Dual mechanism analysis method and device for aggregation rate prediction model of nanoparticles

Abstract

The invention relates to a dual-mechanism analysis method and device for an aggregation rate prediction model of nanoparticles. The method comprises the following steps: collecting experimental data related to the aggregation rate of the nanoparticles as an input feature set; wherein each feature in the input feature set is marked with an aggregation rate label; inputting the input feature set into a machine learning model for training and testing to obtain a nanoparticle aggregation rate prediction model; calculating an SHAP absolute value of each feature in the input feature set by adopting an SHAP method, and screening out at least two features from the input feature set according to the SHAP absolute values to serve as a key drive feature set; and two features are selected from the key driving feature set, and visual verification of interaction of the two selected features is carried out. Therefore, the influence of a single feature is considered, the interaction mechanism between the features and the influence of the interaction mechanism can be revealed, and then the black box model can be converted into a transparent and credible scientific analysis tool.

Description

Technical Field

[0001] This application relates to the interdisciplinary field of environmental science and interpretability modeling, specifically to a dual-mechanism analysis method and apparatus for predicting the aggregation rate of nanoparticles. Background Technology

[0002] The behavior and fate of nanoparticles in the environment are core issues in assessing their ecological risks. Among these, the aggregation process of nanoparticles directly determines their migration capacity, bioavailability, and final sedimentation distribution. Therefore, accurate prediction of the dynamic indicator of the aggregation process—the "aggregation rate"—has significant scientific and practical implications.

[0003] Currently, theoretical assessments of nanoparticle stability are primarily based on the classical DLVO theory. However, this theory often relies on simplified idealized assumptions, making it difficult to capture and characterize the prevalent nonlinear relationships and higher-order interactions among multiple factors (such as DOM, ionic strength, and pH). When faced with high-dimensional, complex real-world experimental data, the predictive power and applicability of these models are severely limited. Therefore, machine learning algorithms, such as gradient boosting trees, have become the preferred method for constructing high-precision predictive models due to their ability to automatically learn complex mapping relationships from data without requiring pre-defined physical equations.

[0004] With the development of high-throughput experimental techniques, researchers can acquire massive amounts of high-dimensional data at unprecedented speeds, which meticulously record the behavior of nanoparticles under different environmental conditions. This provides an opportunity to learn patterns directly from the data, but it also brings new challenges: how to construct a model from this complex and heterogeneous data that can accurately reflect the complex mapping relationship between numerous environmental variables and particle aggregation rates has become a major technical bottleneck in this field.

[0005] Machine learning, especially ensemble algorithms such as gradient boosting trees, can build high-precision predictive models that accurately predict the aggregation rate of nanoparticles in complex systems. However, these models are often considered "black boxes" because their complex internal decision-making logic cannot directly reveal the strength and type (synergistic / antagonistic) of interactions between input variables. This greatly limits the value of these models in exploring mechanisms.

[0006] In view of this, in the prior art, the patent with application number CN202310464321.6 discloses a method for predicting the hardness of high-entropy alloys based on machine learning and interpretive analysis. Specifically, it discloses the use of the XGB model to fuse the SHAP framework for interpretive analysis features; the calculation of the predicted hardness contribution value of each feature; and the further fusion of the XGB model with the PDP framework to analyze the impact of different values ​​on the prediction results of the improved model when different values ​​are applied to features with high feature importance.

[0007] As can be seen from the above, although this method can be combined with the SHAP framework or PDP framework for interpretive analysis of the model, it only considers the influence of a single feature and does not reveal the interaction mechanism between features and its influence, resulting in a low degree of interpretation of the black box model. Summary of the Invention

[0008] In order to overcome the above-mentioned defects and deficiencies in the prior art, the present invention provides a dual-mechanism analysis method and apparatus for predicting the aggregation rate of nanoparticles.

[0009] To address the aforementioned technical problems, this invention provides a dual-mechanism analysis method for predicting the aggregation rate of nanoparticles. The method includes the following steps: Step S1: Collect experimental data related to the aggregation rate of nanoparticles as an input feature set; wherein each feature in the input feature set is labeled with an aggregation rate tag; Step S2: Input the input feature set into a machine learning model for training and testing to obtain a nanoparticle aggregation rate prediction model; Step S3: Calculate the absolute SHAP value of each feature in the input feature set using the SHAP method, and select at least two features from the input feature set as a key driving feature set based on the absolute SHAP values; Step S4: Select two features from the key driving feature set and perform a visual verification of the interaction between the selected two features.

[0010] Furthermore, in step S1, missing value imputation is performed on the features in the input feature set; wherein the missing value imputation method includes: standardizing each feature in the input feature set; determining whether each feature in the standardized input feature set contains missing values, and if so, classifying the features containing missing values ​​into the feature set to be imputed; and using an imputation method based on missing value prediction to imput each feature in the feature set to be imputed.

[0011] Furthermore, the imputation method based on missing value prediction includes: obtaining a feature training set; standardizing each feature in the feature training set; determining whether each feature in the standardized feature training set contains missing values; if so, assigning the features containing missing values ​​to a first feature training set; otherwise, assigning the complete features to a second feature training set; using the features in the first feature training set as the dependent variable and the features in the second feature training set as the independent variable, inputting them into the model for training to obtain a prediction imputation model; and using the prediction imputation model to imput each feature in the feature set to be imputed.

[0012] Further, the imputation method based on missing value prediction includes: obtaining a feature training set; standardizing each feature in the feature training set; determining whether each feature in the standardized feature training set contains missing values; if so, assigning the features containing missing values ​​to a first feature training set; otherwise, assigning the complete features to a second feature training set; using the features in the first feature training set as dependent variables and the features in the second feature training set as independent variables, inputting them into multiple models for training to obtain multiple prediction imputation models; comparing the performance parameters of the multiple prediction imputation models, selecting the prediction imputation model with the largest performance parameter as the target prediction imputation model; and using the target prediction imputation model to imput each feature in the feature set to be imputed.

[0013] Further, in step S2, the training process of the machine learning model is as follows: the input feature set is divided into a training set and a test set according to a certain ratio; the training set is input into the first machine learning model for training to obtain an intermediate state variable set; the intermediate state variable set and the training set are input into the second machine learning model for training to obtain a nanoparticle aggregation rate prediction model; the aggregation rate prediction model is externally validated and its performance is evaluated using the test set.

[0014] Furthermore, each feature in the input feature set is also labeled with a feature category tag, which includes at least nanoparticle attribute category, dissolved organic matter attribute category, and environmental attribute category; step S3 further includes: generating a SHAP summary map based on the SHAP absolute value of each feature in the input feature set; classifying each feature in the input feature set according to the feature category tag; calculating the total SHAP absolute value corresponding to each feature category tag based on the SHAP absolute value of each feature under each classified feature category tag; and generating an analysis map of features and feature categories based on the multiple total SHAP absolute values ​​and the SHAP absolute value of each feature in the input feature set.

[0015] Further, in step S4, the method for visually verifying the interaction between the two selected features includes: generating a SHAP dependency graph based on the absolute SHAP value of each feature in the key driving feature set, and selecting two interactive features based on the SHAP dependency graph; using the two selected features as the X-axis and Y-axis respectively, representing the predicted value of the aggregation rate by the aggregation rate prediction model through color mapping to generate a contour map or heat map; the contour map or heat map is used to show the interaction between the two selected features.

[0016] This application also relates to a dual-mechanism analysis device for predicting the aggregation rate of nanoparticles. The device includes: a collection module for collecting experimental data related to the aggregation rate of nanoparticles as an input feature set; a training module for inputting the input feature set into a machine learning model for training and testing to obtain a prediction model for the aggregation rate of nanoparticles; a screening module for calculating the absolute SHAP value of each feature in the input feature set using the SHAP method, and screening at least two features from the input feature set as a key driving feature set based on the absolute SHAP value; and a verification module for selecting two features from the key driving feature set and performing a visual verification of the interaction between the selected two features.

[0017] The beneficial technical effects achieved by this invention are as follows: The present invention provides a dual-mechanism analysis method and apparatus for predicting the aggregation rate of nanoparticles. First, a prediction model is trained using an input feature set, enabling the model to predict the aggregation rate of nanoparticles. Then, the SHAP method is used to calculate the absolute SHAP value of each input feature, which explains the impact of each input feature on the prediction target. Next, at least two features are selected from the input feature set based on their absolute SHAP values ​​as a key driving feature set, and two of these features are selected for visual verification of their interactions. This approach not only considers the influence of individual features but also reveals the interaction mechanisms and their effects between features, thereby transforming a "black box" model into a transparent and reliable scientific analysis tool. Attached Figure Description

[0018] Figure 1 is a flowchart of the dual-mechanism analysis method for predicting the aggregation rate of nanoparticles according to an embodiment of the present invention; Figure 2 This is a heatmap showing the distribution of missing values ​​in the dataset of an embodiment of the present invention. Figure 3 is a diagram showing the fitting degree of the missing value imputation model in the embodiment of the present invention; Figure 4 This is a graph showing the degree of fit of the relevant models in the embodiments of the present invention; Figure 5 This is a SHAP value graph of the relevant model in the embodiments of the present invention; Figure 6 This is a SHAP dependency graph of key features of the relevant model in the embodiments of the present invention; Figure 7 This is a summary chart of the importance and contribution of SHAP features in the relevant models of this invention. Figure 8 This is a visualization diagram of the interaction between relevant models in embodiments of the present invention; Figure 9This is a structural block diagram of the dual-mechanism analysis device for predicting the aggregation rate of nanoparticles according to an embodiment of the present invention. Detailed Implementation

[0019] The present invention will be further described below with reference to specific embodiments. These embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] like Figure 1 As shown, this application relates to a dual-mechanism analysis method for predicting the aggregation rate of nanoparticles, comprising the following steps: Step S1: Collect experimental data related to the aggregation rate of nanoparticles as an input feature set; wherein each feature in the input feature set is labeled with an aggregation rate tag; The experimental data include input features such as particle radius, Zeta potential, and intersurface separation distance labeled with aggregation rate and nanoparticle attribute tags; input features such as radius of gyration of dissolved organic matter, molecular weight of dissolved organic matter, and concentration of dissolved organic matter labeled with aggregation rate and dissolved organic matter attribute tags; input features such as pH value, ionic strength, absolute temperature, and ion species labeled with aggregation rate and environmental attribute tags; and input features such as Debye length and van der Waals attraction potential labeled with aggregation rate and DLVO-derived attribute tags.

[0022] It's important to understand that the Debye length and van der Waals attraction potential can be calculated from the other experimental data mentioned above. For example, the Debye length can be calculated based on ionic strength and absolute temperature.

[0023] It is also important to understand that the aggregation rate can be measured and calculated using time-resolved dynamic light scattering (DLS) technology.

[0024] We collected 15 experimental data points related to the degree of nanoparticle aggregation directly from experimental data, which served as the input feature set for training the machine learning model. The model was then guided to predict the nanoparticle aggregation rate as its final objective by using labeled aggregation rate tags.

[0025] Step S2: Input the input feature set into the machine learning model for training and testing to obtain a nanoparticle aggregation rate prediction model; The input feature set is randomly divided into a training set and a test set in an 8:2 ratio. The training set is used for building and internally validating the machine learning model, while the test set is used for externally validating and evaluating the performance of the machine learning model, thus obtaining a prediction model for the aggregation degree of nanoparticles.

[0026] In step S2 of this embodiment, the training process of the machine learning model is as follows: The input feature set is divided into a training set and a test set according to a certain ratio; The training set is input into the first machine learning model for training, and an intermediate set of variables is obtained. The intermediate state variable set and the training set are input into the second machine learning model for training to obtain the nanoparticle aggregation rate prediction model. The aggregation rate prediction model was externally validated and its performance evaluated using a test set.

[0027] Specifically, the XGBoost algorithm is first used to establish a preliminary prediction model (first machine learning model) for the intermediate state variables of the system, namely "critical aggregation concentration (CCC)" and "Zeta potential change". Secondly, the intermediate variables predicted in the previous step are used as new, highly condensed input features and incorporated into the input feature set. Then, a gradient boosting regression model is used to build the final cascaded prediction model, specifically designed to predict the "aggregation rate". Because the "aggregation rate" feature exhibits a severely skewed, long-tailed distribution, a Yeo-Johnson transformation is applied to this feature to obtain the optimal model, and key parameters are adjusted using 5-fold cross-validation. Model performance is measured using Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE), calculated as follows:

[0028]

[0029] in, For the sample size, For the true value, These are model predictions.

[0030] In 5-fold cross-validation, the training set is randomly divided into 5 disjoint subsets. Four of these subsets are used for training in turn, and the remaining subset is used for validation. This process is repeated 5 times. The final cross-validation error (CV Error) is the average of the 5 validation errors, as shown in the following formula:

[0031] in, The number of folds (k=5 in this example) It is the mean square error on the i-th validation set.

[0032] To verify the superiority of the cascaded model, its performance was compared with that of a traditional end-to-end model that does not include intermediate variables for prediction. The results are as follows: Figure 4 As shown in the figure, this paper compares the performance of the cascade model proposed in this invention with the traditional end-to-end model. Figure 4 (a) shows that the cascaded model of the present invention performs excellently on the test set, with a determination coefficient R² of 0.5099, and the data points are closely clustered around the diagonal. Figure 4 (b) shows that the traditional end-to-end model has an R² of only 0.2649 on the same dataset, which is far inferior to the cascaded model. This comparison fully demonstrates the advancement and superiority of the cascaded structure adopted in this invention.

[0033] A cascaded model structure was adopted, which first predicts intermediate physicochemical variables (such as CCC) and then inputs them as enhancing features into the final model, thereby simulating the actual physicochemical pathway of nanoparticle aggregation. This design not only significantly improves the predictive performance of the final target "aggregation rate" but also enhances the scientific rationality and robustness of the model itself.

[0034] Step S3: Calculate the absolute SHAP value of each feature in the input feature set using the SHAP method, and select at least two features from the input feature set as key driving feature sets based on the absolute SHAP values. The SHAP (SHapley Additive exPlanations) method was used to analyze the aggregation rate prediction model in order to reveal the influence mechanism of each feature on the aggregation rate.

[0035] The model's predictions can be decomposed into the sum of the contributions of all features:

[0036] in, It is the model's predicted value for the "aggregation rate" of a single sample; It is the average of the predicted values ​​of all samples; It is the contribution of the i-th feature to the predicted value.

[0037] Each feature in the input feature set is also labeled with a feature category label, which includes at least nanoparticle attribute category, dissolved organic matter attribute category, environmental attribute category, and DLVO derived attribute category; Step S3 also includes: Generate a SHAP summary graph based on the absolute SHAP value of each feature in the input feature set; Each feature in the input feature set is categorized according to the feature category label; The total absolute SHAP value corresponding to each feature category label is calculated based on the absolute SHAP value of each feature under each category label after classification. An analysis graph of features and feature categories is generated based on the total absolute SHAP values ​​and the absolute SHAP value of each feature in the input feature set.

[0038] The above method can be used to generate analysis charts of features and feature categories, that is, combining a SHAP feature importance bar chart with a feature source contribution pie chart (see reference). Figure 5 ); and a SHAP summary diagram revealing the importance and direction of influence of each feature (see Figure 6 ).

[0039] Figure 5 In the diagram, the bar chart on the left, by sorting all features in descending order of their average SHAP absolute values ​​(Mean(|SHAP Value|)), visually identifies the three key driving factors with the greatest impact on the aggregation rate: "attachment efficiency," "applied force," and "total DLVO potential." The pie chart on the right categorizes all features into four types based on their source: nanoparticle properties, environmental properties, dissolved organic matter properties, and DLVO-derived properties, quantitatively displaying the total contribution of each type. The results show that environmental features contribute a total of 37.3%, making it the most important factor category dominating the nanoparticle aggregation process, followed by physical information features (30.2%).

[0040] Figure 6 In the graph, each point represents a feature in a sample, and its color indicates the original value of the feature (red for high, blue for low). Its position on the horizontal axis represents its contribution to a single prediction (SHAP value). For example, for the most important feature "attachment efficiency", the majority of its red points (high values) are distributed on the positive half of the horizontal axis, indicating that high attachment efficiency has a strong positive promoting effect on the aggregation rate.

[0041] Step S4: Select two features from the set of key driving features and perform a visual verification of the interaction between the two selected features.

[0042] In step S4 of this embodiment, the method for visually verifying the interaction between the two selected features includes: A SHAP dependency graph is generated based on the absolute SHAP value of each feature in the key driving feature set, and two features with interaction are selected based on the SHAP dependency graph. Using two selected features as the X-axis and Y-axis, the predicted values ​​of the aggregation rate by the aggregation rate prediction model are represented by color mapping to generate a contour map or heat map; the contour map or heat map is used to show the interaction between the two selected features.

[0043] Using the method described above, we can first examine the SHAP dependency graph (see...). Figure 7 Identify which features interact with each other; then use a topline plot or heatmap (refer to...) Figure 8 The interactions between them are verified and visualized.

[0044] Figure 7 (a) Figure 7 (b) shows the SHAP dependency graph of the key intermediate variables. Figure 7 (a) For example, it shows the trend of the predicted SHAP value of CCC (Pred. CCC) as its value changes. At the same time, the color of the scatter points in the figure is mapped to the "molecular weight of DOM". It can be clearly observed that at any given Pred. CCC value (e.g., Pred. CCC=2), the red dots representing high molecular weight DOM generally have lower SHAP values ​​than the blue dots representing low molecular weight DOM. This significant vertical separation phenomenon initially reveals a strong interaction between DOM molecular weight and CCC. Figure 7 (b) In a similar manner, the interaction between the model-predicted Zeta potential changes and the DOM and NP size was revealed.

[0045] like Figure 8 (a)- Figure 8 As shown in (f), this figure presents a set of interaction analysis results used to reveal the nonlinear coupling effects between pairwise features. Figure 8 (a) Taking this graph as an example, the X-axis represents pH value, the Y-axis represents the predicted CCC value (Pred. CCC), and the color in the graph (indicated by the color bar on the right) represents the magnitude of the "aggregation rate" predicted by the model. It can be intuitively seen from the graph that when Pred. CCC is low (<400), the aggregation rate is very sensitive to changes in pH (the color changes drastically with pH); while when Pred. CCC is high, changes in pH have almost no effect on the aggregation rate (the color is basically purple). This quantitatively and intuitively reveals the strong regulatory role of CCC on the pH effect, achieving a deep insight into the interaction between features and providing strong evidence for understanding the aggregation behavior of nanoparticles at the mechanistic level. Through analysis... Figure 8 (a)- Figure 8The series of spectra in (f) can comprehensively verify the synergistic or antagonistic effects between multiple key feature pairs, providing visual evidence for understanding the aggregation behavior of nanoparticles from a mechanistic perspective.

[0046] The dual-mechanism analysis method for predicting the aggregation rate of nanoparticles in this application, by constructing a high-performance cascade model and combining it with deep analysis based on SHAP-based individual contribution attribution and interaction analysis, not only achieves accurate prediction of the aggregation rate of nanoparticles and considers the influence of individual features, but also reveals the interaction mechanism between features and its impact. This transforms the "black box" model into a completely transparent and reliable scientific analysis tool. More importantly, it reveals the influence of key environmental factors on the final environmental fate at the mechanistic level, providing scientific assistance for risk assessment and decision-making in related fields.

[0047] like Figure 2 The heatmap of the missing value distribution matrix clearly reveals the distribution pattern of missing values ​​in the dataset. As can be seen from the graph, the missing values ​​(marked in yellow) are not randomly distributed, but rather concentrated in specific feature columns such as "CCC," "attachment efficiency," and "molecular mass of DOM." This non-random missing value pattern means that using traditional means or medians for imputation will severely distort the original data distribution of these features and destroy the intrinsic correlation between features, thus misleading subsequent model performance and mechanism analysis.

[0048] To avoid the above situation, in step S1 of this embodiment, missing value imputation is also performed on the features in the input feature set; wherein, the missing value imputation method includes: Each feature in the input feature set is standardized; it is determined whether each feature in the standardized input feature set contains missing values. If so, the feature containing missing values ​​is assigned to the feature set to be filled; and a missing value prediction-based filling method is used to fill each feature in the feature set to be filled.

[0049] Furthermore, the imputation method based on missing value prediction includes: obtaining a feature training set; standardizing each feature in the feature training set; determining whether each feature in the standardized feature training set contains missing values; if so, assigning the features containing missing values ​​to a first feature training set; otherwise, assigning the complete features to a second feature training set; using the features in the first feature training set as the dependent variable and the features in the second feature training set as the independent variable, inputting them into the model for training to obtain a prediction imputation model; and using the prediction imputation model to imput each feature in the feature set to be imputed.

[0050] This imputation method based on missing value prediction treats each feature containing missing values ​​(e.g., "CCC") as a temporary dependent variable and all other features in the dataset as independent variables. This data is then fed into a model (e.g., XGBoost or CatBoost) for training, resulting in a predictive imputation model capable of filling in missing values. This model is then used to impute the features to be filled. This method effectively preserves the original data distribution of these features and does not disrupt the intrinsic relationships between them, thus avoiding misleading subsequent model performance and mechanism analysis.

[0051] The effectiveness of this fill interpolation strategy was rigorously and quantitatively verified in this embodiment, and the results are as follows: Figures 3(a)-3(g) As shown. Figures 3(a)-3(g) The performance of the interpolation models for different target variables (such as DOC, Zeta potential, CCC, etc.) is demonstrated. Taking the CCC prediction in Figure 3(g) as an example, the values ​​predicted by the interpolation model (Y-axis) and the true values ​​in the original data (X-axis) are highly concentrated near the ideal 1:1 diagonal, with a determination coefficient (R²) as high as 0.965 and a mean absolute error (MAE) of only 8.45. Similarly, the interpolation models for other key features also show extremely high goodness of fit (R² is generally greater than 0.9). This strongly demonstrates that the interpolation method of this invention can accurately learn and reproduce the complex nonlinear relationships between features, thereby generating a high-fidelity and high-completeness dataset, providing a solid and indispensable foundation for all subsequent accurate modeling and reliable mechanistic analysis.

[0052] In another specific implementation, the imputation method based on missing value prediction includes: obtaining a feature training set; standardizing each feature in the feature training set; determining whether each feature in the standardized feature training set contains missing values; if so, assigning the features containing missing values ​​to a first feature training set; otherwise, assigning the complete features to a second feature training set; using the features in the first feature training set as dependent variables and the features in the second feature training set as independent variables, inputting them into multiple models for training to obtain multiple prediction imputation models; comparing the performance parameters of the multiple prediction imputation models, and selecting the prediction imputation model with the largest performance parameter as the target prediction imputation model; and using the target prediction imputation model to imput each feature in the feature set to be imputed.

[0053] This imputation method based on missing value prediction can use each feature containing missing values ​​(such as "CCC") as a temporary dependent variable and all other features in the dataset as independent variables. It inputs these variables into multiple models (such as XGBoost, CatBoost, etc.) for training, resulting in multiple predictive imputation models capable of filling missing values. Then, based on the comparison of the coefficients of determination, the predictive imputation model with the best performance (the model with the largest coefficient of determination) is selected as the target model for imputing the missing values ​​in the feature set to be filled. Using this predictive imputation model for feature imputation effectively preserves the original data distribution of these features, does not destroy the intrinsic correlation between features, thus avoiding misleading subsequent model performance and mechanism analysis, and makes the predicted imputation results close to the actual imputation results.

[0054] like Figure 9 As shown, this application also relates to a dual-mechanism analysis device for predicting the aggregation rate of nanoparticles, comprising: a collection module 10 for collecting experimental data related to the aggregation rate of nanoparticles as an input feature set; a training module 20 for inputting the input feature set into a machine learning model for training and testing to obtain a nanoparticle aggregation rate prediction model; a screening module 30 for calculating the absolute SHAP value of each feature in the input feature set using the SHAP method, and screening at least two features from the input feature set as a key driving feature set based on the absolute SHAP value; and a verification module 40 for selecting two features from the key driving feature set and performing a visual verification of the interaction between the selected two features. This achieves the same technical effect as the dual-mechanism analysis method for predicting the aggregation rate of nanoparticles.

[0055] The present invention has been disclosed above with reference to preferred embodiments, but it is not intended to limit the present invention. All technical solutions obtained by adopting equivalent substitutions or equivalent transformations fall within the protection scope of the present invention.

Claims

1. A dual-mechanism analysis method for predicting the aggregation rate of nanoparticles, characterized in that, The steps include the following: Step S1: Collect experimental data related to the aggregation rate of nanoparticles as an input feature set; wherein each feature in the input feature set is labeled with an aggregation rate tag; Step S2: Input the input feature set into the machine learning model for training and testing to obtain a nanoparticle aggregation rate prediction model; Step S3: Calculate the absolute SHAP value of each feature in the input feature set using the SHAP method, and select at least two features from the input feature set as key driving feature sets based on the absolute SHAP values. Step S4: Select two features from the set of key driving features and perform a visual verification of the interaction between the two selected features.

2. The dual-mechanism analysis method according to claim 1, characterized in that, In step S1, missing values ​​are also imputed for the features in the input feature set; wherein the method for imputed missing values ​​includes: Each feature in the input feature set is standardized. Determine whether each feature in the standardized input feature set contains missing values. If so, assign the feature containing missing values ​​to the feature set to be filled. A missing value prediction-based imputation method is used to impute each feature in the feature set to be imputed.

3. The dual-mechanism analysis method according to claim 2, characterized in that, The imputation method based on missing value prediction includes: Obtain the feature training set; Each feature in the feature training set is standardized. Determine whether each feature in the standardized feature training set contains missing values. If it does, the feature containing missing values ​​is assigned to the first feature training set; otherwise, the complete feature is assigned to the second feature training set. The features in the first feature training set are used as the dependent variable, and the features in the second feature training set are used as the independent variable. These are then input into the model for training to obtain the prediction filling model. The prediction filling model is used to fill each feature in the feature set to be filled.

4. The dual-mechanism analysis method according to claim 2, characterized in that, The imputation method based on missing value prediction includes: Obtain the feature training set; Each feature in the feature training set is standardized. Determine whether each feature in the standardized feature training set contains missing values. If it does, the feature containing missing values ​​is assigned to the first feature training set; otherwise, the complete feature is assigned to the second feature training set. The features in the first feature training set are used as the dependent variable, and the features in the second feature training set are used as the independent variable. These are then input into multiple models for training to obtain multiple prediction filling models. The performance parameters of multiple prediction filling models are compared, and the prediction filling model with the largest performance parameter is selected as the target prediction filling model. The target prediction filling model is used to fill each feature in the feature set to be filled.

5. The dual-mechanism analysis method according to claim 1, characterized in that, In step S2, the training process of the machine learning model is as follows: The input feature set is divided into a training set and a test set according to a certain ratio; The training set is input into the first machine learning model for training, and an intermediate set of variables is obtained. The intermediate state variable set and the training set are input into the second machine learning model for training to obtain the nanoparticle aggregation rate prediction model. The aggregation rate prediction model was externally validated and its performance evaluated using a test set.

6. The dual-mechanism analysis method according to claim 1, characterized in that, Each feature in the input feature set is also labeled with a feature category label, which includes at least nanoparticle attribute category, dissolved organic matter attribute category and environmental attribute category; Step S3 also includes: Generate a SHAP summary graph based on the absolute SHAP value of each feature in the input feature set; Each feature in the input feature set is categorized according to the feature category label; The total absolute SHAP value corresponding to each feature category label is calculated based on the absolute SHAP value of each feature under each category label after classification. An analysis graph of features and feature categories is generated based on the total absolute SHAP values ​​and the absolute SHAP value of each feature in the input feature set.

7. The dual-mechanism analysis method according to claim 1, characterized in that, In step S4, the method for visually verifying the interaction between the two selected features includes: A SHAP dependency graph is generated based on the absolute SHAP value of each feature in the key driving feature set, and two features with interaction are selected based on the SHAP dependency graph. Using two selected features as the X-axis and Y-axis, the predicted values ​​of the aggregation rate by the aggregation rate prediction model are represented by color mapping to generate a contour map or heat map; the contour map or heat map is used to show the interaction between the two selected features.

8. A dual-mechanism analysis device for predicting the aggregation rate of nanoparticles, characterized in that, include: The collection module is used to collect experimental data related to the aggregation rate of nanoparticles as an input feature set. The training module is used to input the input feature set into the machine learning model for training and testing, so as to obtain a prediction model for the aggregation rate of nanoparticles. The filtering module is used to calculate the absolute SHAP value of each feature in the input feature set using the SHAP method, and to filter at least two features from the input feature set as key driving feature sets based on the absolute SHAP value. The verification module is used to select two features from the set of key driving features and perform visual verification of the interaction between the two selected features.

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