Methods, systems, and storage media for predicting the adsorption performance of noble metal ions in solution by metal-organic framework materials.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- UNIV OF SCI & TECH BEIJING
- Filing Date
- 2025-11-06
- Publication Date
- 2026-06-30
AI Technical Summary
In existing technologies, single machine learning models and grid search methods suffer from overfitting or underfitting in the prediction of noble metal ion adsorption capacity, resulting in limited prediction accuracy. Furthermore, traditional methods cannot effectively utilize prior knowledge for model optimization in small sample scenarios, leading to high R&D costs and low efficiency for noble metal ion adsorption materials.
A stacked ensemble model-based approach was adopted, including random forest, extreme gradient boosting, and lightweight gradient boosting machine as base models, combined with gradient boosting tree as meta-model, and Bayesian optimization for hyperparameter tuning. The importance of variables was analyzed by partial least squares method to construct an adsorption performance prediction system for MOFs materials.
It improves the accuracy of predicting the adsorption performance of noble metal ions, reduces computational costs and time, enhances the generalization ability and prediction accuracy of the model, adapts to complex factors affecting adsorption capacity, and reduces redundant computation.
Smart Images
Figure CN121528353B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of precious metal resource recycling, and in particular to a method, system, and storage medium for predicting the adsorption performance of metal-organic frameworks (MOFs) for precious metal ions in solution based on a stacked integration model. Background Technology
[0002] Precious metals, including gold, silver, and platinum group metals, possess excellent physical and chemical properties and have wide applications in electronics, jewelry, medical devices, aerospace, and other fields. In recent years, the demand for precious metals has continued to grow, while mineral resources are insufficient to meet this increasing demand. Simultaneously, with rapid economic development and improved living standards, a large amount of electronic waste containing precious metals is generated annually. Currently, only a small amount of secondary precious metal resources are effectively recycled, resulting in serious resource waste and environmental pollution. Therefore, the efficient recycling and utilization of secondary precious metal resources is of great significance for economic development and environmental protection.
[0003] Methods for recovering precious metal ions from aqueous solutions mainly include chemical precipitation, membrane separation, solvent extraction, microbial methods, and adsorption. Among these, adsorption refers to the use of adsorbent materials to enrich and recover precious metal ions from solution through physicochemical reactions. Due to its advantages such as simple operation, high efficiency, low cost, and no secondary pollution, it is considered one of the most promising technologies. Commonly used adsorbent materials include activated carbon, resins, and biosorbents, but they all have certain limitations, such as low adsorption capacity and difficult regeneration of activated carbon, poor selectivity of ion exchange resins, and poor mechanical properties and low adsorption capacity of biosorbents. Therefore, there is an urgent need to develop new and highly efficient precious metal ion adsorption materials.
[0004] Metal-organic frameworks (MOFs), also known as porous coordination polymers, possess extremely high specific surface areas, large porosities, and flexible pore structures, making them highly promising for the recycling of precious metal secondary resources. For novel precious metal ion adsorbents, the adsorption capacity is a crucial indicator for evaluating their adsorption performance. Currently, numerous researchers have synthesized various modified MOF materials through extensive experiments, significantly improving the selectivity and adsorption efficiency for precious metal ions. Theoretically, an infinite number of MOF materials can be obtained by changing the types and coordination modes of organic ligands and metal nodes. However, exploring the development of MOF adsorbent materials through artificial experiments is extremely costly in terms of both economic and time resources, limiting the research and development of novel MOF adsorbent materials.
[0005] Machine learning boasts advantages such as low computational cost and strong predictive power, enabling it to analyze patterns from large amounts of data and predict unknown data. Applying machine learning to the research and development of new materials can significantly shorten the development cycle, improve efficiency, and reduce costs. Currently, related technologies often employ a single machine learning model combined with grid search for hyperparameter tuning to predict adsorption amounts. However, the fixed structure and learning preferences of a single model make it difficult to adapt to complex factors influencing adsorption amounts. In scenarios with uneven training sample distribution or strong feature correlations, it is prone to overfitting or underfitting, resulting in limited prediction accuracy. Grid search, as a traditional hyperparameter tuning method, exhaustively searches all possible parameter combinations within a predefined hyperparameter space and selects the optimal combination through cross-validation. However, this method involves high computational costs, and its optimization effect depends on the discretization of candidate hyperparameter values, limiting tuning accuracy. Therefore, the combination of a single model and grid search cannot effectively utilize prior knowledge to assist model optimization in small-sample scenarios, further amplifying performance deficiencies. Summary of the Invention
[0006] To address the shortcomings of existing technologies, this invention proposes a method, system, and storage medium for predicting the adsorption performance of noble metal ions in solution by MOFs based on a stacked integration model, which can improve the accuracy of predicting the adsorption performance of noble metal ions in solution by MOFs materials.
[0007] This invention provides the following technical solution:
[0008] According to a first aspect of the present invention, a method for predicting the adsorption performance of noble metal ions in solution by metal-organic frameworks (MOFs) based on a stacked integration model is provided, characterized by comprising the following steps:
[0009] S1. Collect and organize experimental data on the adsorption of noble metal ions in solution by MOFs materials with transition metal ions as metal centers, including the chemical properties, structural properties and adsorption experimental conditions of the MOFs materials as input variables, and the adsorption amount of noble metal ions as target variables. Organize and screen the data and perform quantitative processing to form a database.
[0010] S2, the database is divided into training set and test set, a stacked ensemble machine learning model is constructed, the stacked ensemble machine learning model is trained based on the training set, and Bayesian optimization is used simultaneously to perform hyperparameter tuning on the model (including base model and meta-model), and then the tuned model is used to predict the test set, and finally the prediction performance of the stacked ensemble machine learning model is obtained.
[0011] S3. Partial Least Squares (PLS) was used to fit the data and calculate the importance scores of the chemical properties, structural properties and adsorption experimental conditions of the MOFs material as different variables. The influence of these variables on the adsorption amount of the noble metal ions was analyzed and variables with low importance scores were removed.
[0012] S4. The trained stacked ensemble model is used to predict new experimental data to evaluate the predictive effect of the stacked ensemble model on the adsorption performance of MOFs.
[0013] Furthermore, in step S1, the noble metal ions include Au(III), Ag(I), and six platinum group metal ions: Pt(IV), Pd(II), Rh(III), Ir(IV), Os(IV), and Ru(IV).
[0014] The chemical properties of the MOFs materials include the topological polar surface area of transition metal centers such as Fe, Cu, Zn, Zr, and Cr, as well as organic ligands. Number of hydrogen bond donors, number of hydrogen bond acceptors, molecular volume The number of dipole moments and different types of chemical bonds;
[0015] The different types of chemical bonds specifically include: CC, CN, CR, CS, C=C, NC, CC, CN, CO, CR,
[0016] C=C(aromatic), C=C(ring), C=N(ring), C=O, C≡N, N=N(ring), OR;
[0017] The terminology is defined as follows:
[0018] (1)(ring): refers to the cyclic structure in MOF organic ligands, including aromatic rings and alicyclic rings, only limited to the fact that both bonding atoms of the chemical bond are located on the ring or bonded to the ring;
[0019] (2)(aromatic): refers to an aromatic unsaturated bond, only limited to the fact that the C=C bond is located within the aromatic ring;
[0020] (3) R: refers to alkyl substituent;
[0021] The structural properties of the MOFs material include BET specific surface area (m²). 2 / g), pore size (nm) and pore volume (cm³) 3 / g);
[0022] The adsorption experimental conditions of the MOFs materials include metal ion concentration (mg / L), adsorbent dosage (mg), reaction time (min), pH value, and reaction temperature (K).
[0023] Here, in S1, the experimental data comes from relevant publications published in the past ten years. Literature is searched and screened in Web of Science and CNKI using keywords such as "MOF materials", "adsorption", and "noble metal ions". All data points are extracted from the text, charts, or supporting information of the literature. For data presented in the graphs without specific text descriptions, the Web Plot Digitizer tool is used to extract data from the graphs to ensure the accuracy of the data source.
[0024] Furthermore, in S1, the transition metal includes five transition metal ions: iron (Fe), copper (Cu), zinc (Zn), zirconium (Zr), and chromium (Cr).
[0025] Furthermore, in step S2, the database is divided into a training set and a test set in a ratio of 80%:20%.
[0026] Further, in step S2, the stacked ensemble machine learning model includes:
[0027] The first layer serves as the base learning layer, including three base models: Random Forest (RF), Extreme Gradient Boosting (XGBoost), and Lightweight Gradient Boosting Machine (LightGBM).
[0028] The generation of training set meta-features for each base model employs Q-fold cross-validation, specifically including: splitting the training set into Q folded subsets, where Q ranges from 5 to 10 to balance computational efficiency and meta-feature reliability; for each base model, training the base model using the remaining Q-1 folded subsets (excluding the i-th folded subset (i = 1, 2, ..., Q), and then using the trained base model to predict the i-th folded subset to obtain the predicted value corresponding to that folded subset; concatenating the predicted values of all folded subsets to form training set meta-features consistent with the number of training set samples, i.e., the first predicted value meta-feature for each base model; retraining each base model using the complete training set; and then, for each base model trained using the complete training set, predicting the test set to obtain the test set meta-feature corresponding to each base model, i.e., the second predicted value meta-feature.
[0029] The second layer serves as the meta-learning layer, including the Gradient Boosting Tree (GBT) model as the meta-model:
[0030] The first predicted value meta-features of each base model obtained in the first layer are concatenated into a meta-training feature matrix, and the meta-model is trained using the amount of noble metal ion adsorption as a label; the second predicted value meta-features of each base model obtained in the first layer are concatenated into a meta-test feature matrix, which is input into the trained meta-model, and the final prediction result of the amount of noble metal ion adsorption corresponding to the test set is output.
[0031] Further, in step S1, the quantitative processing refers to extracting the SMILES codes of the organic ligands of the MOFs material from the PubChem database and calculating their topological polar surface areas using the RDkit toolkit. Number of hydrogen bond donors, number of hydrogen bond acceptors, molecular volume The dipole moment and the number of different types of chemical bonds are used to quantitatively describe the chemical properties of the organic ligands in the MOFs materials.
[0032] Furthermore, in step S1, organizing and filtering the data refers to removing duplicate and invalid data, and statistically analyzing data missing information.
[0033] Furthermore, if data is missing, then step S1 will be followed by:
[0034] Given the presence of some missing values in the original database, the missing values were supplemented using K-Nearest Neighbor (KNN) imputation and mean imputation methods, respectively. The AdaBoost algorithm was then used to evaluate the prediction accuracy, determine the optimal imputation method, and form a complete database.
[0035] Furthermore, the method of evaluating prediction accuracy using the adaptive enhancement algorithm specifically involves using the mean absolute error (MAE) to evaluate prediction accuracy, calculated as follows:
[0036]
[0037] Among them, y i This represents the true value of the noble metal ion adsorption amount for the i-th sample. Let i be the predicted value of the noble metal ion adsorption amount of the i-th sample, where i is the sample index, which takes the value 1, 2, ..., n, and n is the total number of samples to be evaluated (n≥1).
[0038] Furthermore, in step S3:
[0039] Features with an importance score >1 are considered core influence features;
[0040] Features with an importance score of 0.5 or less and ≤1 are considered to have significant influence.
[0041] Features with an importance score ≤ 0.5 are considered to have a weak influence and are thus considered to have a low importance score.
[0042] Furthermore, in step S2, the hyperparameter tuning using Bayesian optimization is as follows:
[0043] Determine the hyperparameter space X hp and the objective function f(x), where x ∈ X hp , x is the hyperparameter of the stacked ensemble machine learning model (including the base model and the meta-model) to be optimized, f(x) is the metric function for measuring the performance of the hyperparameter, and the value is the 3-fold cross-validation mean squared error CV-MSE corresponding to the hyperparameter x. For a given objective function value z, define the conditional probability distribution of the hyperparameter x as p(x|z);
[0044] In the Bayesian algorithm, focus on two types of conditional probability distributions p(x|zI good ) and p(x|zI bad ), where p(x|zI good ) represents that the objective function value CV-MSE is lower than the preset threshold τ, corresponding to "hyperparameter combinations with excellent performance", and the value of τ is the mean of the CV-MSE of 3 groups of hyperparameters in the initial random search stage. p(x|zI bad ) represents that the objective function value CV-MSE is higher than or equal to the threshold τ, corresponding to "hyperparameter combinations with poor performance";
[0045] Use the Gaussian Process (GP) as the probability model to model the mapping relationship between hyperparameters and performance. The prior distribution of the Gaussian process is defined as f(x) ∼ GP(m(x), k(x, x')), where m(x) = 0 is the mean function and k(x, x') is the radial basis kernel function, which is used to measure the similarity between two hyperparameter combinations x and x'. The expression is:
[0046]
[0047] where D is the dimension of the hyperparameter space, that is, the total number of hyperparameters to be optimized, xI d is the value of the d-th hyperparameter of the hyperparameter combination x, xI d ′ is the value of the d-th hyperparameter in another hyperparameter combination x′, lI d is the length scale of the d-th dimension hyperparameter, which is used to control the smoothness of the influence of the hyperparameter in this dimension on the performance. The larger lI d , the smoother the influence of the change of the hyperparameter value on the performance;
[0048] Based on the N groups of hyperparameter-performance data DI set = {(xI hpx , yI hps )丨s = 1, 2, … N} (where xI hpsLet s be the s-th combination of hyperparameters to be optimized, whose dimension is related to the hyperparameter space X. hp The dimension D is consistent, y hps =f(x) hps ) represents the CV-MSE value corresponding to this set of hyperparameters, and for the unknown hyperparameter x hp* performance f hp* Posterior inference is performed, and the posterior distribution remains a Gaussian distribution;
[0049] Select the next hyperparameter evaluation point, perform hyperparameter iteration, and after the iteration is complete, retrieve the data from dataset D. set The combination of hyperparameters with the smallest objective function value CV-MSE is selected as the optimal hyperparameters for the stacked ensemble machine learning model. The hyperparameters are then subjected to type adaptation processing to ensure consistency with the model parameter type requirements.
[0050] Further, in step S2, the predictive performance metric of the stacked integration model is the coefficient of determination (R²). 2 Mean absolute error (MAE) and root mean square error (RMSE), R 2 The RMSE calculation method is as follows:
[0051]
[0052] Among them, y i This represents the true value of the noble metal ion adsorption amount for the i-th sample. This represents the predicted value of noble metal ion adsorption for the i-th sample. Let be the sample mean, i be the sample index, which takes the value 1, 2, ..., n, and n be the total number of samples to be evaluated (n≥1).
[0053] Furthermore, in step S3, partial least squares (PLS) is used to fit the data and give a variable importance score. Based on the score results, the influence of different variables on the adsorption effect of noble metal ions is analyzed. The core formula of PLS is as follows:
[0054] Table 1 Definitions of Basic Symbols
[0055]
[0056]
[0057] Data centerization:
[0058] Among them 1 n It is an n×1 vector of all 1s. Let X be the column mean of the independent variable matrix. By transposing it, matrix operations are used to simultaneously subtract the mean of the corresponding column from the independent variables of all samples, thus eliminating the influence of differences in dimensions.
[0059] Independent variable weights (m-th latent variable):
[0060] X m-1 Let y be the residual matrix of the independent variable after the (m-1)th iteration (initially X0). m-1 Let w be the residual vector of the dependent variable after the (m-1)th iteration (initially y0), and |||2 be the L2 norm (Euclidean distance) used to normalize the weight vector to ensure w m The modulus is 1 to avoid the weight values being affected by the dimensions;
[0061] Independent variable score (m-th latent variable): t m =X m-1 w m ,
[0062] This indicates that the weight vector w m For the residual matrix X m-1 Performing a linear combination yields the m-th latent variable, t m Each element corresponds to a latent variable value of a sample;
[0063] Independent variable loading (m-th):
[0064] The numerator is the covariance of the residual matrix and the latent variables, and the denominator is the variance of the latent variables, P. m To measure the correlation between independent variables and latent variables (the larger the absolute value, the more significant the contribution of the independent variable to the latent variable);
[0065] Final regression coefficient: b = W(P) T W) -1 q,
[0066] W is a p×k weight matrix (each column corresponds to the weight vector w of a latent variable). m );
[0067] P is a p×k loading matrix (each column corresponds to a weight vector P of a latent variable). m );
[0068] (P T W) -1 Let P be a matrix T The inverse matrix of W ensures that the formula is invertible;
[0069] q is a k×1 dependent variable loading vector (in the case of a single dependent variable, each element corresponds to the q value of a latent variable);
[0070] Each element of b in the final b jThis represents the regression coefficient of the j-th independent variable on the adsorption amount, which can be directly used to calculate the variable importance score (the larger the absolute value of the coefficient, the more significant the impact).
[0071] According to a second aspect of the present invention, a system for predicting the adsorption performance of noble metal ions in solution by MOFs based on a stacked integration model is provided. The system includes: a processor and a memory for storing executable instructions; wherein the processor is configured to execute the executable instructions to perform the method for predicting the adsorption performance of noble metal ions in solution by MOFs based on a stacked integration model as described in any of the preceding aspects.
[0072] According to a third aspect of the present invention, a computer-readable storage medium is provided, wherein a computer program is stored thereon, and when the computer program is executed by a processor, it implements the method for predicting the adsorption performance of noble metal ions in solution by MOFs based on a stacked integration model as described in any of the preceding aspects.
[0073] The present invention provides a method for predicting the adsorption performance of noble metal ions in solution by MOFs based on a stacked integration model, which has the following beneficial effects:
[0074] (1) By using SMILES coding and RDkit toolkit to introduce the chemical properties of MOFs materials as descriptors, the types of factors affecting the adsorption amount are enriched. The chemical properties of MOFs materials have a significant impact on the adsorption amount and cannot be ignored. Introducing chemical descriptors as input variables can make the model's prediction effect more comprehensive and accurate.
[0075] (2) The stacked ensemble model employing "XGBoost, RF, and LightGBM as base models + GBT as meta-model" possesses multi-dimensional core advantages. Although the three base models all belong to the category of tree models, their learning mechanisms have different focuses. XGBoost excels at capturing nonlinear correlations such as aperture threshold effects.
[0076] RF can robustly uncover weakly correlated feature combinations between metal centers and ligands, while LightGBM can efficiently handle high-dimensional chemical bond features. These three technologies not only cover the key influencing factors of adsorption capacity but also ensure prediction consistency through the commonalities of tree models, laying a high-quality foundation for subsequent integration. The GBT meta-model can dynamically allocate the weights of the base models, accurately correcting the biases of single base models, balancing accuracy and interpretability, and exhibiting strong generalization ability. Compared to single base models, it achieves a three-dimensional balance of "accuracy-efficiency-interpretability," adapting to the actual needs of MOF adsorption capacity prediction.
[0077] (3) A Bayesian algorithm is introduced to perform hyperparameter tuning on the base model and meta-model. Based on the Gaussian process probability model, it can dynamically predict the optimal hyperparameter region using the searched hyperparameter-performance data. Through "initial random exploration + iterative directional optimization", the computational load of tuning is significantly reduced while accurately locating the globally optimal hyperparameter. Moreover, it quantifies the uncertainty of hyperparameter performance through posterior distribution, which can prioritize the exploration of high-potential regions and avoid the discretization bias of grid search. This optimizes the fitting accuracy and generalization ability of each base model and meta-model, providing key support for the efficient construction of stacked integrated models and high-precision adsorption prediction. At the same time, it takes into account both tuning efficiency and parameter reliability, adapting to the actual needs of MOFs materials with limited experimental data and high feature dimensions.
[0078] (4) By calculating the importance scores of different descriptors, the influence of different descriptors on the adsorption effect can be determined. Only descriptors with high importance scores are selected for fitting and prediction, which can optimize the descriptors, reduce redundancy, and thus save computational resources.
[0079] Source, improve computing speed. Attached Figure Description
[0080] To more clearly illustrate the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the results shown in these drawings without creative effort.
[0081] Figure 1 This is a step sequence diagram of an embodiment of the present invention;
[0082] Figure 2 This is a fitting graph of the predicted values and the true values obtained by training a stacked ensemble model using Embodiment 1 of the present invention;
[0083] Figure 3 This is the optimal number of components selected when calculating the importance score of variables in Embodiment 1 of the present invention;
[0084] Figure 4 These are the results of importance scores for different variables;
[0085] Figure 5 This is a comparison chart of the predicted values of adsorption results using a stacked ensemble model and the experimental results. Detailed Implementation
[0086] The technical solution will now be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the specific embodiments described are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.
[0087] A method for predicting the adsorption performance of noble metal ions in solution by MOFs based on a stacked ensemble model, the method comprising the following steps:
[0088] S1. Collect and organize experimental data on the adsorption of noble metal ions in solution by MOFs materials with five transition metal ions as metal centers: iron (Fe), copper (Cu), zinc (Zn), zirconium (Zr), and chromium (Cr). The chemical properties, structural properties, and adsorption experimental conditions of the MOFs materials are used as input variables, and the adsorption amount of noble metal ions is used as the target variable. The data are organized and screened, and the qualitative data are quantified to form the original database.
[0089] S2. Based on the presence of some missing values in the original database, the missing values are supplemented using K-nearest neighbor (KNN) imputation and mean imputation respectively. The AdaBoost algorithm is used to evaluate the prediction accuracy, determine the best imputation method, and form a complete database.
[0090] S3. The database is divided into training set and test set according to the ratio of 80%:20%. A stacked ensemble machine learning model is constructed. The stacked ensemble machine learning model is trained based on the training set. During the process, Bayesian optimization is used to tune the hyperparameters of each base model and meta-model. The tuned model is then used to predict the test set. Finally, the prediction performance of the single model and the stacked ensemble model are obtained respectively.
[0091] Among them, a stacked ensemble machine learning model is constructed. The first layer, as the base learning layer, includes the Random Forest (RF) model, the Extreme Gradient Boosting (XGBoost) model, and the Lightweight Gradient Boosting Machine (LightGBM) model. These three base models are trained with the training set respectively.
[0092] Using Q-fold cross-validation, each base model is used to predict values on the training set, generating a new set of predicted values (meta-features). Simultaneously, the trained base models are used to predict values on the test set, generating meta-features for the test set.
[0093] The second layer, as a meta-learning layer, uses the Gradient Boosting Tree (GBT) model. It takes the multiple predicted values (meta-features) generated by the first layer as a new input matrix and the original adsorption amount as the output to train the GBT model and obtain the final prediction result.
[0094] S4. Partial Least Squares (PLS) is used for fitting, the importance scores of different variables are calculated, the influence of different factors on the adsorption results is analyzed, and descriptors with higher importance scores are selected to reduce the amount of computation required for model prediction and improve computational efficiency.
[0095] S5. The trained stacked ensemble model is used to predict new experimental data to evaluate the predictive effect of the stacked ensemble model on the adsorption performance of MOFs.
[0096] Furthermore, in step S1, the experimental data comes from relevant publications published in the past decade. Literature is searched and screened in Web of Science and CNKI using keywords such as "MOF materials", "adsorption", and "noble metal ions". All data points are extracted from the text, charts, or supporting information of the literature. For data presented in the graphs without specific text descriptions, the Web Plot Digitizer tool is used to extract the data from the graphs to ensure the accuracy of the data source.
[0097] Furthermore, in step S1, the adsorbed noble metal ions include Au(III), Ag(I), and platinum group metal ions such as Pt(IV) and Pd(II);
[0098] The chemical properties of the MOFs material include the topological polar surface area of five transition metal centers (Fe, Cu, Zn, Zr, and Cr) and organic ligands. Number of hydrogen bond donors, number of hydrogen bond acceptors, molecular volume The dipole moment and the number of different types of chemical bonds, structural properties including BET specific surface area (m²) 2 / g), pore size (nm) and pore volume (cm³) 3 / g), the experimental conditions included metal ion concentration (mg / L), adsorbent dosage (mg), reaction time (min), pH value and reaction temperature (K).
[0099] Furthermore, in step S1, organizing and filtering the data refers to removing duplicate and invalid data, and statistically analyzing data missing information.
[0100] Furthermore, in step S1, quantifying the qualitative data involves extracting the SMILES codes of each organic ligand from the PubChem database and calculating its topological polar surface area using the RDkit toolkit. Number of hydrogen bond donors, number of hydrogen bond acceptors, molecular volume By measuring the dipole moment and the number of different types of chemical bonds, a quantitative description of the chemical properties of organic ligands in MOF materials can be achieved.
[0101] Furthermore, in step S2, the AdaBoost algorithm is used to evaluate the prediction accuracy using the mean absolute error (MAE), calculated as follows:
[0102]
[0103] Among them, y i This represents the true value of the noble metal ion adsorption amount for the i-th sample. Let i be the predicted value of the noble metal ion adsorption amount of the i-th sample, where i is the sample index, which takes the value 1, 2, ..., n, and n is the total number of samples to be evaluated (n≥1).
[0104] Furthermore, in step S3, the hyperparameter tuning of each base model using Bayesian optimization is as follows:
[0105] Determine the hyperparameter space X hp and the objective function f(x), where x∈X hp x is the hyperparameter of the machine learning model to be optimized, f(x) is the index function that measures the performance of the hyperparameter, and the value is the 3-fold cross-validation mean square error (CV-MSE) corresponding to the hyperparameter x. For a given objective function value z, the conditional probability distribution of the hyperparameter x is defined as p(x|z).
[0106] In Bayesian algorithms, the focus is on p(x|z) good ) and p(x|z bad Two types of conditional probability distributions, where p(x|z) good The statement indicates that the objective function value (CV-MSE) is lower than a preset threshold τ, corresponding to a "high-performance hyperparameter combination". τ is the mean of the CV-MSE of the three hyperparameter sets during the initial random search phase. bad ) indicates that the objective function value (CV-MSE) is higher than or equal to the threshold τ, corresponding to "poor performance hyperparameter combination";
[0107] A Gaussian process (GP) is used as the probabilistic model to model the hyperparameter-performance mapping relationship. The prior distribution of the Gaussian process is defined as f(x) ~ GP(m(x), k(x, x')), where m(x) = 0 is the mean function and k(x, x') is the radial basis function kernel function, expressed as:
[0108]
[0109] Where D is the dimension of the hyperparameter space, i.e., the total number of hyperparameters to be optimized, x d Let x be the value of the d-th hyperparameter in the hyperparameter combination x. d$l_d'$ is the value of the $d$-th hyperparameter in another hyperparameter combination $x'$. d $l_d$ d is the length scale of the $d$-th dimensional hyperparameter, which is used to control the smoothness of the influence of the hyperparameter in this dimension on the performance. d The larger $l_d$ is, the smoother the influence of the change in the hyperparameter value on the performance.
[0110] Based on the $N$ groups of hyperparameter-performance data $D$ set set $=\{(x$ hps hps , $y$ hps hps )|$s = 1, 2, \ldots, N\}$ (where $x$ hps hps is the $s$-th group of hyperparameter combinations to be optimized, whose dimension is consistent with the dimension $D$ of the hyperparameter space $X$ hp hp , and $y$ hps hps $= f(x$ hps hps ) is the CV-MSE value corresponding to this group of hyperparameters. For the performance $f$ hp* hp* of the unknown hyperparameter $x$ hp* hp* , posterior inference is performed, and the posterior distribution is still a Gaussian distribution.
[0111] Select the next hyperparameter evaluation point and perform hyperparameter iteration. After the iteration ends, screen out the hyperparameter combination with the smallest objective function value CV-MSE from the dataset $D$ set set as the optimal hyperparameters of the corresponding machine learning model, and perform type adaptation processing on the hyperparameters to ensure consistency with the model parameter type requirements.
[0112] Furthermore, in the step S3, the prediction performance metrics of the single model and the stacked ensemble model are the coefficient of determination ($R$ 2 2 I), the mean absolute error (MAE), and the root mean square error (RMSE). The calculation methods of $R$ 2 <00OO070>and RMSE are as follows:
[0113]
[0114] where $y$ i i is the true value of the precious metal ion adsorption amount of the $i$-th sample, is the predicted value of the precious metal ion adsorption amount of the $i$-th sample, is the sample mean, $i$ is the sample index, taking values of $1, 2, \ldots, n$, and $n$ is the total number of evaluation samples ($n\geq1$);
[0115] Furthermore, in the step S4, PLS is used for fitting to give variable importance scores. According to the scoring results, analyze the influence degree of different variables on the precious metal ion adsorption effect. The core formula of PLS is as follows:
[0116] Table 2 Basic symbol definitions
[0117]
[0118]
[0119] Data centerization:
[0120] Among them 1 n It is an n×1 vector of all 1s. Let X be the column mean of the independent variable matrix. By transposing it, matrix operations are used to simultaneously subtract the mean of the corresponding column from the independent variables of all samples, thus eliminating the influence of differences in dimensions.
[0121] Independent variable weights (m-th latent variable):
[0122] Independent variable score (m-th latent variable): t m =X m-1 w m
[0123] Independent variable loading (m-th):
[0124] Final regression coefficient: b = W(P) T W) -1 q.
[0125] Example 1
[0126] This invention provides a method for predicting the adsorption performance of Au(III) in solution using MOFs based on a stacked integration model. The implementation steps are as follows: Figure 1 As shown:
[0127] (1) Collect and organize experimental data on the adsorption of Au(III) in solution by MOFs materials with five transition metal ions as metal centers: iron (Fe), copper (Cu), zinc (Zn), zirconium (Zr), and chromium (Cr). The chemical properties, structural properties, and adsorption experimental conditions of the MOFs materials are used as input variables, and the adsorption amount of Au(III) is used as the target variable. The data are organized and screened, and the qualitative data are quantified to form the original database.
[0128] The original experimental data on Au(III) adsorption of relevant MOF materials were all obtained from publicly published literature. Literature was searched in Web of Science and CNKI using keywords such as "MOF materials," "adsorption," and "Au(III)" to select relevant publications from the past decade. The chemical properties of the MOF materials included the topological polar surface areas of transition metal centers such as Fe, Cu, Zn, Zr, and Cr, as well as organic ligands. Number of hydrogen bond donors, number of hydrogen bond acceptors, molecular volume The dipole moment and the number of different types of chemical bonds, structural properties including BET specific surface area (m²) 2 / g), pore size (nm) and pore volume (cm³) 3 The experimental conditions included metal ion concentration (mg / L), adsorbent dosage (mg), reaction time (min), pH value, and reaction temperature (K). All data points were extracted from the text, figures, or supporting information in the literature. For data presented in graphs without specific textual descriptions, the Web Plot Digitizer tool was used to extract the data from the graphs to ensure the accuracy of the data sources. After data collection, the data were filtered and organized to form a database.
[0129] Duplicate and invalid data were removed from the database, and data missing information was statistically analyzed. The SMILES codes for each organic ligand were extracted from the PubChem database, and their topological polar surface areas were calculated using the RDkit toolkit. Number of hydrogen bond donors, number of hydrogen bond acceptors, molecular volume By measuring the dipole moment and the number of different types of chemical bonds, a quantitative description of the chemical properties of organic ligands in MOF materials can be achieved.
[0130] (2) Given the presence of some missing values in the original database, K-Nearest Neighbor (KNN) imputation and mean imputation methods were used to fill in the missing values. The AdaBoost algorithm was used to evaluate the prediction accuracy, and the mean absolute error (MAE) was used as the comparison metric, which was obtained through the following formula:
[0131]
[0132] Among them, y i This represents the true value of the noble metal ion adsorption amount for the i-th sample. Let i be the predicted value of the noble metal ion adsorption amount of the i-th sample, where i is the sample index, which takes the value 1, 2, ..., n, and n is the total number of samples to be evaluated (n≥1).
[0133] The mean interpolation method was ultimately determined to be the best interpolation method, thus forming a complete database.
[0134] (3) The database was divided into training and test sets in an 80%:20% ratio. A stacked ensemble machine learning model was constructed using Python tools. The first layer, as the base learning layer, included a random forest (RF) model, an extreme gradient boosting (XGBoost) model, and a lightweight gradient boosting machine (LightGBM) model. Q-fold cross-validation was used to predict the training set with each base model, generating a new set of predicted values (meta-features). At the same time, the trained base models were used to predict the test set, generating meta-features for the test set. The second layer, as the meta-learning layer, used a gradient boosting tree (GBT) model. The multiple predicted values (meta-features) generated by the first layer were used as a new input matrix, and the original adsorption value was used as the output value to train the GBT model, obtaining the final prediction results.
[0135] Stacked ensemble machine learning models are used to train and predict on the training and test sets respectively. During the process, Bayesian optimization is used to tune the hyperparameters of each base model, as detailed below:
[0136] Determine the hyperparameter space X hp and the objective function f(x), where x∈X hp x is the hyperparameter of the machine learning model to be optimized, f(x) is the index function that measures the performance of the hyperparameter, and the value is the 3-fold cross-validation mean square error (CV-MSE) corresponding to the hyperparameter x. For a given objective function value z, the conditional probability distribution of the hyperparameter x is defined as p(x|z).
[0137] In Bayesian algorithms, the focus is on p(x|z) good ) and p(x|z bad Two types of conditional probability distributions, where p(x|z) good The statement indicates that the objective function value (CV-MSE) is lower than a preset threshold τ, corresponding to a "high-performance hyperparameter combination". τ is the mean of the CV-MSE of the three hyperparameter sets during the initial random search phase. bad ) indicates that the objective function value (CV-MSE) is higher than or equal to the threshold τ, corresponding to "poor performance hyperparameter combination";
[0138] A Gaussian process (GP) is used as the probabilistic model to model the hyperparameter-performance mapping relationship. The prior distribution of the Gaussian process is defined as f(x) ~ GP(m(x), k(x, x')), where m(x) = 0 is the mean function and k(x, x') is the radial basis function kernel function, expressed as:
[0139]
[0140] Where D is the hyperparameter dimension, x d Let l be the value of the d-th dimension of the hyperparameter x.d is the length scale of the d-th dimensional hyperparameter;
[0141] Based on the N groups of hyperparameter-performance data D that have been searched set ={(x hps ,y hps )丨s = 1, 2, … N} (where x hps is the s-th group of hyperparameter combinations to be optimized, whose dimension is consistent with the dimension D of the hyperparameter space X hp , and y hps = f(x hps ) is the CV-MSE value corresponding to this group of hyperparameters. Perform posterior inference on the performance f hp* of the unknown hyperparameter x hp* . The posterior distribution is still a Gaussian distribution;
[0142] Select the next hyperparameter evaluation point and perform hyperparameter iteration. After the iteration ends, screen out the hyperparameter combination with the smallest CV-MSE value of the objective function from the dataset D set as the optimal hyperparameters of the corresponding machine learning model, and perform type adaptation processing on the hyperparameters to ensure consistency with the model parameter type requirements.
[0143] Finally, obtain the prediction performances of the single model and the stacked ensemble model respectively. The prediction performance metrics are the coefficient of determination (R 2 ), the mean absolute error (MAE), and the root mean square error (RMSE). The calculation methods of R 2 and RMSE are as follows: <00004As shown in the table above, the prediction performance of the stacked ensemble model is superior to that of a single model. This demonstrates that by using a Gradient Boosting Tree (GBT) model as the meta-learning layer in the second layer, the prediction patterns of each base model for key features are preserved. Furthermore, the GBT model's gradient boosting iterative mechanism achieves error complementarity, significantly improving prediction accuracy. Here, the fitting graph between the predicted and true values obtained from training the stacked ensemble model is shown in the figure. Figure 2 As shown.
[0150] (4) Partial Least Squares (PLS) is used for fitting, the importance scores of different variables are calculated, the influence of different factors on the adsorption results is analyzed, and descriptors with higher importance scores are selected to reduce the amount of computation required for model prediction and improve computational efficiency. The core formula of PLS is as follows:
[0151] Table 4 Definitions of Basic Symbols
[0152]
[0153]
[0154] Data centerization:
[0155] Among them 1 n It is an n×1 vector of all 1s. Let X be the column mean of the independent variable matrix. By transposing it, matrix operations are used to simultaneously subtract the mean of the corresponding column from the independent variables of all samples, thus eliminating the influence of differences in dimensions.
[0156] Independent variable weights (m-th latent variable):
[0157] Independent variable score (m-th latent variable): t m =X m-1 w m
[0158] Independent variable loading (m-th):
[0159] Final regression coefficient: b = W(P) T W) -1 q.
[0160] The higher the importance score, the greater the influence of the variable on the adsorption effect. Figure 3The results show that the validation error is minimized when the number of components is 4. To prevent overfitting, according to the 1SE principle, which is to select the simplest model within the standard error range based on the number of components corresponding to the minimum validation error, the optimal number of components is determined to be 3, which gives the model the best generalization ability. Figure 4 The importance scores of each variable were calculated using the optimal number of components (3). Importance scores measure the importance of features to the model; a VIP score > 1 indicates strong influence, while 0.5 < VIP score < 1 indicates moderate influence. According to the figure, variables with VIP scores > 0.5 include the metal centers Fe and Zr, the number of CO bonds in the organic ligands, the pore size of the MOF material, the concentration of Au(III) in the adsorption experiment, the mass of the adsorbent, adsorption time, and temperature. This indicates that these eight descriptors have a significant impact on the adsorption effect. Using only these eight descriptors as input variables to fit and train the stacked ensemble model, the R-value on the test set was [value missing]. 2 The value reached 0.9334, which is close to the fitting effect compared with training using all 40 descriptors. This indicates that selecting only descriptors with high importance scores for fitting and prediction can reduce descriptor redundancy and effectively save computational resources.
[0161] (5) Figure 5 The comparison figure shows that the trained stacked ensemble model can be used to predict new Au(III) adsorption experimental data, indicating that the stacked ensemble model has good predictive effect and generalization ability for MOF adsorption performance.
[0162] Example 2
[0163] This invention provides a method for predicting the adsorption performance of metal-organic frameworks (MOFs) for Pt(IV) in solution based on a stacked integration model. The implementation steps are as follows: Figure 1 As shown:
[0164] (1) Collect and organize experimental data on the adsorption of Pt(IV) in solution by MOFs materials with five transition metal ions as metal centers: iron (Fe), copper (Cu), zinc (Zn), zirconium (Zr), and chromium (Cr). The chemical properties, structural properties, and adsorption experimental conditions of MOFs materials are used as input variables, and the adsorption amount of Pt(IV) is used as output variable. The data are organized and screened, and the qualitative data are quantified to form the original database.
[0165] The original experimental data on the adsorption of Pt(IV) by relevant MOF materials were all obtained from publicly published literature. Literature was searched in Web of Science and CNKI using keywords such as "MOF materials," "adsorption," and "Pt(IV)" to select relevant publications from the past decade. The chemical properties of the MOF materials include the topological polar surface areas of transition metal centers such as Fe, Cu, Zn, Zr, and Cr, as well as organic ligands. Number of hydrogen bond donors, number of hydrogen bond acceptors, molecular volume The dipole moment and the number of different types of chemical bonds, structural properties including BET specific surface area (m²) 2 / g), pore size (nm) and pore volume (cm³) 3 The experimental conditions included metal ion concentration (mg / L), adsorbent dosage (mg), reaction time (min), pH value, and reaction temperature (K). All data points were extracted from literature text, figures, or supporting information. For data presented in graphs without specific textual descriptions, the Web Plot Digitizer tool was used to extract the data from the graphs to ensure the accuracy of the data sources. After data collection, the data were filtered and organized to form a database.
[0166] Duplicate and invalid data were removed from the database, and data missing information was statistically analyzed. The SMILES codes for each organic ligand were extracted from the PubChem database, and their topological polar surface areas were calculated using the RDkit toolkit. Number of hydrogen bond donors, number of hydrogen bond acceptors, molecular volume By measuring the dipole moment and the number of different types of chemical bonds, a quantitative description of the chemical properties of organic ligands in MOF materials can be achieved.
[0167] (2) Given the presence of some missing values in the original database, K-Nearest Neighbor (KNN) imputation and mean imputation methods were used to fill in the missing values. The AdaBoost algorithm was used to evaluate the prediction accuracy, and the mean absolute error (MAE) was used as the comparison metric, which was obtained through the following formula:
[0168]
[0169] Among them, y i This represents the true value of the noble metal ion adsorption amount for the i-th sample. Let i be the predicted value of the noble metal ion adsorption amount of the i-th sample, where i is the sample index, which takes the value 1, 2, ..., n, and n is the total number of samples to be evaluated (n≥1).
[0170] Ultimately, the KNN interpolation method was determined to be the best interpolation method, and a complete database was formed.
[0171] (3) The database was divided into training and test sets in an 80%:20% ratio. A stacked ensemble machine learning model was constructed using Python tools. The first layer, as the base learning layer, included a random forest (RF) model, an extreme gradient boosting (XGBoost) model, and a lightweight gradient boosting machine (LightGBM) model. Q-fold cross-validation was used to predict the training set with each base model, generating a new set of predicted values (meta-features). At the same time, the trained base models were used to predict the test set, generating meta-features for the test set. The second layer, as the meta-learning layer, used a gradient boosting tree (GBT) model. The multiple predicted values (meta-features) generated by the first layer were used as a new input matrix, and the original adsorption amount was used as the output to train the GBT model, obtaining the final prediction results.
[0172] The stacked ensemble machine learning model was used to train and predict on the training and test sets respectively. During the process, Bayesian optimization was used to tune the hyperparameters of each base model. The prediction performance comparison between the single model and the stacked ensemble model is shown in Table 5.
[0173] Table 5. Comparison of Predictive Performance between Single Model and Stacked Synthesis Model
[0174] Model type <![CDATA[Test set R 2 > Test set MAE Test set RMSE RF 0.8767 57.64 104.74 XGBoost 0.9036 49.28 96.13 LightGBM 0.8925 57.31 106.84 Stacked integration model 0.9451 45.37 89.64
[0175] As shown in the table above, the prediction performance of the stacked ensemble model is better than that of the training performance of the single model. This also proves that because the second layer is used as the meta-learning layer and uses the gradient boosting tree (GBT) model, the scattered information of the base model is transformed into a deep characterization of the adsorption mechanism through the triple action of "bias correction-advantage enhancement-nonlinear adaptation", which ultimately improves the prediction accuracy.
[0176] (4) Partial Least Squares (PLS) is used for fitting, the importance scores of different variables are calculated, the influence of different factors on the adsorption results is analyzed, and descriptors with higher importance scores are selected to reduce the amount of computation required for model prediction and improve computational efficiency. The core formula of PLS is as follows:
[0177] Table 6 Definitions of Basic Symbols
[0178]
[0179]
[0180] Data centerization:
[0181] Among them 1 n It is an n×1 vector of all 1s. Let X be the column mean of the independent variable matrix. By transposing it, matrix operations are used to simultaneously subtract the mean of the corresponding column from the independent variables of all samples, thus eliminating the influence of differences in dimensions.
[0182] Independent variable weights (m-th latent variable):
[0183] Independent variable score (m-th latent variable): t m =X m-1 w m
[0184] Independent variable loading (m-th):
[0185] Final regression coefficient: b = W(P) T W) -1 q.
[0186] The higher the importance score, the greater the influence of the variable on the adsorption effect. Selecting descriptors with high importance scores for fitting and prediction can reduce descriptor redundancy and effectively save computational resources.
[0187] The trained stacked ensemble model was used to predict new Pt(IV) adsorption experimental data to verify the predictive effect and generalization ability of the stacked ensemble model on the adsorption performance of MOFs.
[0188] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.
[0189] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.
[0190] Through the above description of the embodiments, those skilled in the art can clearly understand that the above implementation methods can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of the present invention.
[0191] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.
Claims
1. A method for predicting the adsorption performance of noble metal ions in solution by metal-organic framework (MOF) materials based on a stacked integration model, characterized in that, Includes the following steps: S1. Collect and organize experimental data on the adsorption of noble metal ions in solution by MOFs materials with transition metal ions as metal centers, including the chemical properties, structural properties and adsorption experimental conditions of the MOFs materials as input variables, and the adsorption amount of noble metal ions as target variables. Organize and screen the data and perform quantitative processing to form a database. S2, the database is divided into training set and test set, a stacked ensemble machine learning model is constructed, the stacked ensemble machine learning model is trained based on the training set, the hyperparameters of the model are simultaneously tuned using Bayesian optimization, and the tuned model is then used to predict the test set, and finally the prediction performance of the stacked ensemble machine learning model is obtained. S3. Partial least squares method was used for fitting to calculate the importance scores of the chemical properties, structural properties and adsorption experimental conditions of the MOFs material as different variables, analyze the degree of influence on the adsorption amount of noble metal ions, and screen out variables with low importance scores. S4. Use the trained stacked ensemble model to predict new experimental data and evaluate the predictive effect of the stacked ensemble model on the adsorption performance of MOFs. In step S2, the hyperparameter tuning using Bayesian optimization is specifically as follows: Determine the hyperparameter space and the objective function f(x), where x∈ x is the hyperparameter of the stacked ensemble machine learning model to be optimized, f(x) is the index function for measuring the performance of the hyperparameter, and the value is the 3-fold cross-validation mean square error (CV-MSE) corresponding to the hyperparameter x. For a given objective function value z, the conditional probability distribution of the hyperparameter x is defined as p(x|z). In Bayesian algorithms, the focus is on p(x|z) good ) and p(x|z bad Two types of conditional probability distributions, where p(x|z) good The statement indicates that the objective function value CV-MSE is lower than the preset threshold τ, corresponding to the "high-performance hyperparameter combination". τ is the mean of the CV-MSE of the three hyperparameter sets during the initial random search phase. bad This indicates that the objective function value CV-MSE is higher than or equal to the threshold τ, corresponding to "poor performance hyperparameter combination"; A Gaussian process is used as the probabilistic model to model the hyperparameter-performance mapping relationship. The prior distribution of the Gaussian process is defined as f(x) ~ GP(m(x), k(x, x')), where m(x) = 0 is the mean function, and k(x, x') is the radial basis function kernel function, used to measure the similarity between two hyperparameter combinations x and x'. The expression is: Where D is the dimension of the hyperparameter space, i.e., the total number of hyperparameters to be optimized. Let be the value of the d-th hyperparameter in the hyperparameter combination x. For another combination of hyperparameters The Middle d The values of each hyperparameter, Let be the length scale of the d-th dimension hyperparameter, used to control the smoothness of the impact of this dimension hyperparameter on performance. The larger the value, the more gradual the impact of hyperparameter changes on performance; Based on the N groups of hyperparameter - performance data that have been searched ={( , )|s = 1, 2, … N}, where is the s - th combination of hyperparameters to be optimized, whose dimension is consistent with the dimension D of the hyperparameter space , is the CV - MSE value corresponding to this group of hyperparameters. For the performance of the unknown hyperparameters to perform posterior inference, the posterior distribution is still a Gaussian distribution; Select the next hyperparameter evaluation point, perform hyperparameter iteration, and after the iteration is complete, extract data from the dataset. The combination of hyperparameters with the smallest objective function value CV-MSE is selected as the optimal hyperparameters for the stacked ensemble machine learning model. The hyperparameters are then subjected to type adaptation processing to ensure consistency with the model parameter type requirements.
2. The prediction method according to claim 1, characterized in that, In step S1: The noble metal ions include Au (III), Ag (I), and six platinum group metal ions: Pt (IV), Pd (II), Rh (III), Ir (IV), Os (IV), and Ru (IV); The chemical properties of the MOFs materials include the topological polar surface area (Ų) of transition metal centers such as Fe, Cu, Zn, Zr, and Cr, as well as the number of hydrogen bond donors, hydrogen bond acceptors, and molecular volume (Ų) of organic ligands. 3 ), dipole moment and the number of different types of chemical bonds; The different types of chemical bonds specifically include: (ring) CC (ring), (ring) CN, (ring) CR, (ring)CS (ring), (ring) C=C (ring), (ring) NC (ring), CC, CN, CO, CR, C=C (aromatic), C=C (ring), C=N (ring), C=O, C≡N, N=N (ring), OR; The terminology is defined as follows: (1) (ring): refers to the cyclic structure in MOF organic ligands, including aromatic rings and alicyclic rings, only limited to the two bonding atoms of the chemical bond being located on the ring or bonded to the ring; (2) (aromatic): refers to an aromatic unsaturated bond, only requiring that the C=C bond is located within the aromatic ring; (3) R: refers to alkyl substituent; The structural properties of the MOFs material include BET specific surface area (m²). 2 / g), pore size (nm) and pore volume (cm³) 3 / g); The adsorption experimental conditions of the MOFs materials include metal ion concentration (mg / L), adsorbent dosage (mg), reaction time (min), pH value, and reaction temperature (K); The transition metals include five transition metal ions: iron (Fe), copper (Cu), zinc (Zn), zirconium (Zr), and chromium (Cr).
3. The prediction method according to claim 1, characterized in that, In step S2, the stacked ensemble machine learning model includes: The first layer serves as the base learning layer, including three base models: random forest, extreme gradient boosting, and lightweight gradient boosting machine. The generation of training set meta-features for each base model employs Q-fold cross-validation, specifically including: splitting the training set into Q folded subsets, where Q ranges from 5 to 10 to balance computational efficiency and meta-feature reliability; for each base model, training it using the remaining Q-1 folded subsets (excluding the i-th folded subset), i=1,2,...,Q; then using the trained base model to predict the i-th folded subset to obtain the predicted value corresponding to that folded subset; concatenating the predicted values of all folded subsets to form training set meta-features with the same number of training set samples, i.e., the first predicted value meta-feature for each base model; retraining each base model using the complete training set; and then, for each base model trained using the complete training set, predicting the test set to obtain the test set meta-feature corresponding to each base model, i.e., the second predicted value meta-feature. The second layer serves as the meta-learning layer, including the gradient boosting tree model as the meta-model: The first predicted value meta-features of each base model obtained in the first layer are concatenated into a meta-training feature matrix, and the meta-model is trained using the amount of noble metal ion adsorption as a label; the second predicted value meta-features of each base model obtained in the first layer are concatenated into a meta-test feature matrix, which is input into the trained meta-model, and the final prediction result of the amount of noble metal ion adsorption corresponding to the test set is output.
4. The prediction method according to claim 1, characterized in that, In step S1, the quantitative processing refers to extracting the SMILES codes of the organic ligands of the MOFs material from the PubChem database, and using the RDkit toolkit to calculate their topological polar surface area (Ų), number of hydrogen bond donors, number of hydrogen bond acceptors, and molecular volume (Ų). 3 The number of dipole moments and different types of chemical bonds are used to quantitatively describe the chemical properties of the organic ligands in the MOFs materials.
5. The prediction method according to claim 1, characterized in that, In step S1, organizing and filtering the data means removing duplicate and invalid data and statistically analyzing data missing information. If data is missing, then after S1, the following steps are also included: Given the presence of some missing values in the original database, the missing values are supplemented using K-nearest neighbor imputation and mean imputation methods respectively. An adaptive enhancement algorithm is then used to evaluate the prediction accuracy, determine the optimal imputation method, and form a complete database. Specifically, the adaptive enhancement algorithm for evaluating prediction accuracy is used as follows: the mean absolute error (MAE) is used to evaluate prediction accuracy, and the calculation method is as follows: in, This represents the true value of the noble metal ion adsorption amount for the i-th sample. Let be the predicted value of the noble metal ion adsorption amount of the i-th sample, where i is the sample index, which takes the value 1, 2, ..., n, and n is the total number of samples to be evaluated, and n≥1.
6. The prediction method according to claim 1, characterized in that, In step S3: Features with an importance score >1 are considered core influence features; Features with an importance score of 5 or less and a score of ≤1 are considered to have significant influence. Features with an importance score ≤ 0.5 are considered to have a weak influence and are thus considered to have a low importance score.
7. The prediction method according to claim 1, characterized in that, In step S2, the predictive performance index of the stacked integration model is the coefficient of determination R. 2 Mean absolute error (MAE) and root mean square error (RMSE), R 2 The RMSE calculation method is as follows: in, This represents the true value of the noble metal ion adsorption amount for the i-th sample. This represents the predicted value of noble metal ion adsorption for the i-th sample. Let be the sample mean, i be the sample index, which takes the value 1, 2, ..., n, and n be the total number of samples being evaluated, where n ≥ 1.
8. A prediction system for the adsorption performance of noble metal ions in solution by MOFs based on a stacked ensemble model, the system comprising: A processor and a memory for storing executable instructions; wherein the processor is configured to execute the executable instructions to perform a method for predicting the adsorption performance of noble metal ions in solution by MOFs based on a stacked integration model as described in any one of claims 1 to 7.
9. A computer-readable storage medium, wherein, It stores a computer program, which, when executed by a processor, implements a method for predicting the adsorption performance of noble metal ions in solution by MOFs based on a stacked integration model as described in any one of claims 1 to 7.