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. 2026 Aug 16;98(8):e70527. doi: 10.1002/wer.70527

Prediction, Optimization, and Uncertainty Quantification of Methylene Blue Removal by Biochar Adsorbents Using Ensemble Machine Learning

Gokulan Ravindiran 1,2,✉, Gorti Janardhan 3, Marlinda Abdul Malek 4, Mary Subaja Christo 5,✉, Deepshikha Datta 6, Ali E I Elkhalifah 7,8, Gasim Hayder 9,10
PMCID: PMC13477997  PMID: 42604839

ABSTRACT

This study developed an integrated and uncertainty‐aware machine learning framework to predict and optimize methylene blue (MB) removal efficiency using biochar adsorbents. A dataset comprising 504 literature‐derived adsorption experiments was compiled using five operational parameters, namely, initial dye concentration, contact time, initial pH, adsorbent dosage, and temperature. Four advanced ensemble learning models, namely, XGBoost, CatBoost, LightGBM, and stacking ensemble, were developed and evaluated. The stacked ensemble model achieved the highest predictive performance with R 2 = 0.7740, RMSE = 7.95, and MAPE = 7.04%, demonstrating the ability to capture complex nonlinear adsorption processes. Explainable artificial intelligence (XAI) analysis using SHAP identified temperature, contact time, and adsorbent dosage as the most influential variables governing MB removal. Sensitivity analysis further confirmed the significant influence of contact time, temperature, and adsorbent dosage on prediction variability. Two Bayesian optimization strategies were investigated, mathematical optimization, performed over the complete range of the literature‐derived dataset, and engineering‐constrained optimization, performed within practically feasible operating ranges reported in previous adsorption studies, and both cases reported a maximum predicted removal efficiency of 99.99% with varying input variables. Monte Carlo uncertainty analysis indicated a mean predicted efficiency of 75.05% with a 95% confidence interval of 71.85%–79.54%. Residual diagnostics and Bland–Altman analysis demonstrated satisfactory agreement between predicted and observed values within the investigated dataset. Overall, the proposed framework integrates prediction, explainability, uncertainty quantification, and optimization into a unified workflow, providing a promising decision‐support tool for biochar‐based wastewater treatment.

Keywords: Bayesian optimization, biochar, clean water and sanitation, ensemble machine learning, explainable artificial intelligence (XAI), methylene blue adsorption

Summary

  • A stacked ensemble model predicted methylene blue removal efficiency using five key adsorption operating parameters.

  • Temperature, contact time, and adsorbent dosage were the most influential factors controlling adsorption performance.

  • Bayesian optimization identified operating conditions achieving a predicted removal efficiency of 99.99%.

  • Monte Carlo analysis confirmed high model reliability with narrow uncertainty bounds and stable predictions.

  • The framework supports rapid optimization and decision‐making for sustainable biochar‐based wastewater treatment systems.

An integrated machine learning framework combining prediction, explainable AI, Bayesian optimization, and uncertainty quantification modelled methylene blue removal by biochar adsorbents. A stacked ensemble model achieved the best performance, whereas SHAP analysis, sensitivity assessment, and Monte Carlo simulations provided interpretable and reliable decision support for wastewater treatment.

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1. Introduction

Rapid industrialization and urbanization have led to a large quantity of dye‐contaminated wastewater entering aquatic environments worldwide. This has severe impacts on both ecological and human health (Saravanakumar et al. 2022). Several industries, including textile, leather, plastic, cosmetic, pharmaceutical, and paper manufacturers, use synthetic dyes and generate huge quantities of effluents. Methylene blue (MB) is one of the most widely used synthetic dyes across several industrial sectors, due to its high chemical stability, color intensity, and resistance to biodegradation (Oladoye et al. 2022). MB in water bodies reduces light permeability, inhibits photosynthesis, disrupts aquatic ecosystems, and degrades water quality. Exposure to excessive levels of MB can cause adverse health effects, including eye irritation, skin disorders, respiratory issues, nausea, and hemoglobinemia (Liang et al. 2024). Therefore, there is a significant need for efficient MB removal from wastewater to mitigate adverse environmental impacts and ensure safe drinking water.

Conventional treatment technologies, such as coagulation, membrane filtration, electrochemical oxidation, photolysis, biological treatment, and advanced oxidation processes (AOPs), have been examined for dye removal. Many of the treatment options have several disadvantages, such as high operational costs, sludge generation, membrane fouling, energy consumption, and a limited degree of complete pollutant degradation (Abhisek et al. 2025). Adsorption has proven to be one of the most effective treatment technologies for dye removal because it is relatively inexpensive and simple to implement compared to other treatments. In addition, adsorption allows pollutants to be removed from solutions at very low concentrations (Gupta and Suhas 2009). Recent advances in biochar‐based adsorbents have gained growing interest due to their potential as a sustainable alternative to commercial activated carbon. The advantages of using biochars include lower cost than commercial activated carbon, a renewable source, porous structure, higher specific surface area, and a larger number of surface functional groups (Afshar and Mofatteh 2024; Guo et al. 2022). Biochar can be derived from a variety of organic wastes, including agricultural residues, forestry waste, food waste, sewage sludge, and other types of biomass, which are thermally converted in the presence of limited oxygen or in an oxygen‐free environment. These advantages provide an opportunity to develop novel products that support waste valorization and circular economy principles (Afshar and Mofatteh 2024).

The adsorption performance exhibited by biochar‐based adsorbents indicates that biochar materials can be developed into useful tools for wastewater treatment. However, optimizing adsorption systems continues to be a major challenge because the removal efficiency of dye contaminants can vary depending on several interconnected operational parameters, such as initial dye concentration, contact time, solution pH, amount of adsorbent, and temperature (Laishram et al. 2025). The adsorption behavior typically demonstrates nonlinear characteristics due to the simultaneous occurrence of physical adsorption, electrostatic attraction, pore diffusion, ion exchange, and surface complexation under different experimental conditions (Sen et al. 2026). Traditional experimental optimization procedures involve performing a large number of experiments with different parameter combinations, which is time‐consuming. Moreover, variability in adsorption data can create difficulties when developing generalized predictive equations and limit the suitability of traditional statistical modelling techniques.

Intelligent approaches have been widely used for modelling scientific problems with nonlinear relationships between variables (Baghban, Sasanipour, and Goodarzi 2017). Machine learning (ML) is a data‐driven computational approach that learns complex relationships from data through algorithms and makes predictions or decisions based on these patterns. ML has emerged as a viable computational approach for modelling complex environmental systems. ML differs from traditional regression‐type analytical techniques because ML can learn nonlinear relationships and multidimensional interactions from experimental datasets without making any explicit mechanistic assumptions (Park et al. 2024).

ML techniques used for adsorption modelling can generally be classified into four categories. Classical regression‐based models (linear and polynomial regression) represent simple mathematical representations of a process; however, many of these classical models do not adequately describe the complex nonlinear interaction mechanisms governing adsorption phenomena. Shallow ML algorithms, such as support vector machines (SVM), decision trees (DT), and random forests (RF), offer improved predictive capability and have been successfully applied to various environmental systems. Advanced computational intelligence methodologies such as adaptive neuro‐fuzzy inference systems (ANFIS) and least squares support vector machines (LSSVM) have shown excellent modelling performance when simulating complex physicochemical processes based on their ability to identify and simulate nonlinear relationships between input variables and output responses. In recent years, there has been increasing interest in applying ensemble learning methods, as these approaches use iterative predictions and errors to enhance both model robustness and accuracy by managing heterogeneity within the dataset. Previous studies have successfully employed ML in different environmental systems, namely, hydrogen yield prediction from wastewater (Liu, Li, et al. 2025), phosphate removal from wastewater (Liu et al. 2026), dye removal from wastewater (Liu et al. 2024), degradation of tetracycline (TC) through photocatalysis (Salahshoori et al. 2024), gas adsorption on activated carbon (Dashti et al. 2018) estimating viscosity of ionic liquids (Baghban, Kardani, and Habibzadeh 2017) and ammonia nitrogen adsorption capacity of biochar (Liu, Balasubramanian, et al. 2025). Numerous researchers have utilized ML algorithms, including artificial neural networks (ANN), SVM, DT, RF, adaptive boosting (AB), and gradient boosting (GB), to predict adsorption capacities and contaminant removal efficiencies. In the present study, boosting‐based algorithms, namely, XGBoost, CatBoost, and LightGBM, were selected because they are effective at capturing the heterogeneity in the compilation of literature‐derived data from different biochar feedstocks, experimental conditions, and protocols. Boosting algorithms have a unique ability to successively reduce prediction residuals by identifying complex nonlinear relationships between variables. Additionally, they incorporate regularization into the model building process, which helps reduce overfitting. These characteristics make boosting algorithms well suited for developing an accurate and interpretable predictive framework for MB adsorption.

1.1. Proposed Methodology

An innovative approach for integrating both explainability and uncertainty estimation in a predictive model has also been created using literature‐based data to predict the removal efficiency of MB using different biochars. The proposed framework is illustrated in Figure 1. A dataset consisting of operational parameters, namely, initial concentration, contact time, pH, amount of adsorbent, and temperature, was compiled and cleaned. Outliers were identified, the data were standardized, and the dataset was statistically analyzed using histograms, boxplots, violin plots, and heatmaps to determine the properties of the data and nonlinearities. Subsequently, three ML models based on boosting techniques (XGBoost, CatBoost, and LightGBM) were used sequentially with a stacked generalization model to improve the prediction accuracy. The dataset was split into an 80/20 ratio for training and test sets. RandomizedSearchCV with fivefold cross‐validation was applied to avoid overfitting and improve the accuracy of predictions. Because boosting algorithms can successfully model nonlinear interactions in heterogeneous datasets, a stacking ensemble model using Ridge regression as the meta‐learner was developed by integrating the previously optimized base models. Prediction performance of the developed models was evaluated using statistical parameters, namely, coefficient of determination (R 2), root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), Nash–Sutcliffe efficiency (NSE), residual prediction deviation (RPD), Willmott's index of agreement (d), and mean bias error (MBE). In addition to statistical performance metrics, residual analysis and Bland–Altman plots were employed to assess the consistency of the predictions. To assess the interpretability of the model, SHapley Additive exPlanations (SHAP) was used to determine the contribution of each operational variable to feature importance, dependency, and interaction contributions. OAT and Tornado sensitivity analysis were performed to evaluate the impact of the input parameters on the removal efficiency. Finally, Bayesian optimization was employed to determine optimal operating conditions, whereas Monte Carlo simulation was conducted to assess uncertainty associated with predictions derived from the developed ML framework. Finally, a Gradio‐based graphical user interface (GUI) was developed to allow users to utilize the model for real‐time predictions.

FIGURE 1.

FIGURE 1

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Schematic flowchart of the proposed framework for the prediction of the removal efficiency of methylene blue using biochar. This figure was generated with AI assistance (ChatGPT, OpenAI, and GPT‐5.5) and subsequently reviewed and finalized by the authors.

2. Materials and Methods

2.1. Dataset Development

An adsorption dataset based on a literature review was created to develop an ML approach to predict the removal efficiency of MB. Peer‐reviewed articles reporting on MB adsorption using various operating parameters were identified, and experimental data were extracted (Aigbe et al. 2025; Altamer et al. 2026; Asif et al. 2026; Bahsaine et al. 2024; Deepa et al. 2025; El‐Shafie et al. 2024; Igberase and Mkhize 2025; Khan et al. 2025; Mishra et al. 2025; Nagarajan, Binti Mohd Fekeri, et al. 2024; Nagarajan, Vilosamy, et al. 2024; Prabakaran and Pillay 2025; Ravindiran et al. 2026; Roy, Islam, et al. 2022; Roy, Prantika, et al. 2022; Sharma et al. 2025). A total of 504 experimental datasets were extracted, which consist of five input variables, namely, the initial concentration of MB (mg/L), the contact time (min), the initial pH of the solution, the amount of adsorbent (g/L), and the temperature of the system (°C). The removal efficiency (%) of MB was defined as the target output variable.

2.2. Applicability Domain of the Developed Model

The developed ML models are applicable only within the range of experimental conditions represented in the literature‐derived dataset used for model development. The input variables considered include initial MB concentration (1–390 mg/L), contact time (2–360 min), initial pH (0.7–14), adsorbent dosage (0.006–10 g/L), and temperature (20°C–80°C). Since the models were trained exclusively using observations within these ranges, any predictions made outside of these defined operating conditions will represent an extrapolation. As a result, it cannot be expected that the reliability of the results will be acceptable when applying the proposed framework at or beyond the defined operating conditions until training data is developed across a broader set of operational parameters.

2.3. Exploratory Data Analysis (EDA)

EDA was conducted to better understand the statistical characteristics, distribution behaviors, and associations among the adsorption features before developing an ML model (Da Poian et al. 2023). Descriptive statistics, including the mean, standard deviation, minimum, and maximum, were computed, and histograms and violin plots were used to study the distribution of each variable. This will identify the outliers within each set of data through boxplots. A heatmap was used to study both the magnitude and the directionality of potential linear relationships between adsorption variables and their corresponding removal efficiency. Conducting an EDA will provide valuable insights regarding the differences in variability among the datasets as well as how nonlinearly the adsorption properties relate to one another. This will support the successful application and explanation of the developed models.

3. Results and Discussion

3.1. Dataset Characteristics

Descriptive statistics (Table 1) illustrated significant variations in all variables in the dataset. The initial concentrations of dye varied from 1 to 390 mg/L, with an average of 85.95 mg/L, demonstrating a wide range of operations. Contact times ranged from 2 to 360 min, with a median of 100 min, and showed significant variability with respect to the time required to reach adsorption equilibrium. The majority of pH values were in the range of approximately 6–9; however, the adsorbent dosage was strongly skewed toward the right due to low‐dose conditions. Temperatures were generally in proximity to room temperature (25°C–35°C), whereas the majority of removal efficiencies had high levels of adsorption performance, with a median of 88.38%.

TABLE 1.

Descriptive statistics of adsorption process variables and removal efficiency dataset.

Description Initial concentration (mg/L) Contact time (min) Initial pH Adsorbent dosage (g/L) Temperature (C) Removal efficiency (%)
Count 504 504 504 504 504 504
Mean 85.95 117.34 7.27 1.03 32.44 81.11
Std 84.85 90.38 2.58 1.911 10.82 20.82
Min 1 2 0.7 0.006 20 1.64
25% 15 50 6 0.12 25 71.97
50% 50 100 7 0.2 30 88.37
75% 150 180 9 1 35 97.96
Max 390 360 14 10 80 99.99
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The boxplots in Figure 2 show several outlier values at the extreme ends of the operational range. These outliers are primarily observed as a function of concentration, dosage, and temperature. The histograms (Figure S1) reveal both non‐normality and skewness in the distribution of many of the measured variables; in particular, the initial concentration and adsorbent dose exhibited these behaviors. As shown in the violin plot (Figure S2), density clusters of data exist within certain ranges of operation, indicating a complex, multimodal nature of the adsorption behavior.

FIGURE 2.

FIGURE 2

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Boxplot representation of adsorption process variables and methylene blue removal efficiency.

3.2. Correlation and Data Relationships

Correlation analysis was performed to determine the linear relationship among the adsorption process variables and removal efficiency. A Pearson correlation heatmap (Figure 3) indicated that the input variables were mostly weakly correlated with the removal efficiency. These results indicate an extremely high degree of complexity in the adsorption process, as well as a significant nonlinear relationship. Temperature exhibited the strongest correlation with removal efficiency; however, this association was moderately negative (−0.28). Thus, these results indicate that slight temperature increases will have a small negative effect on adsorption efficiency due to a reduction in the adsorbate–adsorbent interaction. A moderate positive correlation (0.16) existed between removal efficiency and pH. This indicates that MB adsorption is mildly affected by pH levels above neutral. As expected from previous studies, initial concentrations also demonstrated a mild positive correlation (0.14) with removal efficiency. Contact time also displayed a similar trend with removal efficiency, demonstrating a mild positive correlation (0.10). The adsorbent dose demonstrated an almost negligible positive correlation (0.05) with removal efficiency. While it is well established that the adsorbent dose has a significant impact on the overall adsorption capacity of a given adsorbent, the lack of a stronger positive correlation demonstrates that the adsorption system exhibits a higher degree of nonlinearity.

FIGURE 3.

FIGURE 3

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Pearson correlation heatmap illustrating linear relationships among adsorption process variables and methylene blue removal efficiency.

3.3. Effect of Input Variables on Removal Efficiency

The results of the parametric trend analysis (Figure 4) indicate that MB adsorption was nonlinear for each studied parameter. The data confirm the complex nature of the dynamic process involved in MB adsorption. The initial concentration of MB had an inverse relationship with removal efficiency; however, this relationship is fluctuating. There is evidence of saturation occurring for the majority of the active adsorption sites when the concentration increases to 50 mg/L, resulting in an approximate decrease from 79% to 70%. In contrast, there is evidence of higher concentrations (100–250 mg/L) than those used at lower concentrations, producing efficiencies greater than 90%, which may be related to improved concentration‐driven mass transport and interactions between adsorbates (Islam et al. 2026). When using very high concentrations, it appears that the efficiency decreases, which would likely be indicative of adsorbent saturation. The contact time had a significant effect on the adsorption performance. The removal efficiency increased rapidly during the first phase of adsorption, reaching a peak value of approximately 92% after 160 min. This indicates rapid occupancy of the available adsorption sites. After achieving equilibrium conditions, prolonging the contact time caused the removal efficiency to slowly decline, which could be associated with adsorbate desorption and decreasing concentration gradients (Gkika et al. 2025).

FIGURE 4.

FIGURE 4

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Parametric trend analysis showing the variation of average methylene blue removal efficiency with operational adsorption parameters.

The pH of the solution at the beginning of adsorption is one of the most important factors affecting adsorption. As shown in Figure 4, the removal efficiency increases rapidly with pH from acidic to alkaline conditions and reaches its maximum near pH 11. The increase in removal efficiency with increasing pH can be attributed to electrostatic attractions between the negatively charged sites on the adsorbent surface and the positively charged MB molecule under alkaline conditions. A slight decrease in the removal efficiency at excessively high pH can be due to competitive adsorption by OH− ions (Adane 2026).

Adsorbent dosage demonstrated an overall positive relationship with removal efficiency. An increase in the dosage enhanced the adsorption performance due to the availability of additional surface area and active adsorption sites. The maximum removal efficiency was observed at a dosage range of 5–6 g/L. The efficiency gradually decreased with further increases in the dosage. This phenomenon can be attributed to the agglomeration of particles, which reduces the effective use of the surface area (Aljohni et al. 2026). Temperature analysis clearly demonstrates that temperature affects MB adsorption. Adsorption efficiencies were slightly higher in the intermediate ranges, whereas at elevated temperature, the adsorption was slightly reduced. These findings suggest reduced adsorbate–adsorbent interactions and thermodynamic instability at elevated temperatures.

3.4. ML Models Performance

Hyperparameter optimization for the respective ML models was performed using Randomized Search Cross‐Validation (RandomizedSearchCV), with five fold cross‐validation. Moderate search ranges were defined for the learning rate, tree depth, number of estimators, the subsampling ratio, column sampling ratio, and regularization parameters to maintain a suitable balance between predictive performance, computational efficiency, and model complexity to minimize the risk of overfitting. Table 2 summarizes the optimized hyperparameters of the different models. Ridge regression was used as a meta‐learner for the stacking ensemble model to provide an aggregation of the predictions produced from the optimized XGBoost, CatBoost, and LightGBM Models. Ridge regression was selected because it provides L2 regularization, which can handle multicollinearity among the predictions of the base models (reducing overfitting), also providing a stable weighted combination of individual learners. Consequently, the stacking ensemble model exploits the complementary strengths of the three boosting algorithms while improving the robustness and overall predictive performance of the final model.

TABLE 2.

Optimized hyperparameters of the tuned machine learning models used for predicting methylene blue removal efficiency.

Parameters XGBoost (tuned) CatBoost (tuned) LightGBM (tuned) Stacking ensemble (tuned)
Learning rate 0.157 0.1544 0.1793

XGBoost: 0.1570

CatBoost: 0.1544

LightGBM: 0.1793
Max depth 4 5 6

XGB: 4

Cat: 5

LGBM: 6
No. of trees/iterations 200 199 201

XGB: 200

Cat: 199

LGBM: 201
Subsample 0.8166 — 0.8568

XGB: 0.8166

LGBM: 0.8568
Column sample 0.8703 — 0.8801

XGB: 0.8703

LGBM: 0.8801
Num. of leaves — — 52 52 (LightGBM)
L2 regularization — 1.5641 — 1.5641 (CatBoost)
Meta‐learner — — — Ridge Regression
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The predictive capacity of the optimized ML models was analyzed based on model performance metrics as summarized in Table 3 and illustrated in Figure 5. These metrics included R 2, RMSE, MAE, MAPE, NSE, RPD, Willmott's_d, and MBE. The stacking ensemble model performed better than all other models, as indicated by its high R 2 value of 0.7740 with RMSE (7.95), MAE (5.38), MAPE (7.04%), and NSE (0.7740). From these results, the superior performance of the stacking ensemble model was due to the synergistic effects associated with each of the three base learners that were utilized in the model. Ridge regression meta‐learner effectively integrated their predictions and reduced individual model errors.

TABLE 3.

Comparative performance evaluation of tuned machine learning models for the prediction of methylene blue removal efficiency.

Model R 2 RMSE MAE MAPE NSE RPD Willmott_d Bias_MBE
XGBoost 0.7410 8.51 5.54 7.09 0.7410 1.96 0.7882 −1.89
CatBoost 0.7691 8.03 5.49 7.33 0.7691 2.08 0.7817 −1.83
LightGBM 0.7149 8.93 6.58 9.07 0.7149 1.87 0.7438 −1.91
Stacking ensemble 0.7740 7.95 5.38 7.04 0.7740 2.10 0.7869 −2.16
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FIGURE 5.

FIGURE 5

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Comparative R 2 and RMSE analysis of tuned machine learning models for methylene blue removal efficiency prediction.

Among the individual models, CatBoost exhibited the highest predictive capability, with an R 2 of 0.7691, RMSE of 8.03, MAE of 5.49, MAPE of 7.33%, and RPD of 2.08, indicating its effectiveness in modelling the nonlinear adsorption behavior. The XGBoost model showed a correlation coefficient (R 2) of 0.7410 with an RMSE of 8.51. XGBoost demonstrated good predictive power even though the model's predictions were slightly less accurate than the stacking ensemble and CatBoost. The sequential GB mechanism and built‐in regularization enabled XGBoost to effectively capture nonlinear interactions among adsorption variables while maintaining stable model performance. In contrast, LightGBM demonstrated relatively poor predictive ability compared to other models, with an R 2 of 0.7149 and an RMSE of 8.93. The lower performance may be attributed to its leaf‐wise tree growth strategy, which is more sensitive to relatively small and heterogeneous datasets.

The comparison also shows that each model tested performed well, with an NSE > 0.70 and RPD > 2.00 indicating the developed models are capable of predicting the literature‐observed data satisfactorily. Additionally, the low MAE and MAPE suggest that the models adequately predicted the MB removals. A negative MBE was found for all three models tested, and this is indicative of slight under prediction. However, since the MBE value was consistently close to zero, no significant systematic bias was observed. The Actual vs. Predicted plots (Figure 6) were used to evaluate the performance of the ML models in predicting the MB removal. The residual plots (Figure 7) show the difference between the values predicted by the model and those that actually occurred in the experiments.

FIGURE 6.

FIGURE 6

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Actual versus predicted methylene blue removal efficiency plots for tuned XGBoost, CatBoost, LightGBM, and stacking ensemble models.

FIGURE 7.

FIGURE 7

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Residual versus predicted removal efficiency plots for tuned XGBoost, CatBoost, LightGBM, and stacked ensemble models.

Overall, the results demonstrate that boosting‐based ML algorithms are capable of modelling the complex nonlinear relationships between adsorption operating variables and MB removal efficiency. Although the stacking ensemble model achieved the highest overall prediction accuracy by integrating the complementary strengths of the individual learners, the performance differences among the leading models were relatively small. These findings suggest that ensemble boosting techniques provide an effective data‐driven framework for predicting adsorption performance within the investigated literature‐derived dataset.

3.5. Explainable AI Interpretation

To further interpret the best‐performing stacking ensemble model, a SHAP analysis was performed to determine both the overall feature importance and the contribution of individual operational variables to the MB removal efficiency. The results of this analysis are illustrated in Figure 8. Temperature had the highest mean absolute SHAP value, which indicated that, according to the developed model, temperature exhibited the highest contribution to prediction, followed by contact time, adsorbent dosage, initial pH, and initial concentration. These rankings indicate that thermal conditions dominate the model predictions, whereas adsorption kinetics, availability of adsorbents, and chemistry of the solution also significantly affect the adsorption process.

FIGURE 8.

FIGURE 8

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SHAP summary plot and feature importance ranking of the optimized stacking ensemble model for methylene blue removal efficiency prediction.

The SHAP dependence plots (Figure 9) reveal nonlinear relationships between the operational variables and the predicted removal efficiency. Temperature exhibited predominantly negative SHAP values at intermediate to high temperatures, indicating that increasing temperature generally reduced adsorption performance. This behavior is consistent with the predominantly exothermic nature of MB adsorption on biochar, where elevated temperatures decrease the affinity between dye molecules and the adsorbent surface. Contact time showed positive SHAP contributions up to approximately 100–200 min, after which the contribution gradually decreased, suggesting that adsorption equilibrium was progressively attained and additional contact time produced only marginal improvements. Adsorbent dosage exhibited an overall positive contribution, confirming that increasing the dosage provides more active adsorption sites and greater surface area for dye uptake, thereby enhancing removal efficiency. Initial pH also showed a positive influence under neutral to alkaline conditions, reflecting the development of a more negatively charged biochar surface that promotes stronger electrostatic attraction with the positively charged MB molecules. Conversely, increasing the initial dye concentration generally produced smaller or negative SHAP contributions, indicating progressive saturation of the available adsorption sites.

FIGURE 9.

FIGURE 9

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SHAP dependence plots showing the individual effects of operational parameters on methylene blue removal efficiency predicted by the optimized stacking ensemble model.

The SHAP interaction plots (Figure 10) confirm that adsorption of MB was controlled through nonlinear coupling of the factors instead of separate contributions from each variable. There were significant interactions between temperature, contact time, and adsorbent dosage, as well as initial pH levels. This implies that favorable adsorption performance can be achieved when all of the operating parameters are optimized simultaneously.

FIGURE 10.

FIGURE 10

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SHAP interaction dependence plots illustrating pairwise interactions among the major operational parameters in the optimized stacking ensemble model.

Similarly, there were also significant interactions among contact time, adsorbent dosage, and pH, which suggest that kinetic aspects of adsorption, available sites for adsorption and electrostatic interactions contribute to the total adsorption efficiency. Overall, the SHAP analysis demonstrates that the optimized stacking ensemble successfully captures the nonlinear behavior associated with the adsorption of MB. These findings substantially enhance the transparency and interpretability of the developed ML framework and support its application as a practical decision‐support tool for optimizing biochar‐based adsorption systems.

3.6. Sensitivity Analysis

One‐at‐a‐time (OAT) sensitivity analysis was conducted to evaluate the influence of individual operating variables on the predicted MB removal efficiency while maintaining the remaining variables at their mean values. Unlike the trend analysis, which represents the average behavior observed in the literature‐derived dataset, the OAT analysis evaluates the local response of the trained stacked ensemble model to changes in a single parameter. Therefore, the sensitivity plots identify regions where the model predictions are most responsive rather than globally optimal operating conditions. The results (Figure 11) clearly show nonlinear effects of all the variables influencing the biochar adsorption process. These results confirm the complexity of the adsorption process. As shown in Figure 11, the pH sensitivity curve exhibits substantial variability and demonstrates a high sensitivity with respect to pH changes in the range of acidic to neutral values. However, an increase in pH does not necessarily correspond to an optimal value, since a trend analysis and engineering‐constrained Bayesian optimization indicated that typically higher removal efficiencies are obtained at pH levels in the alkaline region where there is increased electrostatic interaction between negative charge on the surface of the biochar particles and positively charged MB cations.

FIGURE 11.

FIGURE 11

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One‐at‐a‐time (OAT) sensitivity analysis illustrating the variation in predicted methylene blue removal efficiency with changes in operational adsorption parameters.

The adsorbent dosage plot (Figure 11) demonstrates a positive relationship with removal efficiency, and it is increasing rapidly as adsorbent dose increases due to increasing availability of adsorption sites. The initial concentration plot (Figure 11) indicates a gradual decline in predicted removal efficiency as dye concentration increases, suggesting progressive saturation of available adsorption sites. In contrast to other variables, contact time initially improves removal efficiency before reaching a relatively stable region, indicating rapid adsorption during the early stages followed by equilibrium‐controlled behavior. Finally, the temperature plot (Figure 11) shows an overall decrease in predicted removal efficiency with increasing temperature, which suggests that lower temperatures favor MB adsorption and highlights the strong influence of temperature on model predictions. Overall, the OAT sensitivity analysis confirms that all operating parameters influence MB removal in a nonlinear manner. These findings complement the SHAP analysis by illustrating the local sensitivity of the predictive model, providing additional insight into the response of the adsorption system under varying operating conditions while supporting practical process optimization.

The tornado sensitivity analysis (Figure 12) indicates that the developed stacking ensemble exhibits varying sensitivity to the investigated operational parameters. Contact time produced the largest deviation from the baseline prediction, identifying it as the most influential variable under the selected operating conditions, followed by temperature and adsorbent dosage. Initial dye concentration showed moderate sensitivity, whereas initial pH exhibited the smallest local influence.

FIGURE 12.

FIGURE 12

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Tornado sensitivity plot showing the relative impact of operational parameter variation on predicted methylene blue removal efficiency.

The use of SHAP interpretation and tornado‐based sensitivity analysis can be used to clearly identify the difference in different input variables in model predictions. The SHAP method describes the significant impact of each input variable on the model's output across the entire dataset. This is achieved through nonlinear interactions between input variables. The SHAP method identified temperature, contact time, and adsorbent dosage as the three most significant inputs that have a greater impact on the model's prediction. It should be noted that the tornado analysis evaluates the local effect of varying one parameter around a fixed baseline, whereas SHAP analysis quantifies the overall global importance across the entire dataset. Consequently, the results are complementary rather than contradictory, providing a comprehensive understanding of the factors governing MB adsorption.

3.7. Bayesian Optimization

Bayesian optimization was performed to find optimal operational parameters for the best MB removal using the best‐performing stacking ensemble model. Two scenarios were investigated: (i) mathematical optimization and (ii) engineering‐constrained optimization, where practical working ranges were used to determine the maximum removal efficiency at different operating ranges. The mathematical optimization reached the global optimum after 50 iterations, achieving a maximum predicted removal efficiency of 99.99%. The corresponding optimal operating conditions were reported as an initial MB concentration of 168.84 mg/L, contact time of 182.36 min, initial pH of 3.32, adsorbent dosage of 5.73 g/L, and temperature of 23.68°C. These ranges were obtained for the multidimensional search space defined by the compiled dataset. Although mathematical optimization provides the globally optimal solution, some operating conditions may not always represent practical wastewater treatment scenarios. Therefore, a second optimization was performed by restricting the search space to engineering‐relevant operating ranges derived from the adsorption literature. Under these constrained conditions, Bayesian optimization reported the same maximum predicted removal efficiency of 99.99% after 50 iterations. The corresponding operating conditions were an initial MB concentration of 300 mg/L, contact time of 236.41 min, initial pH of 7.93, adsorbent dosage of 4.59 g/L, and a temperature of 24.99°C. It was observed that the operating conditions of the engineering‐constrained optimum are more practically feasible than the mathematical optimization, since the engineering optimization is practically feasible in real‐time wastewater treatment.

In particular, the near‐neutral pH and moderate adsorbent dosage are more suitable for large‐scale wastewater treatment, where chemical adjustment and excessive adsorbent consumption should be minimized. Furthermore, the longer contact time is consistent with the equilibrium‐controlled nature of MB adsorption onto porous biochar materials. The convergence behavior shown in Figure 13 demonstrates that Bayesian optimization efficiently identified stable optimal solutions under both unconstrained and constrained search conditions, highlighting the capability of the proposed framework to support both theoretical optimization and practical process design. This dual optimization framework enhances the practical significance of the proposed ML approach and addresses the limitations associated with relying solely on unconstrained mathematical optimization.

FIGURE 13.

FIGURE 13

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Bayesian optimization convergence plot showing progressive improvement in predicted methylene blue removal efficiency during iterative optimization of adsorption operating parameters.

3.8. Monte Carlo Uncertainty Analysis

A Monte Carlo uncertainty analysis was conducted to assess the probabilistic reliability and sensitivity of the ML framework for predicting adsorption as a function of different adsorption process variables. A total of 5000 Monte Carlo simulations were performed, wherein each simulation included randomly selected values for all input parameters used to describe the adsorption system. The output from these simulations resulted in a prediction distribution with relatively low uncertainty bounds, hence, it can be concluded that the developed framework provided consistent and predictable modelling performance. The average removal efficiency value obtained from the Monte Carlo analysis was approximately 75.10%. Additionally, the lower and upper bounds of the 95% confidence interval around this average removal efficiency were 71.85% and 79.54%, respectively (Figure 14). The histogram distribution further demonstrated that most predicted efficiencies were concentrated in a narrow region between approximately 72% and 80%. This indicated low prediction dispersion and a significant amount of confidence in the predictions made by the ensemble learning framework.

FIGURE 14.

FIGURE 14

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Histogram distribution of predicted methylene blue removal efficiency obtained from Monte Carlo uncertainty simulation, showing prediction spread and confidence interval boundaries.

Additionally, the probability density plot (Figure 15) was smooth without excessive tail expansion, which confirmed limited prediction volatility and acceptable uncertainty propagation. The results represent additional support for the proposed ensemble‐based approach in modelling adsorption. Furthermore, the results from the uncertainty analysis demonstrated the capability of the developed model to make probabilistic confidence estimations rather than only single deterministic predictions. Overall, a successful validation of the predictive reliability, uncertainty resilience, and statistical stability of the developed adsorption model has been demonstrated using the Monte Carlo framework.

FIGURE 15.

FIGURE 15

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Probability density distribution of predicted methylene blue removal efficiency generated through Monte Carlo simulation, illustrating probabilistic prediction behavior and uncertainty propagation.

3.9. Statistical Validation: Bland–Altman Plot

The Bland–Altman method is used to measure reliability, or how closely measured results match each other. The Bland–Altman method can be especially helpful in validating a model's performance over and above what would be obtained from evaluating a model using simple regression‐based methods such as R 2. In addition to assessing the overall reliability of predictions, the Bland–Altman method also allows for the assessment of both the systematic bias present in the data and the distribution of the data around the mean prediction. As shown by the Bland–Altman plot in Figure 16, most of the differences between the predicted and experimental MB removal percentages are clustered around the line that represents no bias. This indicates good reliability between the experimental and predicted values. It has been determined through calculation that there was a roughly 2.17% mean difference between predicted and experimental values. This indicates that the ML model does not exhibit significant systematic bias toward underestimating or overestimating removal percentages.

FIGURE 16.

FIGURE 16

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Bland–Altman agreement plot comparing experimentally observed and machine learning‐predicted methylene blue removal efficiencies, showing mean bias and limits of agreement for prediction reliability assessment.

A larger cluster of data in the area of high adsorption performance was found within the higher portion (80%–100%) of the average removal efficiency, where better predictive accuracy is seen when there are good adsorption conditions. Only a few outliers existed outside the acceptable agreement limits, which could be due to nonlinear variations with adsorption, experimental local errors, or atypical operation scenarios within the dataset. The lack of systematic increases in proportionally biased trendlines also confirms that the error did not increase as a function of adsorption efficiency. Therefore, the developed ensemble framework provided similar levels of predictability under both lower and higher adsorption conditions. Overall, the Bland–Altman analysis confirmed that the ML framework described above is reliable and applicable for adsorption prediction.

3.10. GUI Demonstration and Practical Deployment

A user‐friendly GUI was developed using the Gradio framework to facilitate real‐time prediction of MB removal efficiency. The interface accepts five operational input parameters, namely, initial dye concentration, contact time, initial pH, adsorbent dosage, and temperature, and generates the predicted removal efficiency using the optimized stacking ensemble model. The developed GUI enables real‐time prediction on a standard desktop computer without requiring specialized hardware or GPU acceleration. A representative screenshot of the GUI is shown in Figure 17, showing the user interface, input parameters, and prediction output.

FIGURE 17.

FIGURE 17

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Graphical user interface (GUI) developed using the Gradio framework for real‐time prediction of methylene blue removal efficiency using the tuned stacking ensemble model.

3.11. Practical Implications

A well‐developed machine learning framework has significant potential for developing practical adsorption systems and optimizing intelligent wastewater treatments. An ensemble learning approach combined with an explainable artificial intelligence (XAI) approach, Bayesian optimization, and uncertainty quantification has created a comprehensive decision‐making tool to predict MB removal efficiencies based on variable operational parameters. Unlike traditional empirical adsorption research methods, which require expensive and lengthy experimental trials using trial‐and‐error experimentation, the proposed machine learning framework allows for quick predictions and optimizations in adsorption operations at lower costs and times than traditional empirical research methods. Additionally, the XAI component of this study greatly enhances the engineers' ability to interpret results from this study. The XAI method was used to determine that temperature, pH, contact time, and adsorbent dosage were the primary operational variables controlling adsorption behavior. These results will help engineers identify stable operating ranges and to control adsorption processes more effectively. The Monte Carlo uncertainty analysis used will estimate the probability of reliable operation under varying levels of uncertainty that occur during water treatment and changing environmental conditions. Although the model was developed as an additional tool for smart planning of water treatment operations, and also as a model for adaptive control of process strategy, it is superior to traditional models because of its probabilistic and interpretive nature.

3.12. Limitations

The potential of this established predictive framework, based on training data results, is significant. However, there are a few limitations that should be addressed. The first limitation of the existing predictive model is that it is based on a compilation of literature‐derived experimental studies. These studies have been conducted under a variety of adsorption conditions and with various adsorbents, which have different adsorption behaviors. In addition to adsorption conditions and adsorbent characteristics, the experimental methodology used in each study may vary. Although these differences may contribute to uncertainty in some studies, they can result in inconsistencies between studies and potentially affect how well the model can generalize.

The second limitation of the existing predictive model is that it was trained using only a small number of operational variables. It has been demonstrated that additional physicochemical parameters and other adsorption properties may play an important role in determining adsorption behavior. Incorporating such parameters into future models would likely enhance the ability to predict adsorption behavior and provide greater insight into adsorption mechanisms. Finally, while bayesian optimization provided evidence of highly efficient operating conditions, achieving the predicted low‐dose requirements for an effective sorbent‐based treatment process in an industrial setting may not always be feasible. Therefore, before implementing any optimized treatment processes at a large‐scale, engineering confirmation of the optimized results will be required.

4. Conclusions

This study provides a machine learning–based method for predicting and optimizing MB removal efficiency. A comparison of models shows that the stacked ensemble model outperformed XGBoost, CatBoost, and LightGBM for MB removal prediction. Therefore, the model can capture the nonlinear and heterogeneous adsorption behavior that is inherent to multiple datasets of experimental results. Results revealed that temperature, pH, and contact time are factors that significantly affect adsorption efficiency. Additionally, sensitivity analysis illustrates how dependent the removal efficiency is on the operating parameters of an adsorption process. Using Bayesian optimization, the optimal conditions for adsorption were determined, which maximized the removal efficiency. A Monte Carlo simulation was also used to demonstrate the robustness and reliability of the predictive framework developed, including when there are uncertainties in the operation of an adsorption process. In addition to providing explanatory insights into the relationship between adsorption processes and their respective predictors through SHAP, uncertainty in these relationships has been quantified using sensitivity analysis, and optimization analysis and diagnostic agreement have been included as additional elements in evaluating the efficiency of the predictive framework proposed in this study. Although limitations exist due to a lack of specific information about the physical–chemical characteristics of biochars employed in each experiment reported in the literature review, the predictive framework developed provides a reliable and explainable means to predict and optimize adsorption based on literature data. The methodology presented may be used as a basis for future AI‐assisted designs of wastewater treatment systems and intelligent control and optimized designs of adsorption systems.

Author Contributions

Gokulan Ravindiran: conceptualization, methodology, software, formal analysis, data curation, visualization, writing – original draft, writing – review and editing. Gorti Janardhan: methodology, software, formal analysis, validation, investigation, writing – review and editing. Marlinda Abdul Malek: methodology, validation, supervision, investigation, writing – review and editing. Mary Subaja Christo: conceptualization, methodology, supervision, project administration, validation, writing – review and editing. Deepshikha Datta: data curation, investigation, formal analysis, validation, writing – review and editing. Ali. E. I. Elkhalifah: methodology, formal analysis, validation, investigation, writing – review and editing. Gasim Hayder: supervision, resources, methodology, project administration, validation, writing – review and editing.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Figure S1: Histogram distributions with kernel density estimation (KDE) curves for adsorption parameters and removal efficiency.

Figure S2: Violin plot analysis of adsorption variables and removal efficiency.

WER-98-e70527-s001.docx (309.6KB, docx)

Acknowledgments

The authors express their gratitude to the Higher Institution Centre of Excellence (HICoE), Ministry of Higher Education, Malaysia, under the project code 2024001HICOE, as referenced in JPT (BPKI)1000/016/018/34(5). This work was supported by Tenaga Nasional Berhad and Universiti Tenaga Nasional through the BOLD Refresh Postdoctoral Fellowships under the project code J510050002‐IC‐6 BOLDREFRESH2025‐Centre of Excellence. The authors acknowledge the support from the Environmental Engineering Department, College of Engineering, Imam Abdulrahman Bin Faisal University, Dammam, 31451, Eastern Province, Saudi Arabia.

The authors acknowledge the use of ChatGPT (OpenAI, GPT‐5.5; accessed July 2026) to assist with language refinement and improvement of manuscript clarity. The AI tool was also used to provide suggestions for code refinement during model development. All AI‐generated suggestions were carefully reviewed, revised, and verified by the authors. The authors take full responsibility for the study design, data collection, data analysis, interpretation of results, and the accuracy and integrity of the published work.

Contributor Information

Gokulan Ravindiran, Email: gokulravi4455@gmail.com.

Mary Subaja Christo, Email: marysubaja@gmail.com.

Data Availability Statement

The curated dataset comprising 504 literature‐derived adsorption experiments, along with the source code, trained machine learning models, and graphical user interface (GUI), is available on GitHub (https://github.com/gokulravi4455/Methylene‐Blue.git).

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Figure S1: Histogram distributions with kernel density estimation (KDE) curves for adsorption parameters and removal efficiency.

Figure S2: Violin plot analysis of adsorption variables and removal efficiency.

WER-98-e70527-s001.docx (309.6KB, docx)

Data Availability Statement

The curated dataset comprising 504 literature‐derived adsorption experiments, along with the source code, trained machine learning models, and graphical user interface (GUI), is available on GitHub (https://github.com/gokulravi4455/Methylene‐Blue.git).

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