOD reduction, heavy metal biosorption, or nutrient recovery) can benefit from the knowledge gained here, and it is not limited to nitrate removal.

Although Artificial Neural Networks (ANNs) have been utilised in several studies to model bioreactor systems, the current work possesses several unique qualities that distinguish it and render it pertinent. This work incorporates experimental data obtained across a wide range of real-world process conditions, in contrast to many previous studies that rely on idealised or limited operational windows. Few studies thoroughly evaluate ANN and MRA using the same experimental dataset with systematic residual analysis, performance measures, and failure-case evaluations, despite the prior literature frequently asserting that ANN is superior to linear models⁴⁵. The evaluation of the model assesses its behaviour under different settings and physical plausibility, in addition to performance metrics such as R² and RMSE. The use of an ANN in a low-cost, biosorption-driven nitrate removal system is novel in this work. It is particularly pertinent to decentralised and rural treatment systems, especially in developing nations. Thus, this ANN model differs from many black-box techniques found in previous publications in that it not only offers predicted accuracy but also scientific interpretability and engineering value.

Conclusion

The artificial neural network (ANN)-based model developed for predicting nitrate degradation in a draft tube spouted bed reactor has demonstrated superior predictive accuracy compared to the second-order empirical regression model. The ANN model successfully predicted denitrification performance with a correlation coefficient (R²) of 0.988, an average absolute error of 9.25 × 10⁵%, a root mean square error of 0.57%, and a residual sum of squares (RSS) of 30.84. In contrast, the MRA model achieved an R² of 0.90, RMSE of 1.32%, and RSS of 166.63, indicating comparatively inferior performance. With a high correlation coefficient (98.8%), a low average absolute error (9.25 × 10^ (-5) %), a root mean square error of 0.57%, and a significantly lower residual sum of squares (30.84), the ANN model effectively captures the complex, nonlinear dynamics of nitrate degradation. In contrast, the regression model, while functional, exhibited comparatively lower performance metrics due to its sensitivity to variable ranges. In practical applications, the ANN model holds promise for integration into real-time monitoring and control systems for nitrate removal processes. Its fast computational capabilities and high predictive accuracy enable dynamic adjustments in operational parameters, potentially optimising reactor performance continuously. MRA provides transparency and interpretability, but it lacks the flexibility to represent the nonlinear and multiparametric dependencies of the denitrification system. The improved performance of ANN is due to its capacity to learn complex correlations directly from data, without requiring preexisting assumptions about variable interactions.

To support real-time control, the model can be embedded into programmable logic controllers (PLCs) or supervisory control and data acquisition (SCADA) systems, allowing for automated decision-making and response to fluctuating influent conditions. The following steps in scaling this model to full-scale operations involve model validation with larger, more diverse datasets, real-time testing under variable industrial conditions, and integration with sensor-based feedback systems. Additionally, a hybrid modelling approach combining ANN with mechanistic models could enhance interpretability while maintaining accuracy. With further refinement and validation, the ANN framework could become a core component of intelligent, energy-efficient water treatment systems.

Author contributions

Keshava Joshi and Lokeshwari Navalgund, Conceptualization, writing-original draft preparation, and validation. Nabisab Mujawar Mubarak, Vinayaka Babu Shet Writing—Reviewing and Editing.

Data availability

The datasets used and analyzed during the current study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.