Machine Learning Prediction of Phosphate Adsorption on Red Mud Modified Biochar Beads: Parameter Optimization and Experimental Validation

Abstract

Designing phosphate adsorbents is often hindered by trial-and-error optimization that overlooks nonlinear coupling between preparation parameters and operational conditions. Here we present a unified, explainable machine-learning framework that links red mud modified biochar bead (RM/CSBC) preparation (red mud dosage, biomass dosage, and pyrolysis temperature) to operating variables (initial pH, reaction temperature, contact time, and initial phosphate concentration) and directly guides condition selection. Using 95 independent experiments, six regressors were trained and compared. Random Forest (RF) model demonstrated strong prediction accuracy, with R² values of 0.916 for the training set and 0.892 for the test set. Support Vector Regression (SVR) model showed superior performance, achieving R² values of 0.984 and 0.967 for training and test sets, respectively, with low RMSE (0.068 and 0.083) and PBIAS (5.41% and 6.86%). Feature importance analysis revealed red mud and biomass doses positively influenced phosphate adsorption, with surface active sites and phosphate concentration gradient playing significant roles. Experimental verification confirmed RF and SVR models provided accurate predictions under three representative conditions, with deviations between predictions and measurements of +0.66, +0.19, and −0.69 mg·g⁻¹ for SVR and −1.08, −0.79, and −1.15 mg·g⁻¹ for RF, offering reliable guidance for phosphate removal in wastewater using RM/CSBC. This work highlights the potential of using machine learning to optimize waste-based adsorbent materials for wastewater treatment, significantly reducing time and experimental costs.

1. Introduction

Phosphorus (P) is an essential element in the Earth’s life system, playing a vital role in the construction of DNA and RNA, energy metabolism, cellular signal transduction, and the formation of biological membranes [1]. It is not only an indispensable component of fertilizers in agricultural production but also an important raw material in various industrial and food processing sectors [2]. However, with the acceleration of industrialization and urbanization, the discharge of phosphorus-containing wastewater has become a global environmental issue [3]. Excessive phosphorus input into aquatic environments can trigger eutrophication and algal blooms, leading to water quality deterioration, destruction of aquatic habitats, and restriction of water resource utilization [4]. Meanwhile, global phosphorus resources rely almost entirely on non-renewable phosphate rock, which is unevenly distributed and concentrated in a few countries and regions [5]. It is predicted that, at the current rate of exploitation and consumption, high-grade phosphate rock reserves will be depleted within the next 50 to 100 years [6]. These circumstances indicate that the dual pressures of phosphorus resource scarcity and aquatic phosphorus pollution are intensifying, highlighting the urgent need for efficient, economical, and sustainable phosphorus removal and recovery technologies.

Among various techniques for phosphorus removal and recovery, adsorption is widely recognized for its simplicity, low cost, mild operational requirements, adaptability to water quality variations, and potential for adsorbent regeneration [7]. The efficiency of adsorption is strongly influenced not only by the physicochemical properties of the adsorbent—such as specific surface area, pore size distribution, surface functional groups, and isoelectric point—but also by operational conditions, including adsorbent type and dosage, wastewater pH, coexisting ions, contact time, reaction temperature, and pollutant concentration [8]. An ideal adsorbent should possess high adsorption capacity, strong selectivity, environmental safety, low cost, and stable performance under complex water quality conditions [9,10]. Among the various adsorbents, biochar (BC) has attracted considerable attention in recent years due to its abundant feedstock availability, high specific surface area, rich oxygen-containing functional groups, and tunable physicochemical properties [11,12]. However, unmodified biochar often suffers from insufficient surface active sites, electrostatic repulsion from phosphate anions, and limited adsorption capacity [13]. To enhance its performance, chemical modification, mineral loading, and composite material strategies have been widely employed [14,15].

Red mud (RM), a major solid waste from the alumina industry, is produced in large quantities annually and poses severe environmental risks due to long-term storage [16]. Rich in Fe and Al oxides, red mud can react with phosphate to form insoluble precipitates or enhance phosphate adsorption via surface complexation [17]. In recent years, red mud-modified biochar has received increasing attention for phosphorus removal and recovery from wastewater due to its synergistic combination of the porous structure of biochar and the metal active sites of red mud [18,19]. For example, Yang et al. [20] prepared composite biochar (RM-BC) from red mud and walnut shells, and found that RM-BC produced at a mass ratio of 1:1 and pyrolyzed at 320 °C exhibited a phosphate adsorption capacity of 15.48 mg·g⁻¹, more than twice that of pristine biochar, with adsorption mechanisms involving Fe–O–P bond formation, surface precipitation, and ligand exchange. Nevertheless, most existing studies focus on performance evaluation under limited laboratory conditions and lack systematic quantitative analysis of the coupled effects of multiple influencing factors. In addition, conventional experimental optimization methods are time-consuming, costly, and incapable of rapidly predicting adsorption performance under complex conditions, which limits their practical engineering application [21,22].

Machine learning (ML) offers a novel approach for predicting material performance and optimizing operational parameters. By building high-dimensional, nonlinear predictive models from limited experimental data, ML can significantly reduce experimental workload and costs, while revealing key influencing factors to guide adsorbent design and application [23,24]. Recent studies have successfully applied ML to predict adsorption and degradation processes in wastewater treatment. For instance, Rahman et al. [25] employed ANN, RF, and SVM to model antibiotic degradation in UV/persulfate–peroxide advanced oxidation processes, demonstrating high predictive accuracy and interpretability through Shapley value analysis. Lyu et al. [26] compiled 1200 experiments across 190 biochars and fine-tuned RF/CatBoost to predict phosphorus adsorption capacity, achieving CatBoost R² = 0.9573 and showing that adsorbent dosage, initial P concentration, and C content dominate, with partial dependence plots elucidating single- and two-way effects. Although these studies have applied ML to adsorption performance prediction, research focusing on red mud modified biochar for phosphate removal remains scarce, particularly in integrating feature importance analysis with experimental validation [27]. This gap limits the interpretability and reliability of ML models for real-world engineering scenarios.

In this study, red mud modified biochar beads were used as the adsorbent, and six ML models were developed and compared for predicting their phosphate adsorption capacity. Feature importance analysis was conducted to identify the key influencing factors, and experimental validation was performed to assess the accuracy and applicability of the models. This work not only provides a scientific basis for the rapid screening and performance optimization of red mud-modified biochar adsorbents but also demonstrates the potential and practical value of ML in the development of waste-derived functional materials, offering new technical insights for efficient phosphorus removal and resource recovery from wastewater.

2. Materials and Methodology

2.1. Materials and Chemicals

The red mud used in this study was obtained from Xinfa Group Co., Ltd., Liaocheng, Shandong Province, China, while the reed biomass feedstock was collected from the Chanba Ecological Wetland in Xi’an, Shaanxi Province, China. Prior to the experiments, the red mud sample was dried at 100 °C to a constant weight and then ground using a mortar and pestle, whereas the reeds were crushed with a continuous-flow high-speed pulverizer. Both materials were sieved through a 200-mesh screen to control the particle size to less than 1 mm, and the resulting powder samples were dried and sealed for storage. All chemical reagents (e.g., Na₂HPO₄, NaH₂PO₄, HCl, NaOH, CH₃COOH, and NH₄Cl) were of analytical grade and purchased from Sinopharm Chemical Reagent Co., Ltd., Shanghai, China.

2.2. Preparation of Red Mud Modified Biochar Beads (RM/CSBC)

A total of 2 g of chitosan (CS) powder was dissolved in 100 mL of 2% (v/v) acetic acid solution under magnetic stirring in a thermostatic water bath at 60 °C for 1 h until completely dissolved, yielding a CS solution. Red mud (0–3 g) and reed biomass (0–4 g, particle size < 1 mm) powders were subsequently added to the CS solution and stirred for 0.5 h to achieve homogeneous dispersion. The suspension was dropwise added into 125 mL of 2 M NaOH coagulation bath using a rubber dropper, forming spherical gel beads. The beads were allowed to cure at room temperature for 12 h, collected, and rinsed thoroughly with deionized water three times until the wash water reached neutral pH. The cleaned beads were dried in a forced-air oven at 60 °C, then placed in a tubular furnace. After purging with N₂ for 30 min to establish an inert atmosphere, the temperature was increased to the target value (400–1100 °C) at a heating rate of 8 °C·min⁻¹ and maintained for 2 h for pyrolysis. The furnace was allowed to cool naturally to room temperature before removing the biochar bead products, which were designated as RM/CSBC.

2.3. Batch Adsorption Experiments

Based on previous studies and preliminary experiments, the adsorbent dosage was fixed at 1.0 ± 0.01 g·L⁻¹. In a typical experiment, 0.08 g of the prepared RM/CSBC was added to 80 mL of phosphate solution in a conical flask and agitated in a thermostatic orbital shaker at 180 rpm for a predetermined contact time under specified experimental conditions. After equilibration, the supernatant was collected, and the phosphate concentration was determined using the molybdenum blue spectrophotometric method. The adsorption capacity was calculated accordingly, and the results were used to compare the performance of different materials. The equilibrium adsorption capacity and the adsorption capacity at time t can be calculated using Equations (1) and (2):

$${\mathrm{q }}_{\mathrm{e}}={\displaystyle \frac{\left({\mathrm{c}}_0-{\mathrm{c}}_{\mathrm{e}}\right)\mathrm{V}}{\mathrm{m}}}$$

(1)

$${\mathrm{q }}_{\mathrm{t}}={\displaystyle \frac{\left({\mathrm{c}}_0-{\mathrm{c}}_{\mathrm{t}}\right)\mathrm{V}}{\mathrm{m}}}$$

(2)

where q_e (mg·g⁻¹) is the equilibrium adsorption capacity, q_t (mg·g⁻¹) is the adsorption capacity at time t, C₀ (mg·L⁻¹) is the initial PO₄³⁻ concentration, C_e (mg·L⁻¹) is the equilibrium concentration of PO₄³⁻, C_t (mg·L⁻¹) is the concentration of PO₄³⁻ at time t, V (L) is the volume of the solution, and m (g) is the mass of the adsorbent.

2.4. Prediction and Analysis Methods of Machine Learning Model

2.4.1. Machine Learning Model Construction

The construction of the machine learning (ML) model comprised five main steps: database establishment, data splitting, model training, model prediction, and performance evaluation. The model database consisted of the dependent variable (y) and independent variables (x). The adsorption capacity of phosphate by RM/CSBC was used as the output variable (y), while the red mud dosage, biochar dosage, pyrolysis temperature of the beads, reaction temperature in the phosphate solution, contact time, initial pH, and initial phosphate concentration were used as input variables (x). Six regression algorithms were employed for model development and comparison: support vector regression (SVR), k-nearest neighbors regression (KNN), elastic net regression (ENR), Poisson regression (PR), Bayesian linear regression (BLR), and random forest regression (RF) [28,29,30,31,32,33]. All input and output variables were obtained from the batch adsorption experiments described above, and their numerical values are provided in Table S1 (Supplementary Information). In total, 95 datasets were collected from laboratory-scale batch adsorption experiments. To ensure effective validation of the model’s generalization and predictive performance, the dataset was randomly divided into training and testing subsets in an 80:20 ratio, with 76 samples used for model training and parameter optimization, and the remaining 19 samples used for independent evaluation of the prediction performance.

2.4.2. Performance Evaluation of Machine Learning Model

Model performance evaluation is an essential method to assess the reliability of the model. To further evaluate the simulation performance of the model, three statistical indicators were employed: the coefficient of determination (R²), the root mean squared error (RMSE), and the percentage bias (PBIAS).

The coefficient of determination (R²) measures the degree of fit between the model predictions and the observed data, reflecting their linear correlation. The value of R² ranges from 0 to 1. An R² value of 1 indicates a perfect fit, where all observed values are exactly the same as the predicted values, whereas an R² value of 0 indicates that the model has no predictive power and the predictions are unrelated to the observations. The calculation is shown in Equation (3):

$$R^2={\displaystyle \frac{{\left({\displaystyle {\sum }_{i=1}^n\left(y_i-\overline{y}\right)\left(\widehat{y_i}-\overline{y_i}\right)}\right)}^2}{{\displaystyle {\sum }_{i=1}^n{\left(y_i-\overline{y}\right)}^2{\left(\widehat{y_i}-\overline{y_i}\right)}^2}}}$$

(3)

where $\widehat{y_i}$ is the model-predicted value, $y_i$ is the observed/benchmark value, $\overline{y_i}$ is the mean of the predicted values, $\overline{y}$ is the mean of the observed values, and n is the sample size.

The root mean squared error (RMSE) quantifies the overall deviation between the predicted and observed values, reflecting the average magnitude of the errors. RMSE is the square root of the mean of the squared errors and is sensitive to large deviations. A smaller RMSE indicates higher prediction accuracy, while a larger RMSE suggests greater prediction error. The formula is given in Equation (4):

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle {\sum }_{i=1}^n{\left(\widehat{y_i}-y_i\right)}^2}}$$

(4)

The percentage bias (PBIAS) evaluates the systematic bias between the model predictions and the observed data, indicating whether the model systematically over- or under-estimates the observations. A positive PBIAS indicates a tendency toward overestimation, while a negative PBIAS indicates underestimation. A PBIAS value close to zero suggests no significant systematic bias. The formula is expressed in Equation (5):

$$PBIAS={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n\left|y_i-\widehat{y_i}\right|}}{{\displaystyle {\sum }_{i=1}^n{y}_i}}}\times 100\%$$

(5)

The parameters in Equations (4) and (5) are the same as those in Equation (3).

2.4.3. Interpretability Analysis of Machine Learning Model

Feature importance analysis is employed to quantitatively evaluate the role and contribution of each feature variable in the model prediction. The Increase in Mean Squared Error (IncMSE) is a widely used metric for this purpose, also referred to as MSE-based variable importance. Unlike the Gini Index or Node Purity, IncMSE measures the extent to which the model’s mean squared error (MSE) increases when the values of a particular feature are randomly permuted (i.e., feature shuffling). This approach avoids bias introduced by data distribution, making the evaluation of features more unbiased. It is particularly suitable for small datasets and can effectively reduce overfitting. By quantifying the influence of each feature on model predictions, IncMSE identifies features with a substantial impact—if shuffling a feature leads to a significant increase in MSE, the feature is considered important for prediction; conversely, a minimal change in MSE suggests the feature has limited contribution and may be redundant. The calculation is shown in Equation (6):

$$IncMSE={\displaystyle \frac{1}{n}}{\displaystyle \sum i}={\left(\widehat{y_i}-y_i\right)}^2-{\displaystyle \frac{1}{n}}{\displaystyle \sum i}=1^n{\left({\widehat{y_{i,j}}}^{perm}-y_i\right)}^2$$

(6)

where $\widehat{y_i}$ is the model-predicted value, $y_i$ is the observed or reference value, ${\widehat{y_{i,j}}}^{perm}$ is the model-predicted value after shuffling variable j, and n is the sample size.

The Shapley Additive exPlanations (SHAP) method originates from the Shapley value theory in cooperative game theory, providing a quantitative framework for assessing feature contributions in machine learning models. By decomposing the marginal contribution of each feature to the prediction, SHAP constructs an additive feature attribution model, enabling visual interpretation of the model’s decision-making process. Specifically, SHAP values quantify the contribution of each feature to every individual prediction, offering an intuitive and measurable explanation that reveals whether a feature exerts a positive or negative influence on the model output. SHAP values were calculated to quantify the effect of each feature on the prediction results for each sample, thereby offering interpretable insights into the underlying decision-making mechanism of the model. The formulation is shown in Equation (7):

$$y_i=y_{\mathrm{base}}+f(x_{i1})+f(x_{i2})+\dots +f(x_{ik})$$

(7)

where $y_i$ represents the value of the jth feature for the ith sample, and f(x_ij) denotes the corresponding SHAP value. The sign of f(x_ij) indicates whether the feature value x_ij has a positive or negative effect on the model’s prediction.

Partial Dependence Plots (PDPs) are used to visualize the marginal relationship between one or more features and the model output. In this study, bivariate PDPs were employed to analyze the relationships between specific features (e.g., red mud dosage, pyrolysis temperature of the beads, reaction temperature) and the phosphate adsorption capacity. By examining the shape of the PDP curves, we can identify whether the effect of a feature on the outcome is linear or nonlinear, thereby providing valuable guidance for feature selection and model optimization. The calculation is expressed in Equation (8):

$${\widehat{f}}_s(x_s)=E_{X\mathrm{e}}\left[{\widehat{f}}_s(x_s,X_c)\right]={\displaystyle \int {\widehat{f}}_s}(x_s,X_c)dP(X_c)$$

(8)

where x_s is the target feature, x_c represents all other features, and ${\widehat{f}}_s$ denotes the machine learning model. By systematically varying the value of x_s, the corresponding changes in model predictions are obtained.

2.5. Prediction of Phosphate Adsorption Capacity

The optimal model selected from the six above machine learning algorithms was used to predict the phosphate adsorption capacity of RM/CSBC. The input parameters included water quality characteristics of the actual wastewater—namely, initial phosphate concentration and pH; reaction conditions, including reaction time and reaction temperature; and material preparation parameters, including red mud dosage, biochar dosage, and pyrolysis temperature. The machine learning model was then applied to predict phosphate adsorption capacity under the given adsorption conditions. In this study, three sets of experimental conditions were designed, with the seven input variables specified as follows: (1) 250 mg·L⁻¹, 6, 21 h, 35 °C, 3 g, 4 g, 800 °C; (2) 150 mg·L⁻¹, 7, 21 h, 25 °C, 3 g, 3 g, 900 °C; (3) 50 mg·L⁻¹, 8, 21 h, 15 °C, 3 g, 4 g, 1000 °C. Finally, the accuracy of the model was evaluated by comparing the predicted phosphate adsorption capacities with the corresponding experimental results. The validation workflow is shown in Figure 1.

3. Results and Discussion

3.1. Analysis of Data Distribution Characteristics

The frequency distribution histograms of the input and output variables in the RM/CSBC phosphate adsorption model are presented in Figure 2. It can be observed that most input variables exhibit a certain degree of skewness. The red mud and biochar dosages are predominantly concentrated in the range of 2–3 g, while the pyrolysis temperature is mainly distributed between 900 and 1000 °C, indicating that the optimization of the red mud-to-biochar mass ratio and high-temperature pyrolysis conditions was particularly emphasized during the experiments. The reaction temperature and initial pH are primarily clustered at 25 °C and within the weakly acidic to neutral range (pH 5–7), reflecting an experimental focus on simulating typical treatment conditions for real wastewater.

The output variable, phosphate adsorption capacity, exhibits a well-spread distribution, with values mainly ranging from 20 to 50 mg·g⁻¹. This indicates that the training samples capture adsorption behaviors across low, medium, and high levels, thereby providing a robust basis for the fitting and generalization of the subsequent machine learning predictive models. Overall, the frequency distribution histograms demonstrate that the model database established in this study possesses strong representativeness and coverage in both the setting of experimental conditions and the acquisition of response values, thus satisfying the fundamental prerequisites for machine learning modeling and ensuring the feasibility of conducting regression analysis and variable interpretation.

3.2. Pearson Correlation Analysis

The Pearson correlation coefficient heatmap (Figure 3) shows that, in terms of RM/CSBC preparation parameters, both the red mud dosage and biochar dosage exhibit positive correlations with phosphate adsorption capacity, with correlation coefficients of 0.32 and 0.28, respectively. This indicates that both factors contribute to enhancing phosphate adsorption. A negative correlation (correlation coefficient = −0.18) was observed between red mud dosage and biochar dosage, suggesting that the proper adjustment of their mixing ratio is crucial. Both dosages are positively correlated with pyrolysis temperature, implying that appropriately increasing the red mud and biochar contents facilitates the pyrolysis process, leading to the formation of beads with more porous structures and active sites, thereby improving their phosphate adsorption capacity [34]. Regarding water quality conditions, phosphate adsorption capacity shows the strongest positive correlation with initial phosphate concentration, indicating that higher phosphorus levels in wastewater result in greater adsorption capacity of the beads. This can be attributed to the higher availability of phosphate ions for adsorption and the accelerated diffusion rate of phosphate at elevated concentrations. Reaction time and temperature also exhibit certain positive correlations with phosphate adsorption capacity, while correlations among the other parameters are relatively weak.

3.3. Comparative Analysis of Predictive Model Performance

Six machine learning models—Bayesian Linear Regression (BLR), K-Nearest Neighbors (KNN), Elastic Net Regression (ENR), Poisson Regression (PR), Random Forest (RF), and Support Vector Regression (SVR)—were employed to predict the phosphate adsorption capacity of red mud-modified biochar beads (RM/CSBC), as illustrated in Figure 4. The performance of each model on both the training and testing datasets was evaluated using three metrics: coefficient of determination (R²), normalized root means square error (RMSE), and percent bias (PBIAS). The detailed values are provided in

Table 1. Performance evaluation metrics for the adsorption capacity predictions by the six machine learning models.

Model	Training Set			Testing Set
	R2	RMSE	PBIAS	R2	RMSE	PBIAS
BLR	0.763	0.252	21.18%	0.884	0.182	15.06%
ENR	0.828	0.209	17.01%	0.693	0.324	25.13%
KNN	0.852	0.201	15.41%	0.853	0.188	14.45%
PR	0.704	0.285	23.40%	0.822	0.214	17.39%
RF	0.916	0.158	12.31%	0.892	0.133	11.43%
SVR	0.984	0.068	5.41%	0.967	0.083	6.86%

. ENR model exhibited relatively large deviations on the testing dataset, indicating lower prediction accuracy for this problem. KNN and PR models showed moderate performance; while they achieved satisfactory fitting in certain datasets, their overall predictive capability was slightly inferior to that of SVR and RF. RF model demonstrated excellent predictive performance on both the training and testing datasets, particularly achieving an R² value of 0.916 on the testing dataset, indicating strong fitting capability, small prediction errors, and minimal bias. SVR model achieved R² values of 0.984 and 0.967 on the training and testing datasets, respectively, and its RMSE values were 0.068 and 0.083 mg·g⁻¹. Taken together, these metrics indicate that SVR delivered the strongest generalization, as it combined the highest testing R² with the lowest testing RMSE and maintained a small gap between training and testing performance, which is consistent with a model that captures the signal rather than overfitting noise. Methodologically, SVR’s margin-based kernel learning suits small samples, nonlinear adsorption, and preparation–operation interactions, explaining its superiority over the other methods evaluated.

3.4. Feature Importance Analysis

Understanding the influence of various features on adsorption capacity is essential for developing efficient adsorbents and optimizing the phosphate removal process. Based on the constructed Random Forest (RF) model, the relative importance of all input variables was evaluated, and the results are shown in Figure 5. The order of importance was as follows: initial phosphate concentration > contact time > red mud dosage > pyrolysis temperature > biochar dosage > reaction temperature > initial pH, which is consistent with the Pearson correlation coefficient analysis. Among the material preparation parameters, all three features exhibited substantial influence, indicating that the rational adjustment of preparation conditions is critical for phosphate adsorption. The most significant effect was observed for the water quality parameter, initial phosphate concentration, consistent with previous conclusions. This can be attributed to the concentration gradient and the utilization efficiency of active sites on the adsorbent surface. Higher initial concentrations lead to an increased concentration gradient, which facilitates the diffusion of phosphate species from the solution to the adsorbent surface, while also enhancing the occupancy of active sites, thereby amplifying its impact [26].

3.5. SHAP Value Analysis

As shown in the SHAP summary plot (Figure 6), the SHAP values for initial phosphate concentration are predominantly positive and relatively high for most samples, indicating that higher phosphate concentrations promote adsorption. The SHAP values for red mud dosage are also largely positive, suggesting that increasing its content enhances the interaction between active components and the biochar surface, thereby providing more sites for phosphate binding. Mechanistically, a higher RM dosage increases the density of Fe/Al oxy-hydroxyl sites that participate in ligand exchange and promotes Fe–O–P inner-sphere complexation and surface precipitation, which together raise the predicted capacity.

In contrast, biochar dosage exhibits a certain degree of negative SHAP value clustering, implying that excessive biochar loading does not necessarily increase adsorption capacity per unit mass. This phenomenon may be associated with an imbalance in the red mud-to-biochar ratio. When RM is diluted by excess biochar, the effective Fe/Al site density per unit sorbent decreases, weakening ligand-exchange and precipitation pathways and thus reducing per-mass capacity. Furthermore, pyrolysis temperature tends to yield positive SHAP values when it is in the moderately high range, indicating that appropriately increasing the pyrolysis temperature can improve pore structure and surface activity. However, excessively high temperatures may lead to pore collapse or the loss of surface functional groups, thus preventing a linear increase in adsorption performance [35]. The SHAP values for contact time are mostly concentrated in the slightly positive range, suggesting that extending the reaction time moderately can enhance phosphate adsorption, although its contribution becomes limited in the later stages of adsorption. The SHAP values for initial pH show a bipolar distribution, with acidic conditions (lower pH) being more favorable for phosphate uptake.

To place these observations in context,

Table 2. Phosphate adsorption of biochar materials and corresponding ML performance.

Material	Morphology	Preparation Method	Qm (mg·g−1)	ML Models	Test Performance	References
RM–walnut-shell BC	powder	1:1 mass ratio; pyrolysis with 320 °C, 58 min	15.48	/	/	[20]
Bayer RM–modified BC	powder	Acid impregnation to extract/disperse Fe/Al/Ca; pyrolysis at 800 °C	137.68	/	/	[36]
RM–water-hyacinth BC	powder	Co-pyrolysis with 835 °C, 66 min	6.48	/	/	[37]
RM-modified rape-straw BC	powder	Pyrolysis at 750 °C	11.78	/	/	[38]
Various biochar	mixed (mostly powder)	About 1200 experiments across 190 biochars	/	RF, CatBoost (best)	R2 = 0.9573; RMSE = 8.02 mg·g−1	[26]
Various adsorbents	mixed	Multi-adsorbent dataset	/	LR, KNN, SVM, GBDT (best), MLP	R2 > 0.967; RMSE < 0.182 (limited key features); after data enrichment: R2 > 0.869; RMSE < 0.344	[39]
RM/CSBC	beads	Pyrolysis with 900 °C, 2 h	86.15	SVR (best), RF, KNN, ENR, PR, BLR	R2 = 0.967; RMSE = 0.083 mg·g−1	This work [40]

provides a quantitative benchmark of RM/BC phosphate adsorption capacities alongside machine-learning performance (R², RMSE), allowing direct comparison of our RM/CSBC beads and models with prior studies.

3.6. Feature Partial Dependence Analysis

To further investigate the phosphate adsorption process of RM/CSBC, bivariate partial dependence plots (PDPs) were employed to illustrate the interactive effects of two features on the target variable, with results presented as 3D surfaces in Figure 7. As shown in Figure 7a, the combination of higher biomass dosage and red mud dosage significantly enhanced phosphate adsorption capacity, indicating a synergistic effect between the two. This synergy is consistent with the simultaneous increase in pore/surface area contributed by biomass carbon and in Fe/Al active sites supplied by RM, which jointly promote ligand exchange and Fe–O–P complexation. Figure 7b,c reveal interactions between red mud dosage, biomass dosage, and pyrolysis temperature, suggesting that simultaneously increasing pyrolysis temperature and the dosages of red mud and biomass is beneficial for improving adsorption capacity.

Figure 7d–g demonstrated that, under various RM/CSBC preparation conditions, acidic environments and high phosphate concentrations consistently favor phosphate adsorption. At lower pH, protonated surfaces favor ligand exchange with H₂PO4⁻; at higher C₀, the increased local phosphate activity promotes the formation/growth of Fe–O–P complexes and surface precipitates, in line with the positive PDP trends. However, a higher biomass dosage is not always more effective; at an initial phosphate concentration of 300–400 mg·L⁻¹, a biomass dosage of 1–3 g resulted in higher adsorption capacity than 4 g. This finding suggests that the red mud-to-biomass mass ratio must be appropriately balanced to maximize the synergistic effect of metal site activity and pore adsorption, thereby improving adsorption efficiency.

Figure 7h shows that, at lower reaction temperatures, initial pH had minimal influence on phosphate adsorption capacity. However, as the reaction temperature increased, the effect of initial pH became more pronounced. This implies that higher temperatures may alter the adsorbent surface properties, affecting its interaction with phosphate, especially under different pH conditions. At pH > 6, the adsorption capacity increased markedly with rising temperature. This is likely due to changes in the ionic species of phosphate in aqueous solution at higher pH, which enhance electrostatic interactions with the adsorbent surface, thus increasing adsorption. Particularly under neutral to mildly alkaline conditions, phosphate molecules are more prone to react with functional groups on the biochar surface, thereby enhancing phosphate removal efficiency. Additionally, elevated temperature can facilitate nucleation/growth of Fe/Al–phosphate precipitates, reinforcing the positive PDP slope at higher pH.

As shown in Figure 7i, the influence of initial phosphate concentration on adsorption capacity increased with reaction temperature. This may be attributed to accelerated phosphate diffusion and elevated surface reactivity of biochar at higher temperatures, which promote phosphate adsorption. At lower reaction temperatures, however, the impact of initial phosphate concentration was relatively small, indicating that reaction temperature is one of the key factors for improving adsorption performance.

3.7. Experimental Verification of SVR and RF Predictions

Based on the results of the model performance analysis, the Support Vector Regression (SVR) and Random Forest (RF) models were selected to predict the phosphate adsorption capacity of red mud-modified biochar beads (RM/CSBC) under different experimental conditions, followed by validation through actual experiments. The results are shown in Figure 8. Under the three experimental conditions, the predicted phosphate adsorption capacities of the SVR model were 37.64 mg·g⁻¹, 25.79 mg·g⁻¹, and 13.08 mg·g⁻¹, while those of the RF model were 35.90 mg·g⁻¹, 24.81 mg·g⁻¹, and 12.62 mg·g⁻¹, respectively. When compared with the experimental results, the SVR model showed deviations of +0.66 mg·g⁻¹, +0.19 mg·g⁻¹, and −0.69 mg·g⁻¹ for experimental conditions 1, 2, and 3, respectively; the RF model showed deviations of −1.08 mg·g⁻¹, −0.79 mg·g⁻¹, and −1.15 mg·g⁻¹ for the same conditions. It is evident that both SVR and RF models exhibited small errors and could accurately predict phosphate adsorption capacity. Among them, the SVR model achieved slightly higher predictive accuracy than the RF model, particularly under experimental conditions 1 and 2. Overall, the differences between the predicted and experimental values were within an acceptable range, indicating high accuracy and reliability, and providing valuable guidance for phosphate recovery from actual wastewater using RM/CSBC.

4. Conclusions

This study systematically evaluated RM/CSBC beads for phosphate removal using six machine-learning models. Support vector regression (SVR) was the best-generalizing model, achieving a test-set R² of 0.967, an RMSE of 0.083 mg·g⁻¹, and a PBIAS of 6.86%, and laboratory verification under three representative conditions showed small prediction–measurement deviations of +0.66, +0.19, and −0.69 mg·g⁻¹. These results confirm that the model is reliable in practical settings. The novelty of this work lies in an integrated framework that links RM/CSBC preparation and operating variables with explainable modeling and experimental validation. The model-identified drivers align with known adsorption processes: higher initial phosphate concentration and appropriate red-mud dosage favor ligand exchange and Fe–O–P inner-sphere complexation, and moderately elevated pyrolysis temperature and suitable pH support pore development and surface precipitation, which is consistent with the partial-dependence and SHAP trends. This framework enables data-driven selection of preparation–operation windows while reducing time and cost. Future work will validate and scale the workflow in real wastewater and in column systems with regeneration, and it will extend the framework to other waste-derived adsorbents and multi-contaminant scenarios.