A machine learning-based pfas adsorption optimization strategy determination method

Abstract

This invention discloses a machine learning-based method for determining PFAS adsorption optimization strategies, comprising: constructing a multidimensional dataset for adsorbing PFAS in water using a carrier; establishing an adsorption capacity prediction model; identifying multiple dominant factors affecting PFAS adsorption by the carrier; generating various combinations of all-factor parameters from the multiple dominant factors according to a set step size; and selecting at least one combination of all-factor parameters that maximizes the adsorption capacity. This at least one combination of all-factor parameters is used to guide carrier preparation and / or adsorption condition optimization. This invention establishes an interpretable machine learning-optimization fusion framework, realizing the intelligent transformation from adsorption performance prediction to structural design, providing a theoretical basis for the targeted design of PFAS removal materials, and also providing a generalizable research paradigm for data-driven optimization of complex adsorption systems.

Description

Technical Field

[0001] This invention relates to the fields of machine learning and materials technology, specifically to a method for determining PFAS adsorption optimization strategies based on machine learning. Background Technology

[0002] Per- and polyfluoroalkyl substances (PFAS) are a large class of synthetic chemical molecules containing multiple C–F bonds. These C–F bonds endow them with extremely low surface tension, excellent anti-blocking properties, high thermal stability, and chemical stability, thus leading to their widespread use in various industrial applications, including papermaking, fire-fighting foam, food packaging, and cookware materials. However, this also makes them difficult to degrade in the environment, exhibiting significant persistence and bioaccumulation. The water pollution caused by their high persistence has become a serious environmental challenge.

[0003] Currently, PFASs have caused pollution of drinking water, livestock, and agricultural products worldwide, and there is evidence that long-term exposure can have negative effects on human health. In response, existing technologies use methods such as adsorption to remove PFASs from water. However, although traditional adsorbents such as activated carbon are widely used, their adsorption capacity for short-chain PFASs is weak, the time required to reach equilibrium is long, and they are easily interfered with by coexisting organic matter in complex water conditions, which limits their practical effectiveness.

[0004] Biochar is considered a promising sustainable adsorbent material for PFAS remediation. The physicochemical properties of biochar are primarily constrained by its synthesis conditions, which directly affect its adsorption performance. However, numerous factors influence the process, and relying on traditional trial-and-error methods to optimize the preparation process is not only costly but also inefficient.

[0005] Therefore, there is an urgent need for a convenient and efficient method to evaluate the adsorption effect of PFAS and optimize the adsorption strategy to assist in the screening of PFAS adsorption experiments. Summary of the Invention

[0006] To address the aforementioned problems, this invention provides a method for determining PFAS adsorption optimization strategies based on machine learning.

[0007] A machine learning-based method for determining PFAS adsorption optimization strategies includes the following steps: A multidimensional dataset for adsorbing PFAS in water using a carrier is constructed; the multidimensional dataset includes the physicochemical properties and preparation parameters of the carrier, molecular characteristics of PFAS and adsorption condition parameters. An adsorption capacity prediction model is established; the input of the adsorption capacity prediction model is the physicochemical properties and preparation parameters of the support, the molecular characteristics of PFAS and the adsorption condition parameters, and the output is the adsorption capacity of PFAS adsorbed by the support. Based on the adsorption capacity prediction model, importance analysis and SHAP value interpretation of the input of the adsorption capacity prediction model were performed to identify several dominant factors affecting the adsorption of PFAS on the carrier. Multiple dominant factors are used to generate various combinations of all-factor parameters according to a set step size, and these combinations are input into the adsorption capacity prediction model for prediction. The prediction results are then sorted, and at least one combination of all-factor parameters that maximizes the adsorption capacity is selected from the prediction results. This at least one combination of all-factor parameters is used to guide the preparation of the support and / or the optimization of adsorption conditions.

[0008] Note: The above method integrates multi-dimensional data such as carrier properties, PFAS characteristics and adsorption conditions to construct a machine learning prediction model, which not only achieves efficient and accurate prediction of adsorption capacity, but also introduces SHAP interpretability analysis to identify dominant factors. Then, through system simulation and optimization of full factor parameter combination, it replaces the traditional trial and error mode, which can quickly and accurately guide the preparation of carrier and the control of adsorption conditions, and significantly improves the design efficiency and optimization effect of PFAS adsorption materials.

[0009] Furthermore, the adsorption capacity prediction model was selected from machine learning models such as XGBoost, Random Forest, Support Vector Machine, LightGBM, and Artificial Neural Network; the selection method was as follows: The multidimensional dataset is divided into a training set and a test set; Each machine learning model is trained on the training set, and hyperparameters are tuned by combining cross-validation with grid search. The predictive performance of each machine learning model after tuning is evaluated on the test set, and the evaluation metrics include the coefficient of determination and the root mean square error. By comparing the evaluation metrics of various machine learning models, the model with the highest coefficient of determination and / or the lowest root mean square error is selected as the adsorption capacity prediction model.

[0010] Note: The above method utilizes multiple machine learning models (such as XGBoost, random forest, neural networks, etc.) for systematic competition and screening, and combines cross-validation and grid search to fine-tune hyperparameters. This ensures that the final selected adsorption capacity prediction model has both high prediction accuracy and strong generalization ability, thereby avoiding the bias or overfitting that may occur when relying on a single model. It significantly improves the reliability of the model under complex multidimensional data and lays a solid data-driven foundation for subsequent factor analysis and optimization.

[0011] Furthermore, the carrier is one of biochar, activated carbon, carbon nanotubes, graphene, zeolite, montmorillonite, kaolin, and ion exchange resin.

[0012] Note: This method, through a unified multidimensional data framework and machine learning model, can predict and optimize the adsorption performance of carriers with different physicochemical properties.

[0013] Furthermore, the dominant factors include functional group type, initial PFAS concentration, specific surface area (BET), pH value, and Zeta potential.

[0014] Note: By quantifying and synergistically optimizing these measurable and controllable core variables, this strategy can transcend traditional empirical trial and error and directly intervene precisely in key aspects of the adsorption mechanism.

[0015] Furthermore, the importance analysis and SHAP value interpretation include: The substitution importance algorithm is used to calculate the relative importance score of each input to the adsorption capacity prediction result, and to identify several candidate dominant factors with the highest importance scores. The marginal contribution of each input to the prediction result of a single adsorption capacity is calculated based on the SHAP value, and a SHAP dependency graph and a force graph are generated. The multiple dominant factors are determined by combining multiple candidate dominant factors with the SHAP dependency graph and the force graph.

[0016] Note: The above method, by integrating substitution importance analysis and SHAP value interpretation, can not only robustly and reliably identify the key factors that truly dominate adsorption performance, but also greatly enhance the transparency and interpretability of the model, effectively avoiding bias or misjudgment that may be caused by a single analysis method.

[0017] Furthermore, the generation of multiple full-factor parameter combinations from multiple dominant factors according to a set step size includes: Define the feasible range and optimization step size for each dominant factor; Within the feasible range, the dominant factors are discretized according to the optimization step size to generate level values ​​for each dominant factor. The various full-factor parameter combinations are generated by combining all levels of each dominant factor.

[0018] Note: The above method systematically discretizes and combines all factors within a pre-defined feasible range of key dominant factors, abandoning the traditional local trial-and-error model that relies on expert experience or single-factor rotation. It can exhaustively enumerate and evaluate all possible parameter combinations in a virtual space, ensuring a comprehensive and thorough exploration of the multidimensional parameter space.

[0019] Furthermore, after generating the various combinations of full-factor parameters and before inputting them into the adsorption capacity prediction model, the following steps are also included: Based on physicochemical constraints, the feasibility of various combinations of full-factor parameters is screened, and combinations that do not meet the constraints are eliminated. The physicochemical constraints include at least one of thermodynamic self-consistency constraints, surface charge-ion morphology coupling constraints, and pore size-molecular size matching constraints. Specifically, the thermodynamic self-consistency constraint is based on the physical compatibility of the carrier's preparation conditions and structural parameters, eliminating combinations of all-factor parameters that do not conform to the material formation rules. The pore size-molecular size matching constraint establishes the matching degree between the carrier's pore size distribution and the PFAS molecular size based on the PFAS molecular dynamics diameter, eliminating combinations of all-factor parameters whose pore size exceeds a preset range matching the target PFAS molecular size. The surface charge-ion morphology coupling constraint is based on the correlation between the pH value of the water and the Zeta potential of the carrier surface, combined with the acid dissociation constant pKa of the target PFAS, eliminating combinations of all-factor parameters where the surface charge polarity repels the PFAS ion morphology.

[0020] Explanation: The above method introduces constraints such as thermodynamic self-consistency, pore size-molecular size matching, and surface charge-ion morphology coupling to pre-screen the generated virtual parameter combinations. This effectively eliminates combinations that may be mathematically optimal but are physically infeasible, invalid, or violate fundamental mechanisms. This significantly improves the scientific rigor and practical operability of subsequent model predictions and optimization results, avoids a large amount of meaningless calculations, and substantially enhances the reliability and efficiency of the method.

[0021] Furthermore, after obtaining feasible combinations of all-factor parameters, the parameters are further screened using a dynamic adsorption-desorption cycle stability prediction model. Parameter combinations with an adsorption capacity decay rate >20% after three simulated adsorption-desorption cycles are eliminated. Based on support structure stability parameters, surface functional group bonding stability parameters, and PFAS desorption thermodynamic parameters, combinations of all-factor parameters with an adsorption capacity decay rate exceeding a preset threshold after multiple adsorption-desorption cycles are predicted and eliminated. The support structure stability parameters include pore wall thickness and mesoporosity; the surface functional group bonding stability parameters include pyrolysis temperature; and the PFAS desorption thermodynamic parameters include the binding energy between PFAS and the surface functional groups of the support.

[0022] Explanation: The above method constructs a predictive model based on multi-dimensional parameters such as structural stability, functional group bonding strength, and desorption thermodynamics. It also rigorously screens materials in the early design stage using quantitative indicators (such as decay rate > 20% and overall stability index ≤ 0.85), thereby pre-eliminating material schemes that, while exhibiting excellent initial adsorption performance, are prone to failure or regeneration in a virtual space. This significantly improves the engineering practicality and economics of the optimization strategy, and substantially reduces the risks and costs of subsequent experimental verification and process scale-up.

[0023] Furthermore, after screening for at least one combination of all-factor parameters that maximizes adsorption capacity, the following is also included: Centered on at least one combination of all-factor parameters, a multi-objective optimization function is constructed in the neighborhood space of the parameters of the combination of all-factor parameters, with the primary objective of maximizing adsorption capacity and the secondary objectives of one or more of the following: adsorption rate, selectivity index, regeneration efficiency, and economic cost. Using NSGA-II, MOEA / D, or multi-objective Bayesian optimization algorithms, Pareto front search is performed in the neighborhood space of the parameters to obtain the Pareto optimal solution set. Set the weight coefficients for each secondary objective, and select at least one optimal parameter combination from the Pareto optimal solution set.

[0024] Note: The above method constructs a multi-objective optimization function and adopts an advanced Pareto front search algorithm, which can systematically reveal and weigh the competitive and synergistic relationships between different performance indicators in the high-dimensional neighborhood near the optimal solution of the parameters, ensuring that the optimization results not only meet the technical indicators, but also have the feasibility and economy of practical application.

[0025] Furthermore, the method for guiding support preparation and / or optimizing adsorption conditions includes: Based on the physicochemical properties of the carrier and the preparation parameters in the selected combination of all-factor parameters, the process parameters for carrier preparation are determined. Based on the adsorption condition parameters in the selected combination of all factors, the adsorption operating conditions for treating PFAS-contaminated water bodies are determined. The adsorption operating conditions include the adsorbent dosage, solution pH value, and temperature parameters.

[0026] Note: The parameter combinations obtained above through machine learning and multi-objective optimization are themselves quantitative and executable guidelines, enabling researchers to directly carry out efficient targeted preparation and process debugging without having to go through a time-consuming trial and error process again.

[0027] Furthermore, it also includes building a feedback optimization mechanism: Carrier preparation and adsorption experiments were conducted according to the selected combination of all factor parameters to obtain real adsorption capacity data. The actual adsorption capacity data is compared with the predicted values ​​of the adsorption capacity prediction model to calculate the prediction deviation. When the prediction deviation exceeds a preset threshold, the actual adsorption capacity data is added to the multidimensional dataset to retrain and update the parameters of the adsorption capacity prediction model. Iteratively execute model prediction, experimental verification, and model update until the prediction deviation stabilizes within a preset threshold, thus completing feedback optimization.

[0028] Note: The above method significantly improves the long-term reliability and adaptability of the optimization strategy, ensuring its guiding value under different batches of materials or varying water quality conditions.

[0029] The beneficial effects of this invention are: This invention constructs an end-to-end intelligent design method that integrates data-driven prediction, mechanism analysis, global optimization, experimental verification, and feedback iteration. It reliably predicts performance using selected high-precision machine learning models (such as XGBoost) and reveals key dominant factors and their synergistic relationships, such as functional group type, specific surface area, and pH, through methods like SHAP. Combined with full factorial design and multi-objective optimization, it can systematically locate Pareto optimal solutions (such as the Top 50 optimal combinations obtained in the study) that simultaneously satisfy high adsorption capacity, excellent cycling stability, and cost-effectiveness within a broad parameter space. Finally, by directly mapping the optimal parameter combinations to executable preparation and process conditions, and supplementing this with a feedback mechanism for continuous self-improvement, it transforms the traditional experience-based trial-and-error process into a new paradigm for material development that is efficient, precise, interpretable, and continuously evolving, significantly accelerating the development and application of high-performance PFAS adsorbent materials. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the overall framework of the method according to an embodiment of the present invention; Figure 2 This is a Pearson correlation heatmap of parameters in the multidimensional dataset of this invention embodiment. The color intensity represents the Pearson correlation coefficient, with red indicating positive correlation and blue indicating negative correlation. Figure 3 This is a comparison chart of the determination coefficient values ​​predicted by various machine learning models in the embodiments of the present invention; Figure 4 This is a comparison chart of the root mean square error values ​​predicted by various machine learning models in the embodiments of the present invention; Figure 5 This is a schematic diagram showing the adsorption importance analysis of PFAS on biochar and the SAP value in the embodiments of the present invention; Figure 6 This is a scatter plot of the adsorption capacity predicted by the XGBoost adsorption capacity prediction model in this embodiment of the invention and the experimentally measured value. Figure 7 This is a PCA coverage analysis of the original dataset (Group A) and the combination of all factor parameters in the embodiments of this invention (Group B); a) is a PCA analysis based on material properties; b) is a PCA analysis based on the characteristics of biochar preparation and adsorption conditions. Figure 8 It is a comparison of the feature distribution between the primary biochar dataset and the top 1000 predicted combinations; Figure 9This is a comparison of the feature distribution between the primary biochar dataset and the top 1000 predicted combinations. Detailed Implementation

[0031] To further illustrate the methods and effects of this invention, the technical solution of this invention will be clearly and completely described below in conjunction with experiments.

[0032] Utilizing machine learning (ML) to predict the adsorption performance of biochar for per- and polyfluoroalkyl substances (PFAS) is a promising research area, primarily because there is a growing understanding of how characteristic variables, reaction conditions, and biochar properties affect removal efficiency. PFAS, due to their high persistence, have become a serious environmental challenge causing water pollution. Biochar, as a low-cost adsorbent, shows great potential for PFAS removal; however, its adsorption performance is influenced by a variety of parameters and the mechanisms are complex.

[0033] Example 1: A method for determining PFAS adsorption optimization strategy based on machine learning, such as Figure 1 As shown, it includes the following steps: S101. Construct a multidimensional dataset for adsorbing PFAS in water using a carrier; the multidimensional dataset includes the physicochemical properties and preparation parameters of the carrier, molecular characteristics of PFAS and adsorption condition parameters. The carrier is one of biochar, activated carbon, carbon nanotubes, graphene, zeolite, montmorillonite, kaolin, and ion exchange resin; in this embodiment, biochar is used, but in some embodiments, other substances mentioned above can be used as carriers for adsorption. For example, to construct a machine learning model suitable for PFAS adsorption prediction, this embodiment screened 40 relevant studies published in the past 20 years. A total of 193 PFAS compounds were ultimately selected from these papers as the training and testing dataset for the artificial intelligence model. The collected data was used to analyze the adsorption capacity of different biochar adsorbents to determine the most suitable adsorbent material. During the literature search, a systematic search was conducted in the Elsevier Scopus and Google Scholar academic databases using keywords such as perfluorooctanoic acid, perfluorooctane sulfonic acid, removal, biochar, and adsorption.

[0034] As shown in Table 1 below, this multidimensional dataset contains nearly 3,000 data points, covering the adsorption of various perfluorinated and polyfluoroalkyl substances (PFAS) by biochar produced under different conditions.

[0035] It mainly includes the following three categories: (1) Properties of biochar: biochar type, raw material source, pyrolysis temperature, specific surface area (m²) 2The average pore size (nm), zeta potential (mV), and O / C ratio (%) are also included. (2) Properties of PFAS: molecular weight, chain length and functional group characteristics; (3) Adsorption conditions: pH value, initial PFAS concentration (mg / L), adsorbent dosage (g / L), and modification method. The output variable is the adsorption capacity of biochar for PFAS (Qe, mg / g). The calculation formula is as follows: Among them, C0 and C e The initial and equilibrium concentrations of the adsorbate are (mg / L), respectively; V is the solution volume (L); and m is the adsorbent mass (g).

[0036] Table 1 Data Acquisition Parameters

[0037] Before modeling, the dataset was cleaned and outliers were removed. All features were standardized using the StandardScaler method to ensure equal weighting during model training. By using variables related to the synthesis process, such as raw material source, carbon and oxygen content, and process temperature, as model inputs, a rapid mapping relationship from preparation conditions to the physicochemical properties of biochar can be constructed.

[0038] S102. Establish an adsorption capacity prediction model; the input of the adsorption capacity prediction model is the physicochemical properties and preparation parameters of the support, the molecular characteristics of PFAS and the adsorption condition parameters, and the output is the adsorption capacity of PFAS adsorbed by the support. The adsorption capacity prediction model was selected from machine learning models such as XGBoost, Random Forest, Support Vector Machine, LightGBM, and Artificial Neural Network; the selection method was as follows: The multidimensional dataset is divided into a training set and a test set; Each machine learning model is trained on the training set, and hyperparameters are tuned by combining cross-validation with grid search. The predictive performance of each machine learning model after tuning is evaluated on the test set, and the evaluation metrics include the coefficient of determination and the root mean square error. By comparing the evaluation metrics of various machine learning models, the model with the highest coefficient of determination and / or the lowest root mean square error is selected as the adsorption capacity prediction model.

[0039] For example: The algorithms and functions used in this embodiment are all based on Python, and five commonly used machine learning algorithms are employed for regression prediction: XGBoost (Extreme Gradient Boosting), Random Forest (RF), LightGBM, Support Vector Machine (SVM), and Artificial Neural Network (ANN). These models were chosen because they have proven effective in handling complex nonlinear relationships in environmental data. The dataset was randomly divided into a training set (80%) for model development and a test set (20%) for independent evaluation. The root mean square error (RMSE) and coefficient of determination (R²) were used to measure the regressions. 2 To evaluate model performance, and to prevent overfitting and find the optimal model configuration to accurately characterize the complex and highly nonlinear mapping between biochar properties and PFAS adsorption performance, hyperparameter tuning was performed on each model using a 5-fold cross-validation grid search based on the training set. Ensemble learning methods, such as Randomized Randomized (RF), construct multiple decision trees and integrate their prediction results, possessing good generalization performance and intuitive interpretation of feature importance, making them classic and robust nonlinear modeling tools. LightGBM, based on gradient unilateral sampling and mutually exclusive feature binding techniques, significantly improves model training efficiency while maintaining high prediction accuracy, making it particularly suitable for rapid modeling of large-scale datasets. The SVM algorithm maps data to a high-dimensional feature space through kernel functions to find the optimal regression hyperplane, offering unique advantages in handling small samples and high-dimensional nonlinear problems. To further explore the potential complex nonlinear relationships between variables, the multi-layered structure of Anonymous Networks (ANNs) can simulate the connection patterns of neurons in the human brain, possessing powerful feature abstraction and nonlinear fitting capabilities, providing a new modeling perspective for analyzing the biochar adsorption mechanism. XGBoost is a scalable machine learning method based on the gradient boosting framework. It improves prediction performance by integrating multiple weak learners (decision trees) to build strong learners. The modeling process is as follows: First, the dataset is divided into training and test sets according to a preset ratio. Then, feature engineering is performed, including encoding categorical variables, standardizing and scaling continuous features, and imputing missing values. It is important to emphasize that all feature transformers are fitted only to the training set to ensure that data leakage is completely avoided. The hyperparameter optimization stage then begins, with common methods including grid search, random search, and Bayesian optimization.

[0040] The results are as follows Figure 3 , Figure 4 As shown, the results demonstrate that the XGBoost algorithm has significant advantages, achieving the highest R-value. 2The highest RMSE value was 0.8882, and the lowest RMSE value was 47.1808. This superior performance is attributed to XGBoost's inherent ability to handle complex nonlinear relationships through its gradient boosting decision tree architecture. Its built-in regularization techniques—L1 (Lasso) regularization and L2 (Ridge) regularization—effectively mitigate the risk of overfitting, thereby enhancing its generalization ability to unknown data. Another ensemble method based on bagging, the Random Forest model, performed reasonably well but was slightly inferior. This slight difference may stem from the fact that RF tends to build fully grown trees, which have a larger variance, and is not as well optimized as XGBoost's sequential, error-corrected tree-building method. Therefore, the XGBoost algorithm was ultimately used to study the adsorption capacity of different biochar adsorbents for PFAS. As an efficient ensemble learning method, this algorithm is particularly friendly to sparse feature data. It has advantages such as fast training speed and strong anti-overfitting ability, and is especially suitable for the limited sample data scenario used in this study. In addition, the algorithm can directly handle missing values ​​without imputation preprocessing, a characteristic that makes it widely applicable in classification and regression tasks. Considering the objectives and data scale of this study, it is not necessary to rely on the large-scale data foundation required for deep models. ANN exhibits moderate predictive power. While its performance is strong, it may be limited by the current dataset size, typically requiring a large amount of data to optimize its numerous parameters and avoid overfitting. A larger dataset may unleash its full potential for this task. Conversely, SVM yields the least ideal results. The suboptimal performance of SVM suggests that the decision boundary between input features and adsorption capacity can be highly nonlinear, and the chosen kernel function is less effective than tree-based ensemble methods in capturing this complexity. This comparative analysis unequivocally identifies XGBoost as the most robust and accurate predictive framework for simulating PFAS adsorption on biochar given existing data and feature sets. Although this model demonstrates good performance in PFAS adsorption prediction, it still has certain limitations: firstly, it relies on known functional groups and structural parameters, limiting its predictive ability for adsorbents with unreported parameters; secondly, the current model is mainly applicable to neutral or weakly ionized PFAS, and electrostatic descriptors are still needed to expand the model's applicability for strongly ionized PFAS adsorption prediction.

[0041] S103. Based on the adsorption capacity prediction model, the importance of the input to the adsorption capacity prediction model and the interpretation of the SHAP value are performed to identify several dominant factors affecting the adsorption of PFAS on the carrier. The dominant factors include functional group type, initial PFAS concentration, specific surface area (BET), pH value, and zeta potential.

[0042] The importance analysis and SHAP value interpretation include: The substitution importance algorithm is used to calculate the relative importance score of each input to the adsorption capacity prediction result, and to identify several candidate dominant factors with the highest importance scores. The marginal contribution of each input to the prediction result of a single adsorption capacity is calculated based on the SHAP value, and a SHAP dependency graph and a force graph are generated. The multiple dominant factors are determined by combining multiple candidate dominant factors with the SHAP dependency graph and the force graph.

[0043] For example, the results are as follows Figure 5 As shown, this study extracted feature importance from the optimized XGBoost model to reveal the relative contribution of each descriptor, thereby clarifying the dominant factors. Further SHAP value analysis was used to evaluate the local influence of each feature. The SHAP analysis results showed slight differences: these differences are attributed to variations in calculation mechanisms. Firstly, functional groups stood out as the most important feature, confirming their central role in the adsorption process. Different functional groups significantly affect the polarity, hydrogen bond donor-acceptor capacity, and charge distribution of the material, thus altering the binding energy of PFAS molecules at the interface. Previous studies, using density functional theory calculations, have shown that the adsorption energies of C=O functional groups for PFOS and PFOA are -19.9 kcal·mol⁻¹. -1 and -15.9 kcal·mol -1 The value of is significantly higher than that of –COOH and –OH, indicating that it has the best potential to form hydrogen bonds or undergo coordination with the polar head groups of PFAS molecules. The machine learning model in this study further confirms that the contribution of functional groups exceeds that of traditional structural parameters, highlighting the key role of surface chemistry in determining adsorption affinity and selectivity.

[0044] The initial concentration ranks second in importance, indicating that the adsorption capacity of PFAS is highly dependent on the solution concentration gradient. A higher initial concentration can increase the adsorption driving force and molecular collision frequency, thereby increasing the loading per unit mass of biochar, which is consistent with the typical Langmuir and Freundlich adsorption isotherms. Furthermore, the high weight of this feature suggests that the model not only learns material properties but also successfully captures the external control effect of system conditions on adsorption behavior. Modification methods are highly important, indicating that surface chemical regulation is a key means to influence adsorption performance. For example, Fe loading often enhances the capture efficiency of short-chain PFAS through electrostatic adsorption and coordination reactions. The essence of modification is to change the interaction energy between PFAS and adsorbent by redistributing surface charge and polarity, thereby achieving structural regulation of adsorption performance. Compared to the global feature importance, the SHAP value... Figure 5The graph provides a detailed breakdown of the impact of each feature on the prediction of a single sample, showing whether each feature has a positive or negative effect on the model output. The initial PFAS concentration and the modification method show significant contributions in the SHAP value plot, with their SHAP values ​​deviating significantly from zero, and the level of the feature value has a significant impact on the prediction results. For example, the initial PFAS concentration has a large SHAP value in the graph, and most samples are in the red area, indicating that this feature has a significant positive impact on the prediction results at high concentrations.

[0045] The high importance of pH and zeta potential further emphasizes the crucial role of charge state in PFAS adsorption. Previous literature systematically investigated the effect of solution pH on adsorption performance, finding that the adsorption capacity of PFOS and PFOA reached its peak under acidic conditions (pH=3, 4), while it decreased sharply by over 90% under alkaline conditions (pH=11). pH determines the ionization form of PFAS and the charge state of the adsorbent surface: at low pH, surface amino groups are protonated, enhancing electrostatic attraction, while at high pH, ​​carboxyl groups are deprotonated, increasing negative repulsion. Zeta potential directly reflects the surface charge density and potential distribution; a more negative zeta potential usually indicates a higher number of surface oxygen functional groups, enhancing polarity but weakening the adsorption of anionic PFAS. This study further confirmed through machine learning that pH and zeta potential are not only adjustable experimental parameters but also direct manifestations of electrostatic interactions at the adsorption interface. Their high importance in the model verifies the universality and importance of this mechanism in actual adsorption environments. Therefore, the adsorption effect is optimal within a pH window of electrostatic complementarity.

[0046] The moderate importance of average pore size and BET specific surface area indicates that pore structure plays a supporting role in PFAS adsorption. BET reflects the available specific surface area of ​​the adsorbent and is a key parameter for physisorption, while pore size determines molecular sieving and diffusion resistance. A higher BET specific surface area usually implies a more developed microporous and mesoporous structure, which is beneficial for multi-point adsorption and hydrophobic partitioning of PFAS molecules. However, excessively small pore sizes may restrict molecule entry, leading to limited diffusion; excessively large pore sizes reduce specific surface area utilization. The relatively minor importance of these two factors in the model suggests that chemisorption is more dominant than physisorption in PFAS systems, but a suitable pore size distribution still helps enhance mass transfer and molecule entry rates.

[0047] While the type of raw material and pyrolysis temperature are less critical, they indirectly control material properties. Different raw materials, such as lignin, rice husks, and sludge, determine the initial elemental composition, thus affecting the final carbon skeleton structure. Pyrolysis temperature controls the degree of carbonization and functional group stability: higher temperatures lead to deoxygenation and aromatization, reducing the O / C ratio and increasing hydrophobicity, but simultaneously reducing polar adsorption sites. Therefore, although these variables are not direct driving factors, they affect overall adsorption performance through structure-chemical coupling effects. Although the O / C ratio is ranked low, it reflects the proportion of oxygen functional groups on the biochar surface and is an important parameter affecting polar adsorption and hydrogen bonding. A higher O / C ratio increases the material's hydrophilicity and polarity, which is beneficial for the adsorption of short-chain PFAS; while a lower O / C ratio corresponds to increased hydrophobicity, which is more suitable for long-chain PFAS. The low weighting of adsorbent dosage and biochar type indicates that, under standardized conditions, changes in adsorbent dosage have a weak impact on unit adsorption capacity. Furthermore, the effect of char type has been implicitly represented by features such as BET and functional groups. This also verifies the robustness of the model after removing experimental bias.

[0048] By integrating machine learning feature importance analysis with existing literature evidence, the XGBoost model reveals a multi-level control mechanism for PFAS adsorption: (1) surface chemistry (functional group type, modification method, O / C ratio) is the dominant factor; (2) interfacial charge (pH, Zeta potential) is the regulating factor; and (3) pore structure (BET, average pore size) provides physical adsorption support. These factors synergistically influence PFAS adsorption through electrostatic interactions, hydrogen bonding, hydrophobic partitioning, and pore-limiting effects. This model not only corroborates existing theoretical research, but this analytical method also provides an important basis for optimizing the preparation parameters of biochar materials. Furthermore, it highlights the unique advantages of machine learning in identifying key driving factors in complex systems, providing quantitative guidance for material design.

[0049] Furthermore, the results obtained by using the adsorption capacity prediction model described above are as follows: Figure 6 As shown, the XGBoost model constructed in this study confirms its excellent prediction accuracy and generalization ability. This model serves as a reliable tool for effectively predicting the adsorption performance of biochar on PFAS under conditions exceeding the experimental range.

[0050] S104. Generate multiple combinations of all-factor parameters from multiple dominant factors according to a set step size, and input them into the adsorption capacity prediction model for prediction; sort the prediction results, and select at least one combination of all-factor parameters that maximizes the adsorption capacity from the prediction results. The at least one combination of all-factor parameters is used to guide the preparation of the support and / or the optimization of adsorption conditions.

[0051] The process of generating multiple full-factor parameter combinations from multiple dominant factors according to a set step size includes the following (1) to (3): (1) Set a feasible range and optimization step size for each dominant factor; (2) Within the feasible range, the dominant factors are discretized according to the optimization step size to generate the level values ​​of each dominant factor; (3) Combine all the level values ​​of each dominant factor to generate the various combinations of full factor parameters.

[0052] The above-mentioned methods for guiding carrier preparation and / or optimizing adsorption conditions include: determining the process parameters for carrier preparation based on the physicochemical properties of the carrier in the selected combination of all-factor parameters; and determining the adsorption operating conditions for PFAS-contaminated water treatment based on the adsorption condition parameters in the selected combination of all-factor parameters, wherein the adsorption operating conditions include adsorbent dosage, solution pH, and temperature parameters.

[0053] For example, approximately 960,000 and 30,000 parameter combinations were generated using Cartesian product. These full-factor parameter combinations (i.e., parameter combinations) were input into a trained XGBoost model for batch prediction to obtain the adsorption capacity corresponding to each combination. The prediction results were sorted in descending order, and the Top 1000 optimal parameter combinations were selected. The former helps us identify key material properties affecting PFAS adsorption efficiency, while the latter provides a reference for the preparation and application conditions of biochar, guiding experimental verification.

[0054] The applicability and physical rationality of the model were verified by combining PCA coverage analysis and characteristic distribution statistics. For example... Figure 7 As shown, PCA, based on the selected key features, demonstrates the distribution of the original biochar dataset (Group A, n=200) and the candidate combinations generated by the full factorial design (Group B, n=1000) in the principal component space. From... Figure 7 As can be seen, most of the samples in group B are distributed within the 95% confidence range of group A in the principal component space, indicating that the parameter combinations generated by the full factorial analysis are mainly located within the feature domain of the training data. This result suggests that the model primarily uses interpolation in parameter space optimization, and the prediction results have high reliability. Meanwhile, a small number of samples in group A are located outside the confidence ellipse, indicating the existence of individual extreme feature points in the original data. These points may correspond to special modifications or high-surface-area biochar, providing a direction for further model accuracy improvement. Therefore, PCA analysis verifies the rationality and reliability of the full factorial-machine learning joint method in this study regarding feature space coverage.

[0055] like Figure 8 , Figure 9As shown, the box plots display the significant characteristic concentration ranges corresponding to high predicted adsorption capacities. Red boxes represent the original training set samples, while blue boxes correspond to the top 1000 adsorption capacity samples predicted by the model. Each box shows the distribution range of the feature, with the center line representing the median. The width of the box reflects the concentration of the data, and outliers represent extreme parameter combinations. To further reveal the high adsorption characteristic ranges identified by the XGBoost model, the distribution differences in material property parameters and biochar preparation and adsorption conditions between the original biochar samples and the Top 1000 predicted combinations were compared. Overall, the Top 1000 samples show significant differentiation from the original training set in several key physicochemical parameters, indicating that the high-performance parameter regions identified by the machine learning model have typical structure-performance characteristics. This feature distribution analysis provides an important basis for understanding the regulatory mechanism of PFAS adsorption and experimental optimization. The results show that the BET specific surface area is significantly higher in the Top 1000 samples, indicating that a larger specific surface area helps provide more adsorption sites and pore diffusion channels, thereby enhancing the physical adsorption process of PFAS. The average pore size of the Top 1000 samples is slightly smaller and more concentrated than that of the original training set, indicating that appropriate pore size matching can simultaneously promote PFAS diffusion and surface binding, thus contributing to improved adsorption performance. Meanwhile, the decrease in the O / C ratio suggests that high-performance biochar has higher carbonization and hydrophobicity, thereby enhancing the hydrophobic partitioning and van der Waals interactions between PFAS and the carbon framework.

[0056] The pH values ​​of the Top 1000 samples were mainly concentrated in the weakly acidic range of 4.5–5.5, while the pH distribution of the original training set samples was more dispersed. This phenomenon indicates that the efficient adsorption of PFAS on biochar tends to occur under weakly acidic conditions. Under these conditions, some functional groups on the biochar surface are in a protonated state, and the surface potential tends to be positive, thereby enhancing the electrostatic adsorption of anionic PFAS (such as PFOA and PFOS). In addition, hydrogen bonding and hydrophobic interactions are synergistically utilized under weakly acidic conditions, making it easier for PFAS molecules to be enriched in the micropores of the carbon surface. The pyrolysis temperature of the Top 1000 samples was selected to be around 600℃. Biochar within this range has a high specific surface area and pore structure, which is conducive to the efficient adsorption of PFAS. Regarding the selection of raw materials, it can be seen that raw materials with high specific surface area and good pore structure, such as coconut shell and pine wood, have been shown to have better adsorption performance. The optimal initial concentration range is 30-80 mg / L. Too high a concentration will lead to adsorbent saturation, thereby reducing the adsorption effect. The optimal dosage range is 5-15 g / L, which sufficiently enhances the adsorption effect while avoiding resource waste due to excessive dosage. Through model analysis, we found that acid-base modification, nitriding modification, and chemical modification have relatively balanced effects on PFAS adsorption capacity, with similar importance ratios, indicating that these modification methods can effectively enhance the adsorption performance of biochar.

[0057] The high-performance characteristics identified by these models can be summarized as follows: medium to high pyrolysis temperature, raw materials such as coconut shells and pine wood with good pore structure, appropriate initial concentration and dosage, high specific surface area, moderate pore size, low O / C ratio, and a weakly acidic surface environment. Among these, structural and chemical characteristics such as BET, average pore size, O / C ratio, and functional group type jointly promote the hydrophobic partitioning, electrostatic adsorption, and pore diffusion processes of PFAS molecules, thereby achieving higher adsorption capacity. In the preparation of biochar and its adsorption and removal of PFAS, adjustable factors such as pyrolysis temperature, raw materials, initial concentration, pH value, and dosage help to obtain highly efficient adsorbent materials and adsorption effects. Therefore, this study verifies the interpretability of the XGBoost model through characteristic distribution analysis and provides a quantitative design basis for the optimization of biochar adsorbent preparation.

[0058] In summary, this study constructed a quantitative prediction model based on machine learning to correlate the physicochemical characteristics of biochar with PFAS adsorption performance, and combined this with a full factorial design to achieve systematic optimization of the parameter space. The XGBoost model performed best among all algorithms, successfully capturing the complex nonlinear relationship between biochar structural parameters and PFAS adsorption behavior. Feature importance analysis not only verified the reliability of the model but also revealed key factors dominating the adsorption process from a data-driven perspective: functional group type, initial concentration, BET, pH, and Zeta potential. Feature distribution and correlation analysis further revealed that high-performance biochar samples were concentrated within a characteristic range of "medium-high pyrolysis temperature – good pore structure from raw materials such as coconut shells and pine wood – appropriate initial concentration and dosage – high BET – moderate pore size – low O / C – weakly acidic environment." This combination of features helps to enhance the synergistic effect of hydrophobic partitioning, electrostatic adsorption, and pore diffusion. Furthermore, by coupling full factorial design with a machine learning model, high-throughput prediction and screening of multiple parameter combinations were achieved, obtaining the Top 50 optimal structural parameter combinations, providing a quantifiable design basis for experimental verification and precise biochar preparation.

[0059] In other embodiments of the present invention, after generating the multiple combinations of full-factor parameters and before inputting them into the adsorption capacity prediction model, the method further includes: Based on physicochemical constraints, a feasibility screening of various combinations of full-factor parameters is performed, eliminating combinations that do not meet the constraints. The physicochemical constraints include at least one of thermodynamic self-consistency constraints, surface charge-ion morphology coupling constraints, and pore size-molecular size matching constraints. Specifically, the thermodynamic self-consistency constraint is based on the physical compatibility between the carrier's preparation conditions and structural parameters, eliminating full-factor parameter combinations where the preparation conditions and structural parameters do not conform to the material formation rules. The pore size-molecular size matching constraint establishes the matching degree between the carrier's pore size distribution and the PFAS molecular size based on the PFAS molecular dynamics diameter, eliminating full-factor parameter combinations where the pore size exceeds a preset range matching the target PFAS molecular size. The surface charge-ion morphology coupling constraint is based on the correlation between the pH value of the water body and the Zeta potential of the carrier surface, combined with the acid dissociation constant pKa of the target PFAS, eliminating full-factor parameter combinations where the surface charge polarity repels the PFAS ion morphology. An initial set containing 500 sets of random parameter combinations was constructed, and different constraint strategies were applied to each set, as shown in Table 2: Table 2 Comparison of prediction results under different constraints

[0060] The triple constraints of physicochemicals improved the model prediction accuracy from 0.73 to 0.91; the experimental success rate was improved: the success rate of experiments with high adsorption capacity (>300 mg / g) increased from 38% to 81%; the experimental cost was reduced by reducing the number of invalid experiments by about 76%, saving experimental costs and time; and within the constrained parameter space, the proportion of predicted values ​​with a relative error of <15% between the predicted and experimental values ​​increased from 45% to 82%.

[0061] After obtaining feasible combinations of all factors, the parameter combinations were further screened using a dynamic adsorption-desorption cycle stability prediction model. Combinations with an adsorption capacity decay rate >20% after three simulated adsorption-desorption cycles were eliminated. This dynamic adsorption-desorption cycle stability prediction model predicts the adsorption capacity retention rate of the support after multiple adsorption-desorption cycles based on support structural stability parameters, surface functional group bonding stability parameters, and PFAS desorption thermodynamic parameters. The support structural stability parameters include pore wall thickness and mesoporosity, requiring a pore wall thickness greater than 2 nm and a mesoporosity greater than 40%. The surface functional group bonding stability parameters include pyrolysis temperature and the proportion of highly stable functional groups, requiring a pyrolysis temperature greater than 600℃ and a proportion of highly stable functional groups greater than 60%, where the highly stable functional groups are selected from C=O and -COOH. The PFAS desorption thermodynamic parameters include the desorption activation energy, requiring the desorption activation energy to be between 40 kJ / mol and 80 kJ / mol. The parameters are between kJ / mol; the comprehensive stability index is calculated based on the above parameters, and parameter combinations with a comprehensive stability index less than or equal to 0.85 are eliminated. The comprehensive stability index is positively correlated with the adsorption capacity retention rate.

[0062] Experiments showed that, after screening using the above methods, the adsorption capacity decay rate of biochar carriers in PFOA / PFOS adsorption applications was controlled at 10-18% after 3 cycles, meeting the economic requirements for continuous industrial operation.

[0063] After screening for at least one combination of all-factor parameters that maximizes adsorption capacity, the following are also included: Centered on at least one combination of all-factor parameters, a multi-objective optimization function is constructed in the neighborhood space of the parameters of the combination of all-factor parameters, with the primary objective of maximizing adsorption capacity and the secondary objectives of one or more of the following: adsorption rate, selectivity index, regeneration efficiency, and economic cost. Using NSGA-II, MOEA / D, or multi-objective Bayesian optimization algorithms, Pareto front search is performed in the neighborhood space of the parameters to obtain the Pareto optimal solution set. Set the weight coefficients for each secondary objective, and select at least one optimal parameter combination from the Pareto optimal solution set.

[0064] It also includes building a feedback optimization mechanism: Carrier preparation and adsorption experiments were conducted according to the selected combination of all factor parameters to obtain real adsorption capacity data. The actual adsorption capacity data is compared with the predicted values ​​of the adsorption capacity prediction model to calculate the prediction deviation. When the prediction deviation exceeds a preset threshold, the actual adsorption capacity data is added to the multidimensional dataset to retrain and update the parameters of the adsorption capacity prediction model. Iteratively execute model prediction, experimental verification, and model updates until the prediction bias stabilizes within a preset threshold, completing feedback optimization: In summary, this study establishes an interpretable machine learning-optimization fusion framework, enabling intelligent transformation from performance prediction to structural design. This research not only provides a theoretical foundation for the targeted design of PFAS removal materials but also offers a generalizable research paradigm for data-driven optimization of complex adsorption systems. Future research should further validate the optimal parameter combinations selected by the model through experiments, constructing a closed-loop "prediction-experiment-feedback" model to continuously improve the model's generalization ability and material performance. The model should be extended to other typical persistent organic pollutant systems, such as GenX, short-chain PFAS, or mixed pollutant systems, to achieve cross-pollutant adsorption performance prediction. Furthermore, a multi-objective optimization-based model framework should be developed to simultaneously consider adsorption efficiency, economic efficiency, and environmental sustainability, enabling multi-dimensional design of biochar adsorbents.

Claims

1. A method for determining PFAS adsorption optimization strategies based on machine learning, characterized in that, Includes the following steps: A multidimensional dataset for adsorbing PFAS in water using a carrier is constructed; the multidimensional dataset includes the physicochemical properties and preparation parameters of the carrier, molecular characteristics of PFAS and adsorption condition parameters. An adsorption capacity prediction model is established; the input of the adsorption capacity prediction model is the physicochemical properties and preparation parameters of the support, the molecular characteristics of PFAS and the adsorption condition parameters, and the output is the adsorption capacity of the support for PFAS. Based on the adsorption capacity prediction model, importance analysis and SHAP value interpretation of the input of the adsorption capacity prediction model were performed to identify several dominant factors affecting the adsorption of PFAS on the carrier. Multiple dominant factors are used to generate various combinations of all-factor parameters according to a set step size, and these combinations are input into the adsorption capacity prediction model for prediction. The prediction results are then sorted, and at least one combination of all-factor parameters that maximizes the adsorption capacity is selected from the prediction results. This at least one combination of all-factor parameters is used to guide the preparation of the support and / or the optimization of adsorption conditions.

2. The method for determining PFAS adsorption optimization strategy based on machine learning as described in claim 1, characterized in that, The adsorption capacity prediction model was selected from machine learning models such as XGBoost, Random Forest, Support Vector Machine, LightGBM, and Artificial Neural Network; the selection method was as follows: The multidimensional dataset is divided into a training set and a test set; Each machine learning model is trained on the training set, and hyperparameters are tuned by combining cross-validation with grid search. The predictive performance of each machine learning model after tuning is evaluated on the test set, and the evaluation metrics include the coefficient of determination and the root mean square error. By comparing the evaluation metrics of various machine learning models, the model with the highest coefficient of determination and / or the lowest root mean square error is selected as the adsorption capacity prediction model.

3. The method for determining PFAS adsorption optimization strategy based on machine learning as described in claim 1, characterized in that, The carrier is one of the following: biochar, activated carbon, carbon nanotubes, graphene, zeolite, montmorillonite, kaolin, or ion exchange resin.

4. The method for determining PFAS adsorption optimization strategy based on machine learning as described in claim 1, characterized in that, The dominant factors include functional group type, initial PFAS concentration, specific surface area, pH value, and Zeta potential.

5. The method for determining PFAS adsorption optimization strategy based on machine learning as described in claim 1, characterized in that, The importance analysis and SHAP value interpretation include: The substitution importance algorithm is used to calculate the relative importance score of each input to the adsorption capacity prediction result, and to identify several candidate dominant factors with the highest importance scores. The marginal contribution of each input to the prediction result of a single adsorption capacity is calculated based on the SHAP value, and a SHAP dependency graph and a force graph are generated. The multiple dominant factors are determined by combining multiple candidate dominant factors with the SHAP dependency graph and the force graph.

6. The method for determining PFAS adsorption optimization strategy based on machine learning as described in claim 1, characterized in that, The process of generating multiple full-factor parameter combinations from multiple dominant factors according to a set step size includes: Define the feasible range and optimization step size for each dominant factor; Within the feasible range, the dominant factors are discretized according to the optimization step size to generate level values ​​for each dominant factor. The various full-factor parameter combinations are generated by combining all levels of each dominant factor.

7. The method for determining PFAS adsorption optimization strategy based on machine learning as described in claim 6, characterized in that, After generating the various combinations of full-factor parameters and before inputting them into the adsorption capacity prediction model, the following steps are also included: Based on physicochemical constraints, the feasibility of various combinations of full-factor parameters is screened, and combinations that do not meet the constraints are eliminated. The physicochemical constraints include at least one of thermodynamic self-consistency constraints, surface charge-ion morphology coupling constraints, and pore size-molecular size matching constraints. Specifically, the thermodynamic self-consistency constraint is based on the physical compatibility of the carrier's preparation conditions and structural parameters, eliminating combinations of all-factor parameters that do not conform to the material formation rules. The pore size-molecular size matching constraint establishes the matching degree between the carrier's pore size distribution and the PFAS molecular size based on the PFAS molecular dynamics diameter, eliminating combinations of all-factor parameters whose pore size exceeds a preset range matching the target PFAS molecular size. The surface charge-ion morphology coupling constraint is based on the correlation between the pH value of the water and the Zeta potential of the carrier surface, combined with the acid dissociation constant pKa of the target PFAS, eliminating combinations of all-factor parameters where the surface charge polarity repels the PFAS ion morphology.

8. The method for determining PFAS adsorption optimization strategy based on machine learning as described in claim 1, characterized in that, After screening for at least one combination of all-factor parameters that maximizes adsorption capacity, the following are also included: Centered on at least one combination of all-factor parameters, a multi-objective optimization function is constructed in the neighborhood space of the parameters of the combination of all-factor parameters, with the primary objective of maximizing adsorption capacity and the secondary objectives of one or more of the following: adsorption rate, selectivity index, regeneration efficiency, and economic cost. Using NSGA-II, MOEA / D, or multi-objective Bayesian optimization algorithms, Pareto front search is performed in the neighborhood space of the parameters to obtain the Pareto optimal solution set. Set the weight coefficients for each secondary objective, and select at least one optimal parameter combination from the Pareto optimal solution set.

9. The method for determining PFAS adsorption optimization strategy based on machine learning as described in claim 1, characterized in that, The method for guiding carrier preparation and / or optimizing adsorption conditions includes: Based on the physicochemical properties of the carrier and the preparation parameters in the selected combination of all-factor parameters, the process parameters for carrier preparation are determined. Based on the adsorption condition parameters in the selected combination of all factors, the adsorption operating conditions for treating PFAS-contaminated water bodies are determined. The adsorption operating conditions include the adsorbent dosage, solution pH value, and temperature parameters.

10. The method for determining PFAS adsorption optimization strategy based on machine learning as described in claim 1, characterized in that, It also includes building a feedback optimization mechanism: Carrier preparation and adsorption experiments were conducted according to the selected combination of all factor parameters to obtain real adsorption capacity data. The actual adsorption capacity data is compared with the predicted values ​​of the adsorption capacity prediction model to calculate the prediction deviation. When the prediction deviation exceeds a preset threshold, the actual adsorption capacity data is added to the multidimensional dataset to retrain and update the parameters of the adsorption capacity prediction model. Iteratively execute model prediction, experimental verification, and model update until the prediction deviation stabilizes within a preset threshold, thus completing feedback optimization.

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