Machine learning modeling to predict the photocatalytic degradation rate constant in wastewater using TiO₂

Abstract

Many researchers have studied the application of titanium dioxide (TiO₂​) for photodegradation, but optimization is time-consuming and resource-intensive due to the complexity of various experimental parameters. In this study we developed a machine learning model for enhancing the photocatalytic efficiency of TiO₂ photocatalyst for pollutant degradation. Therefore, we compiled a dataset of 150 experimental results from published literature. This dataset was compiled based on various parameters that influence the reaction rate constant (k), such as pollutant type, catalyst particle size, surface area, pollutant concentration, TiO₂ dosage, pH, light intensity, and temperature. Several machine learning models were trained and tested, among them the CatBoost model, demonstrating the prediction with R² of 0.9044 and MAE of 0.1052. Analysis revealed that catalyst load, light intensity, and pollutant concentration were the most influential factors in the model’s predictions. The optimized CatBoost model successfully predicted a degradation rate constant of 0.1383 min^− 1 for methylene blue, which was experimentally validated as equivalent to the rate constant of 0.1278 min^− 1, confirming the potential of machine learning. This work confirms the potential of machine learning models for optimizing the photocatalysis efficiency of TiO₂ photocatalysts for environmental applications.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-51108-7.

Introduction

All living organisms’ life depend on water; however, its contamination poses a significant threat to public health and global environmental sustainability. Industrial processes, agricultural activities, and human waste all contribute to the pollution of water resources¹. The wastewater may contain dyes, phenols, pesticides, and pharmaceuticals that are resistant to conventional wastewater treatment methods due to their complex structures and low biodegradability². Advanced oxidation processes are effective alternative methods to decompose these complex pollutant compounds into less harmful substances like CO₂, H₂O, and minerals³. Among advanced oxidation process (AOP), heterogeneous photocatalysis has been extensively studied, with titanium dioxide serving as the most widely studied photocatalyst due to its chemical stability, non-toxicity, low cost, and high photoactivity^4,5.

The photocatalytic performance of the TiO₂ catalyst depends on several operational parameters, including particle size, surface area, catalyst dosage, type of pollutant, initial pollutant concentration, solution pH, light intensity, and reaction temperature^6,7. Optimizing these parameters through conventional experimental approaches is time-intensive and fails to capture complex interactions between variables. In recent years, machine learning (ML) has proven effective in modeling complex, non-linear systems across various scientific and engineering domains⁸. ML algorithms can learn patterns and relationships from structured data, making them suitable for predicting the performance of intricate processes like photocatalysis⁹. By training ML models on datasets comprising experimental parameters and corresponding degradation efficiencies, it is possible to develop predictive tools that can rapidly estimate process performance under different conditions. We use some popular ML models like Artificial Neural Networks (ANN), Support Vector Regression (SVR), CatBoost, Random Forest (RF), and XGBoost to predict the photocatalytic degradation rate constant of model organic pollutants using TiO₂ nanoparticles under varying experimental conditions. In this study, a dataset consisting of approximately 150 experimental data points was compiled from peer-reviewed literature, covering eight key variables: pollutant type, UV light intensity, TiO₂ particle size, catalyst surface area, TiO₂ dosage, initial pollutant concentration, pH, and reaction temperature. For model development, the dataset was randomly divided into 75% training data (≈ 112 data points) and 25% testing data (≈ 38 data points) to evaluate predictive performance. In addition, five-fold cross-validation was applied during training to further assess the robustness and generalization capability of the model. Despite extensive research on TiO₂-based photocatalysis for pollutant degradation, optimizing operational parameters remains challenging due to the large number of experimental variables and the time- and resource-intensive nature of traditional trial-and-error approaches. To address this gap, this study adopts a machine learning–driven strategy to enhance the efficiency and predictability of photocatalytic processes. The objectives of this work were to: (i) generate a structured dataset of experimental results covering multiple key parameters, (ii) develop, train, and evaluate multiple ML models while comparing their predictive performance using standard metrics (R², MAE, and RMSE), and (iii) identify the main parameters influencing the degradation rate constant through feature importance analysis. Final model predictions were further validated through experimental studies on representative pollutants, ensuring reliability and practical relevance. By integrating interpretable machine learning with experimental validation, this work provides a cost-effective, rapid, and generalizable approach for optimizing photocatalytic systems, highlighting the potential of computational intelligence to guide environmental remediation strategies.

Methodology

Data collecting

In this study, we employed machine learning models using a dataset consisting of 150 experimental data points obtained from published literature sources^3,10–39. All 150 experimental data points collected from ScienceDirect, PubMed, Elsevier, etc., with 96% of data points originating from Q1 and Q2 journals. The full database is listed in supplementary information. Each data point contains eight experimental parameters such as types of pollutant, particle size, surface area, initial concentration of pollutant (mg/L), TiO2 dosage (g/L), the solution of pH, light intensity (mW/cm2), and experimental temperature (°C).

Fig. 1.

Schematic diagram of the methodology of (I) data collection, (II) modelling and (III) experimental.

Machine learning models training and evaluation

Supervised machine learning models have the ability to optimize and handle complex system factors in wastewater treatment⁴⁰. ML models such as Support Vector Regression (SVR), Random Forest (RF), XGBoost, CatBoost, and Artificial Neural Networks (ANN) are powerful tools for predicting photocatalytic activity based on experimental parameters⁴¹, and therefore we used these models in this work. All data processing and modeling were performed using Python with libraries such as Pandas for data manipulation, Scikit-learn⁴² for ML algorithms, model selection, and metrics, and Matplotlib and Seaborn for visualization. Categorical variables (pollutant types) were transformed using one-hot encoding to enable their use in ML algorithms⁴³.

The final dataset comprised 150 data points. Input features (X) included type of pollutant, particle size (nm), surface area (m²/g), TiO₂ dosage (g/L), initial pollutant concentration (mg/L), pH, experimental temperature (°C), and light intensity (mW/cm²). The output variable (Y) was the degradation rate constant (k). This value was converted into -log (k) to transform tiny values of k into a more manageable scale for visualization⁴⁴.

Prior to modeling, preprocessing steps were performed. These included handling missing values and scaling features using StandardScaler from Scikit-learn to normalize the range and improve model convergence⁴². The dataset was divided into a training set (75%) and a testing set (25%). The training data were used to develop the machine learning model, while the testing data were used to evaluate its predictive performance. Model accuracy was assessed using standard statistical metrics, including the coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE), as presented in Eqs. (1)–(3). Model parameters were optimized using the gradient boosting approach, where each successive tree is trained to minimize the residual error from the previous iteration. In addition, the Shapley Additive Explanations (SHAP) method was applied to interpret the model by quantifying the contribution and importance of each input feature in predicting the degradation rate constant. The evaluation metrics the equation as follow:

1

2

3

Where: experimental rate constant value, predicted rate constant value generated by the CatBoost model, : the mean value of experimental rate constants in the dataset in terms of -log(k) and : the total number of data points in the testing or training set.

Photo catalytic activity measurements

The photocatalytic activity was studied with the model pollutants methylene blue (MB), tetracycline (TC) and rhodamine B (RhB). In this study, we adjusted the reaction vessel (250 ml reaction vessel) is 10 cm and Cary 60 UV-Vis Spectrophotometer used for all experiments. In this process, a 50 mg sample was added to 100 ml of methylene blue (10 mg/L) solution. To establish adsorption-desorption equilibrium was magnetically stirred in the dark for 30 min; subsequently, 5 ml of samples were withdrawn at time intervals of 0, 6, 12, 18, 24, and 30 min, respectively, under irradiation under a UV lamp (300 W) with continuous stirring. Similarly, 40 mg was introduced into 50 ml of RhB (10 mg/L) solution, and adsorption-desorption was established for 45 min. Then 3 ml of sample was taken at the time intervals of 0, 10, 20, 30, 40, and 50 min. In the same experimental condition 50 mg catalyst was added into 100 ml of TC (10 mg/L) solution, and 5 ml of sample was withdraw at time interval of 0, 10, 20, 30, 40, 50, and 60 min. Finally, each sample studied at different time intervals is analyzed by a Cary 60 UV-Vis Spectrophotometer.

Result and discussion

Model performance comparison

The ML models considered in this work such as ANN, RF, SVR, CatBoost, and XGBoost models were trained and tested based on the variety of parameters that affect the photodegradation performance, i.e., types of pollutant, particle size, surface area, light intensity, TiO₂ dosage, initial concentration of pollutant, experimental temperature, and the solution of pH. They were evaluated by R², RMSE, and MAE, which are summarized in supplementary information Table S1. Scatter plots comparing predicted vs. actual degradation efficiencies for each model are shown in Fig. 2. The CatBoost model exhibits a very good match between the training and testing sets with R² values 0.9963 and 0.9044 in Fig. 2a respectively. The model predicts reasonably well the experimental values. The testing set performance is still strong. The optimal results from model training and testing indicate strong generalization ability. Figure 2b training and testing set with a very high R² of 0.9960 and 0.9022 respectively, XGBoost shows a great fit to the training data. Strong prediction potential on the trained data is indicated by the close clustering of the data points around the ideal line. Training and testing set in Fig. 2c, the ANN model’s R² value of 0.9715 and 0.8743 respectively, indicates a good fit, showing good agreement with the experimental data. Figure 2d Training and testing of RF model, it is R² of 0.9400 and 0.8152 respectively, set for testing indicates a considerable decline in performance on the testing set.

Fig. 2.

Regression plots of experimental versus predicted photodegradation rate constant for (a) CatBoost, (b) XGBoost, (c) ANN, (d) RF, and (e) SVR models, (f) R² values for different models comparisons.

Feature importance analysis

The model’s performances were determined, and its training and testing R² values were compared in Fig. 3b. The CatBoost model exhibited very good generalization to unknown data and strong prediction capability. A feature importance CatBoost used to forecast a rate of reaction constant is shown in Fig. 3a. The most significant features are shown according to the CatBoost. concentration of pollutant, light intensity, temperature, catalyst, particle size, surface area, and pH were identified as the most significant features respectively. In addition, the dataset includes multiple types of pollutants like methylene blue (MB), Rhodamine B (RhB), phenol, and others. In Fig. 3a, pollutant–phenol appears as the 8th most important feature; it is one of the categorical features which refers to whether the target pollutant belongs to the phenolic class of compounds, meaning it contains a phenol functional group (an aromatic ring bonded to a hydroxyl group, –OH). In the dataset, this feature is used as a categorical indicator to distinguish phenolic pollutants from non-phenolic compounds, as phenolic structures can influence adsorption behavior and photocatalytic degradation efficiency.

Fig. 3.

(a) Importance order of input features of CatBoost, and (b) the comparison of trained machine learning models on R² test set.

The CatBoost model’s SHAP (SHapley Additive exPlanations) summary plot, shown in Fig. 4a, offers a more thorough understanding of how each feature affects the model’s output. Meaning: Every row denotes a feature, with the most significant features at the top, and every dot represents a dataset instance. The SHAP value for that feature and instance is indicated by the dot’s location on the x-axis. When a feature has a positive SHAP value, the model’s output is increased; when it has a negative value, it is decreased. The original feature value is indicated by the color of the dot, which is blue for low values and red for high values.

Fig. 4.

(a) SHAP value, positive and negative impacts of each input of CatBoost of k. and (b) Pearson correlation matrix depicting correlation of all input features with degradation rate (k).

The most important characteristics seem to be concentration, temperature, light of intensity, particle size, surface area, and catalyst. The model output tends to be greater for high pollutant concentration (mg/L) values (red dots on the right) and lower for low values (blue dots on the left). Conversely, low temperature (°C) values tend to drive the output higher, while high values tend to drive it lower. Both high and low values have an impact on surface area (m²/g), indicating a mixed effect. The top features have a greater overall influence than features like pH and different types of pollutants.

The Pearson correlation coefficients between each pair of features are shown in Fig. 4b Pearson Correlation Matrix of Features. Color Scale: Lighter hues (yellow/orange) denote weaker connections, while red denotes a positive correlation and blue a negative correlation. The range of values extends from Blue (-0.6) to dark red (0.8). When a feature is perfectly correlated with itself, the diagonal is dark red. Particle size (nm) and light intensity (mW/cm²), as well as surface area (m²/g) and dosage (g/L), exhibit strong positive correlations (dark red). Strong Negative Correlations (Dark blue): Surface area (m²/g) and pollutant concentration (mg/L); particle size (nm) and surface area (m²/g): pH and dosage (g/L): -log(k) min^− 1 and pH. Lighter shades imply weak to moderate relationships between many features. Generally speaking, Fig. 4a shows which features are most crucial for the model’s predictions and how their values affect the output, whereas Fig. 4b shows how these features are related to one another and interdependent. In general, the results of the SHAP analysis in our study indicate that catalyst dosage, light intensity, and pollutant concentration are the most influential parameters affecting the photocatalytic degradation rate constant (k).

Comparative analysis

A comparison of the predictive strengths of various machine learning models in different studies for the photocatalytic degradation demonstrated in Table 1. The lower test set R² (0.9044) in our study compared to previous study ref. 46 and 43 R² (0.991 and 0.997 respectively) is basically due to the higher complexity and diversity of our dataset. From Table 1, cited studies such as ref. 46, 43, and 48 their models trained on a single pollutant. In contrast, our model predicts the degradation of multiple pollutants. The cited study ref. 49 with multiple pollutants and they reported a test R² of 0.90. Our model demonstrates a slightly higher test R² (0.9044). The other cited study ref. 43 uses 1200 data points with a single pollutant, whereas our study utilizes 150 points with multiple pollutants. The lower dataset and multiple pollutants are challenging in the regression task. The CatBoost model in this study R² value above 0.9044 under this condition.

Table 1.

Comparison of the predictive strengths of various ML models for the photocatalytic degradation of numerous organic pollutants.

No. pollutant	ML models	No. Input	Best model	Photocatalyst	No.data points	Model performance				Ref.
						R 2		MAE	RMSE
						Training	Testing
1	RSM, ANN-GA and ANN-PSO	4	ANN-GA	Mn-doped Fe/rGO	30	0.994	-	-	0.0223	45
1	AB, Bagging, CB, DT, ET, GB, HGB, LGBM, RF and XGB	4	HGB	CuWO₄@TiO₂	189	0.999	0.991	0.354	0.454	46
1	Bagging, CB, DT, ET, GB, HGB, LGBM, ANN and LightLSTM	10	CB	BiFeO3	1200	0.999	0.997	0.64	1.34	43
2	DT, RF, ET	4	ET	MgFeAl-LTH	40	0.997	-	5.11	11.42	47
1	CatBoost, LightGBM, XGBoost, AdaBoost, GBDT, ET, DT and RF	7	CatBoost	MIL-88 A	374	0.99	0.98	-	2.7824	48
18	KNN and RF	7	RF	MgSnO3	597	0.994	0.900	0.09	0.12	49
54	RF, ANN, CatBoost, XGBoost and SVR	8	CatBoost	TiO2	150	0.9963	0.9044	0.1052	0.1318	This Study

Optimized ML model & photocatalytic conditions

In this study, the prediction of the photocatalytic degradation rate constant (k) was performed using the CatBoost Regressor, a gradient boosting algorithm based on an ensemble of decision trees. The model iteratively constructs sequential trees, where each new tree is trained to minimize the residual error of the previous ensemble by optimizing a mean squared error (MSE) loss function. The final prediction is obtained as the additive combination of all decision trees in the ensemble. Model training was conducted using 75% of the dataset, while 25% was reserved for testing, and model robustness was further assessed using five-fold cross-validation. Key hyperparameters were optimized with max_depth = 6, iterations = 500, and learning_rate = 0.1, while R² was used as the primary scoring metric. The interpretability of the trained model was evaluated using Shapley Additive Explanations (SHAP) to quantify the contribution and relative importance of each input feature influencing the photocatalytic degradation rate constant. The optimized experimental parameters were methylene blue (MB) concentration of 10 mg/L, TiO₂ particle size of 20 nm, catalyst surface area of 65 m²/g, TiO₂ dose of 0.5 g/L, pH of 7, experimental temperature of 20 °C, and light intensity of 50 mW/cm². The main output variable (Y) for model optimization was the degradation rate constant (k). Among them, the CatBoost machine learning model predicted a degradation rate constant (k) of 0.1383 min.

Limitations and practical considerations of ML models

The developed machine learning models demonstrate high prediction within the scope of the training dataset and must acknowledge some limitations to contextualize test practical considerations. The ML models particularly the high performing CatBoost (categorical boosting) is highly efficient at pattern recognition and categorical feature handling. The dataset was organized from diverse literature source; maybe it occurred experimental noise due to variations in reactor geometry, intensity of light measurement techniques, and catalyst preparation methods across different laboratories. A critical limitation is that the machine learning algorithms are primarily trained on data derived from synthetic solution (distilled water with pollutant). The performance of ML model like CatBoost model is determined based on the quality of the literature source data. In the field of photocatalysis, there is a lack of reporting the key features like intensity of light, surface area of catalyst, and string speed.

photocatalytic activity

The photocatalytic degradation of methylene blue (MB), rhodamine B (RhB) and tetracycline (TC) was studied using a pure TiO₂ catalyst. The absorbance spectra of MB, RhB, and TC degradation clearly show a decrease in absorbance intensity over time, indicating the degradation of the dye in Fig. 5.

Fig. 5.

Photocatalytic degradation analysis of Methylene Blue (MB), Rhodamine B (RhB), and Tetracycline (TC). Figure 5 (a, d, g) shows absorbance, Fig. 5 (b, e, h) displays concentration degradation, and Fig. 5 (c, f, i) represents the reaction rate constants for MB, RhB, and TC, respectively.

The TiO₂ catalyst’s effective photocatalytic breakdown of methylene blue (MB) is shown in Fig. 5a. The absorbance of MB peaks at 665 nm dramatically decreases with increasing irradiation period, as can be seen in the UV-Vis spectra. The concentration degradation curves (Fig. 5b), which demonstrate a high MB clearance effectiveness of 98.34% within 30 min, provide additional support for this, while a little reduction occurs without TiO₂ due to photolysis. In excellent agreement with the machine learning model’s predicted value of 0.1383 min⁻¹, the pseudo-first-order kinetic plot (Fig. 5c) shows that the degradation of this model has an R² value of 0.99, resulting in a linear response rate constant (k) of roughly 0.1278 min⁻¹.

The RhB peak, which is shown in Fig. 5d at approximately 550 nm, decreasing with increasing time (from − 45 min to 50 min). Figure 5e displays the normalized concentration of RhB (C_t/C₀) as a function of time. C_t represents the concentration at time t, and C₀ represents the initial concentration. It shows excellent deteriorating efficiency, with nearly complete diminished in 50 min. Figure 5f shows pseudo-first-order kinetics, which are crucial for figuring out reaction rate. The degradation R² value of this kinetics model is 0.96, and its degradation rate constant (k) is around 0.106 min^− 1. Meanwhile, the machine learning model’s predicted value of 0.098 min⁻¹. Tetracycline (TC) is photocatalytic degraded using a TiO₂ catalyst, as seen in Fig. 4(g-i), taken together. The peak of tetracycline in Fig. 5g degraded a gradual drop in its UV-Vis absorbance around at 358 nm with increasing of time. The normalized concentration of TC in Fig. 5h, which is quick degraded with TiO₂ under UV light, while a slight reduction occurs without TiO₂ due to photolysis in Fig. 5i. The TiO₂ catalyst degradation also follows pseudo-first-order kinetics with reaction rate constant (k) is 0.0307 min^− 1, and the machine learning model’s predicted value of 0.0461 min⁻¹.

A TiO₂ catalyst demonstrated highly effective photocatalytic degradation of methylene blue (MB), rhodamine B (RhB), and tetracycline (TC). All of the three models of pollutants exhibited rapid degradation under UV irradiation with TiO₂. The degradation processes consistently followed pseudo-first-order kinetics, with a high degradation rate constant (k) of around 0.1278 min^[-1(R² = 0.99) for MB and a rate constant (k) of approximately 0.1063 min^[-1(R² = 0.98) for RhB but exhibited a lower reaction rate constant (k) of 0.0307 min^[-1(R² = 0.89) for TC. For MB, preliminary observations and literature reports indicate that its degradation under TiO₂ photocatalysis proceeds more rapidly due to its favorable adsorption on the catalyst surface and strong light absorption characteristics compered to TC and RhB pollutants. Therefore, shorter sampling intervals were employed to accurately capture the rapid concentration changes and avoid loss of kinetic information during the early reaction stages.

The effect of catalyst loading on the degradation rate constant (k) is illustrated in Fig. 6a. Increasing the TiO₂ dosage from 25 mg to 75 mg enhanced the degradation rate, with higher k values observed at 50 mg and 75 mg compared with 25 mg. This behavior is commonly reported in photocatalytic systems and can be attributed to the increased number of available active sites and enhanced generation of reactive oxygen species as the catalyst amount increases. However, further increasing the catalyst loading to 100 mg and 150 mg resulted in a decrease in the degradation rate constant, suggesting the presence of an optimal catalyst loading. At higher catalyst dosages, particle aggregation, increased turbidity, and light scattering may reduce photon penetration and limit the effective utilization of the catalyst surface, thereby decreasing the photocatalytic efficiency. Figure 6b compares the reaction rate constants obtained experimentally with those predicted by the machine learning (ML) model. The experimental k values were calculated from the pseudo-first-order kinetic plots derived from the degradation data shown in Fig. 6a. Overall, the ML-predicted values closely follow the experimental trend across the studied catalyst loading range, indicating that the model successfully captures the general relationship between catalyst dosage and photocatalytic activity. Similarly, the influence of pollutant concentration on the degradation kinetics is presented in Fig. 6d. The results show that the reaction rate constant decreases as the initial pollutant concentration increases. This phenomenon is widely observed in photocatalytic processes and can be explained by several factors, including increased competition for active sites on the catalyst surface, reduced light penetration due to higher solution absorbance, and the accumulation of intermediate products that may inhibit active sites.

Fig. 6.

Photocatalytic degradation analysis of methylene blue using TiO₂ nanoparticles: Fig. 6 (a) & (c) Pseudo-first-order kinetic plots showing for various catalyst loadings and concentration, Fig. 6 (b) & (d) Comparison of reaction rate constants (k) of experimental and ML model predicted values at varying catalyst loading and concentration respectively.

The comparison between ML-predicted and experimental reaction rate constants at different pollutant concentrations is shown in Fig. 6c. While the model reproduces the overall decreasing trend with increasing concentration, minor deviations are observed at higher concentration levels. These discrepancies may arise from the limited number of high-concentration data points available in the training dataset and the inherent variability of experimental conditions across different literature sources used for data compilation. Additionally, photocatalytic reactions often exhibit complex non-linear behavior at higher pollutant concentrations due to mass transfer limitations and photon attenuation effects, which may not be fully captured by the model. Despite these deviations, the strong agreement between the predicted and experimental values and the consistent reproduction of the overall trends demonstrate the robustness of the ML model in predicting the photocatalytic degradation kinetics of TiO₂-based systems.

Conclusion

This study demonstrates the potential of machine learning to predict and optimize the photocatalytic degradation rate constant of Titanium dioxide systems for multiple pollutants. A structured dataset of 150 experimental data points was compiled from literature, and several models were trained and evaluated using standard metrics (R², MAE, and RMSE), with the CatBoost model showing the best predictive performance. Feature importance and Shapley Additive Explanations (SHAP) analysis identified catalyst dosage, light intensity, and pollutant concentration as the most influential factors governing photocatalytic efficiency. Experimental validation using Methylene blue confirmed the reliability of the optimized model, as the predicted degradation rate constant (0.1383 min⁻¹) closely matching the measured value (0.1278 min⁻¹). Although the dataset was compiled from heterogeneous literature sources and limited parameter ranges, the results highlight the potential of integrating machine learning with experimental validation as a cost-effective strategy to guide the design and optimization of photocatalytic systems for environmental remediation.

Electronic Supplementary Material

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Author contributions

Moges Mitku: Writing-original draft, Methodology; Investigation; Analysis. Yunxiang Zhang: Conceptualization; Methodology; Validation of results; Analysis. Getachew G. Kebede: Supervision; Conceptualization; Methodology; Validation of results; Analysis. Yuxin Zhang: Data curation; Validation of results; Analysis. Wang Shou: Data curation; Validation of results; Analysis. Qinfang Zhang: Conceptualization; Supervision; Data curation; Validation of results; Revie and editing; Approved the final manuscript. Fekadu Gashaw Hone: Conceptualization; Supervision; Data curation; Validation of results; Revie and editing; Approved the final manuscript. All authors reviewed the manuscript.

Data availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.