Machine Learning-driven models for predicting CO2 Uptake in Metal-Organic Frameworks (MOFs)

Machine Learning-driven models for predicting CO2 Uptake in Metal-Organic Frameworks (MOFs) | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Machine Learning-driven models for predicting CO2 Uptake in Metal-Organic Frameworks (MOFs) Sofiene Achour, Zied Hosni This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4058963/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract This study advances the discourse on the application of machine learning (ML) algorithms for the predictive analysis of CO 2 uptake in Metal-Organic Frameworks (MOFs), with a nuanced focus on the CATBoost model's capability to navigate the complexities inherent in MOFs' heterogeneous landscape. Building upon and extending the comparative analysis, our investigation underscores the CATBoost model's remarkable predictive prowess, characterized by a significant reduction in root mean square error (RMSE) and an enhanced R-squared (R²) value, thereby affirming its superior accuracy and reliability in forecasting CO 2 adsorption. A pivotal aspect of our research is the integration of SHAP values for a detailed assessment of feature importance, which not only corroborated 'Pressure' and 'Surface Area' as pivotal determinants of CO 2 uptake but also illuminated the model's advanced analytical capabilities in handling categorical features and mitigating overfitting, even within a dataset marked by intricate and non-linear patterns. Our quantitative and conceptual analysis, showcasing up to a 15% improvement in (RMSE) over previous models, reveals the CATBoost model’s unparalleled efficiency in discerning the multifaceted interplay of factors influencing CO 2 adsorption. This is crucial for the strategic engineering of MOFs with optimized properties. Beyond 'Pressure' and 'Surface Area', our SHAP analysis highlighted other descriptors with substantial values, elucidating their nuanced contributions to CO 2 uptake and providing invaluable insights for the MOF design process. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction MOFs are significant in materials science and engineering due to their customizable nature, high porosity, and programmable functionalities. They have potential applications in various areas such as catalysis, gas storage, drug delivery, and sensing.[ 1 ] The study of MOFs using quantitative structure-property relationship (QSPR) methodologies is important because it allows for reasonable estimates of their properties and performance. QSPRs provide insights into the relationship between MOF properties, such as density, pore volume, and surface area, and their performance in areas like gas storage capacity.[ 2 ] By developing QSPRs from experimental data, it is possible to improve the design of MOFs and optimize their properties for specific applications. This approach is valuable as it provides a more accurate understanding of MOF behavior compared to simulation-based methods like Grand Canonical Monte Carlo (GCMC).[ 3 ] Machine learning techniques have been applied to QSPR studies of MOFs and similar materials, offering opportunities for advancements in the field. One approach is the use of machine learning models to predict the properties of MOFs based on their structure and composition. For example, Zhang et al. developed neural network models trained on a dataset of porphyrin-based MOFs to accurately predict their band gaps.[ 4 ] Another approach is the use of machine learning models to screen large databases of MOFs and identify materials with specific properties. Hernández Casas et al. used a gradient-boosted regression trees model to predict the methane adsorption capacity of over 130,000 hypothetical MOFs.[ 5 ] Additionally, machine learning potentials have been developed to model MOFs using a data-efficient incremental learning scheme, allowing for accurate predictions even for flexible frameworks with multiple phases.[ 6 ] A reliable QSPR model was established for predicting the evolution rate of CO 2 photoreduction over porphyrin-based MOFs as photocatalysts.[ 7 ] The model showed high accuracy with a determination coefficient (R 2 ) of 0.999 and low root-mean-squared error of prediction (RMSEP).[ 8 ] However, challenges and limitations still exist. One challenge is the limited electrical conductivity, micropore size, and poor stability of MOFs, which hampers their practical applications.[ 9 ] Another challenge is the potential toxicity associated with the degradation and metabolism of MOFs inside the body, which needs further investigation.[ 10 ] Additionally, there is a need for more diverse and comprehensive studies on different MOFs, as some compounds have been overstudied.[ 11 ] The correlation between gas adsorption and diffusion in MOFs also requires more attention. CO 2 capture is important in addressing climate change as it helps reduce anthropogenic carbon emissions and mitigate the impact of global warming.[ 12 ] The process involves capturing CO 2 and storing it underground in deep saline or depleted hydrocarbon reservoirs, preventing it from being released into the atmosphere.[ 13 ] This technique is being explored by oil and gas companies to reduce their CO 2 footprint.[ 14 ] In agricultural land use systems, carbon sequestration in soils can help offset CO 2 emissions and enhance productivity.[ 15 ] The potential of this approach in croplands includes erosion control, preservation of degraded soils, and better cropping systems.[ 16 ] Carbon sequestration in mafic rocks has also been studied as a stable long-term storage option. CO 2 uptake in MOFs is relevant because of the potential to reduce greenhouse gas emissions and mitigate the effects of global warming.[ 17 ] MOFs have high porosity, tunable composition, and good chemical stability, making them excellent candidates for capturing CO 2 .[ 18 ] Functionalized MOFs allow for the development of materials with tunable properties for various applications, including gas adsorption and separation.[ 19 ] Mixed-metal MOFs, composed of different metals, offer enhanced stability and gas absorption capabilities.[ 20 ] Organic functional groups in MOFs have a significant effect on CO 2 adsorption.[ 21 ] Machine learning is used to investigate CO 2 uptake in MOFs by developing predictive models based on experimental data.[ 22 ] Additionally, quantum-informed machine learning force fields (QMLFFs) are employed to simulate CO 2 adsorption in MOFs. These simulations provide accurate results with significantly reduced computational cost compared to first-principle simulations.[ 23 ] Another approach combines molecular simulations and machine learning algorithms to computationally design MOF composites for CO 2 adsorption. Molecular simulations are used to screen different composites, and the results are used to develop machine learning models that accurately predict the adsorption and separation performances of the composites.[ 24 ] Graph-based convolutional neural networks are also utilized to predict and rank gas adsorption properties of MOF adsorbents, solely based on structural input files.[ 25 ] This study aims to develop and rigorously validate machine learning-based QSPR models, enabling precise predictions of CO 2 uptake in MOFs that outperform the existing models and give better insights on the mechanism that drives this capture. Methodology A dataset comprising 236 unique MOFs was curated to model and predict CO 2 uptake capabilities, underscoring the interplay between structural and chemical properties of MOFs and their adsorption performance.[ 26 ] An exploratory data analysis facilitated a nuanced understanding of the data's distribution, variability, and potential outliers, informing our strategy for data normalization and transformation. Notably, the dataset underwent a series of preprocessing steps to standardize the feature set, including normalization to scale numerical predictors within a defined range and the application of logarithmic transformations to address skewness in CO 2 uptake values, enhancing model compatibility. The dataset was judiciously partitioned into training and testing sets. A training set, constituting 80% of the dataset, was employed to train the machine learning models, while the remainder was reserved for testing, ensuring a comprehensive assessment of each model's predictive accuracy and generalizability. A critical component of this study was the systematic optimization of machine learning models through hyperparameter tuning.[ 27 ] This was accomplished by exploring a range of parameter settings for various algorithms, including Random Forest[ 28 ], Support Vector Machine[ 29 ], XGBoost[ 30 ], LightGBM[ 31 ], Neural Networks[ 32 ] from Pytorch[ 33 ] library, Symbolic regression[ 34 ] and Gaussian Processes Regressor[ 35 ] and CATBoost[ 36 ] to ascertain the Configuration that most effectively predicted CO 2 uptake. This optimization process was guided by cross-validation techniques to ensure the models' robustness and generalizability. The Configuration details for each algorithm, along with the ranges applied during the tuning of hyperparameters, are provided in the Supplementary Information for further reference. The models' predictive performances were rigorously evaluated using standard metrics, supplemented by learning curve analyses to assess their efficiency and potential for overfitting. Additionally, SHAP (SHapley Additive exPlanations)[ 37 ] as interpretative examination of the models' feature importance was conducted, leveraging a modern explanation framework to elucidate the molecular descriptors' influence on CO 2 uptake predictions. Results and Discussion The predictive performance of machine learning models, notably the CATBoost algorithm is explored. Our focus is on understanding the interplay between MOF structural characteristics and their adsorption capabilities, assessing model effectiveness, and interpreting the influence of key features on CO 2 capture efficiency. The discussion aims to illuminate the broader implications of our analysis for the design and application of MOFs, setting a foundation for future advancements in carbon sequestration technologies. The boxplots in Fig. 1 convey a comparative analysis of CO 2 uptake and pore volume across different metals utilized in MOFs. In the CO 2 uptake boxplot (A),, the interquartile range (IQR), which signifies the middle 50% of data points, varies significantly across different metals, suggesting a substantial disparity in CO 2 uptake capabilities contingent on the metal type. Some metals are associated with a wider spread of CO 2 uptake values, indicating a more variable performance within the MOF samples containing those metals. Outliers, as denoted by points beyond the whiskers of the boxplots, are present in several metal categories, signifying instances of MOFs with exceptionally high CO 2 uptake, potentially attributable to unique structural features or synergistic effects at the molecular level. The pore volume boxplot (B) exhibits a similar variability, with the median pore volume differing markedly between metal types. This variability hints at the structural diversity of MOFs and the consequential effects on their porosity. Metals that facilitate larger pore volumes could be indicative of frameworks conducive to higher adsorption capacities, although the relationship between pore volume and CO 2 uptake is not necessarily linear or direct, as other factors such as pore geometry and surface functionality may play significant roles. The pairplot presented in Fig. S1 serves as a multidimensional visualization, encapsulating the distribution of individual features along with pairwise relationships among them. The univariate distributions, that is prominently situated along the diagonal of the pairplot, shows that certain features such as 'Surface Area' and 'CO 2 Uptake' display a pronounced right-skewness. This skewness suggests that while the bulk of the MOFs populate lower values for these attributes, there exists a subset characterized by significantly higher surface areas and CO 2 uptakes, potentially indicating a subset of highly porous MOFs with superior adsorption capacities. Conversely, the distributions for 'Pressure' and 'Temperature' appear relatively uniform, with the MOFs ' performance relatively invariant across a wide range of operational conditions. This uniformity might imply a degree of resilience in CO 2 uptake efficiency across the assessed temperature and pressure ranges. In the context of bivariate relationships, the scatter plots in Fig. S1 provide a granular view of potential correlations. Notably, a positive trend is discernible between 'Surface Area' and 'CO 2 Uptake', supporting the postulation that increased surface areas are conducive to enhanced CO 2 adsorption. This relationship is foundational to MOF design, where maximizing surface area is often a primary objective in the development of materials for gas capture applications. The categorical variable 'METAL', representing the type of metal incorporated within the MOF structure, manifests as discrete clusters within the plots. This clustering signifies the potential influence of metal type on MOF properties, including CO 2 uptake. For instance, certain metals may correlate with higher uptakes, suggesting a specificity in the interaction between metal types and adsorption efficacy. Furthermore, the plots featuring 'Pressure' and 'Temperature' against 'CO 2 Uptake' do not exhibit a discernible trend, reinforcing the premise that CO 2 uptake efficiency remains relatively stable across various operational conditions. However, a deeper statistical analysis would be required to confirm the absence of subtle trends or thresholds within these operational parameters. The visual complexity and density of the scatter plots, while informative, also indicate a level of variance that underscores the multifaceted nature of MOF performance. This variance suggests that while some general trends can be deduced, individual MOF performance is likely influenced by a combination of features, necessitating a comprehensive analysis that considers the interplay between surface area, pore volume, metal type, and operational conditions. The heatmap in Fig. S2 provided in Fig. S2 delineates the correlation matrix for key features in the dataset of MOFs related to CO 2 uptake. 'Surface Area' and 'Pore Volume' demonstrate a robust positive correlation with CO 2 uptake, as indicated by correlation coefficients of approximately 0.68 and 0.52, respectively. This strong positive association suggests that as the surface area and pore volume increase, there is a commensurate rise in CO 2 uptake, affirming the hypothesis that larger surface areas and pore volumes are conducive to higher adsorption efficiency. Furthermore, 'Pressure' exhibits a notable positive correlation with CO 2 uptake, with a correlation coefficient of 0.71. This relationship underscores the sensitivity of CO 2 uptake to the operational pressure, aligning with the principles of gas adsorption where increased pressure can amplify the amount of gas a MOF can adsorb.[38] Conversely, 'Temperature' presents a negligible correlation with CO 2 uptake, as evidenced by a correlation coefficient close to zero and slightly negative observed in the study performed by Bonjour et al. [39]. This finding suggests that within the considered range of temperatures, the influence on CO 2 uptake is minimal, or other factors may mask its effects. The absence of a strong correlation with temperature might also indicate that the MOFs in the dataset maintain their adsorption capabilities across the studied temperature spectrum. Interrelationships among the MOF features themselves are also revealed; 'Surface Area' and 'Pore Volume' are highly correlated, as expected due to their intrinsic physical connectivity. Both features are integral to the MOFs ' structure, with larger surface areas typically accompanied by greater pore volumes, contributing to the material's adsorption potential. The heatmap further illustrates the correlations among the operational conditions—'Pressure' and 'Temperature'—and their individual relationships with structural attributes. While 'Pressure' shows a moderate correlation with 'Surface Area' and 'Pore Volume', suggesting that these structural properties may influence how pressure impacts CO 2 uptake, 'Temperature' remains largely uncorrelated with other variables, reaffirming its ostensibly limited role in the adsorption process within the dataset's scope. The boxplot in Fig. S3 illustrates the distribution of several key features within a dataset prior to the application of preprocessing steps, such as outlier removal. These features include 'Surface Area', 'Pore Volume', 'Pressure', and 'Temperature', which are fundamental to understanding the physical and operational characteristics of MOFs. The 'Surface Area' shows a relatively broad range with several outliers extending significantly beyond the upper quartile, indicating some MOFs with exceptionally high surface areas.[40] This suggests a subset of structures with potentially greater adsorption capabilities, an attribute that could be critical for applications such as gas storage or separation. For 'Pore Volume', the spread is moderate, but outliers are also present, highlighting variations in the porosity of MOFs within the dataset. Pore volume is a crucial factor that can influence the storage capacity and selectivity of MOFs. The 'Pressure' feature displays a more compact interquartile range but is accompanied by numerous outliers. The presence of outliers in pressure data may be attributed to variations in the synthesis or operational conditions of the MOFs. 'Temperature' data reveals a tight clustering with outliers on both the lower and higher ends of the spectrum. The outliers could represent extreme conditions under which certain MOFs have been tested or anomalous readings that warrant further scrutiny. Turning to the CO 2 uptake by metal type, the boxplot indicates a marked variability in uptake values across different metals. This variation highlights the influence of the metal center on the adsorption properties of MOFs, potentially offering insights into the design of MOFs tailored for specific applications. The scatter plot provided in Fig. S4 illustrates the performance of a baseline model, based on a Random Forest regressor, in predicting CO 2 uptake, presumably CO 2 uptake for MOFs. The plot compares the actual values against the predicted values obtained from the model. The Root Mean Squared Error (RMSE) of 8.04 indicates that, on average, the model's predictions deviate from the actual values of CO 2 uptake by approximately 8 mmol/g. Given the scale of the actual values, which extend up to 50, an (RMSE) of 8.04 can be considered moderately high, suggesting that there is considerable room for improvement in the model's predictive accuracy. The coefficient of determination, R², is 0.74, which means that roughly 74% of the variance in the actual data is accounted for by the model. While this is a respectable Fig. for a baseline model, it also implies that about a quarter of the variance is unexplained, which could be due to model simplicity, omitted variable bias, or inherent noise within the dataset. It is noteworthy that several points are scattered away from this line, especially in the higher range of actual values, indicating discrepancies in the model's predictions. The model appears to underestimate the actual values in certain cases, especially for higher magnitudes, which is where the greatest deviations occur. The baseline model's performance before preprocessing suggests that the initial model has captured the general trend in the data but lacks the refinement that preprocessing steps, such as outlier removal, feature scaling, and transformation, could provide. Preprocessing could potentially enhance the model's accuracy by normalizing feature scales, reducing the influence of outliers, and transforming features to better capture nonlinear relationships. The learning curve plot in Fig. 2 illustrates the evolution of the training and cross-validation scores of CATBoost Model model as the number of training examples increases. It provides valuable insights into the learning process and the model's capacity to generalize from its training data. The training score, represented by the red line, remains relatively high and constant across the number of training examples. This suggests that the Random Forest model is able to fit the training data well, regardless of the dataset's size. The high score indicates a strong performance on the training set, which is typical for Random Forest models given their complexity and capacity for capturing intricate patterns in the data. In contrast, the cross-validation score, denoted by the green line, starts off lower, indicating that initially, the model does not generalize as well to unseen data. However, as more training examples are provided, the cross-validation score improves, which is evidenced by the upward trend. The confidence intervals, shown as the shaded areas around the lines, also narrow with more data, suggesting that the model's performance estimates become more precise as it learns from a larger set of examples. The gap between the training and cross-validation scores signifies the model's variance. A high variance often implies overfitting; however, in this case, the fact that the cross-validation score is increasing suggests the model is learning effectively and could benefit from even more data. The convergence of the training and cross-validation scores, should it continue with more data, would be indicative of a well-fitting model. The scatter plot in Fig. 3 visualizes the performance of the CATBoost Gradient Boosting Machine (CATBoost) model, contrasting predicted values against actual values for both training and testing datasets. For the training dataset, denoted by blue points, there is a remarkable congruence with the line of perfect fit, signaling an excellent predictive accuracy as substantiated by a Root Mean Squared Error (RMSE) of 0.07 and a coefficient of determination (R²) of 0.99. These metrics suggest the model is capable of capturing the underlying patterns in the data with high precision. In the case of the testing dataset, represented by red points, while the alignment with the perfect fit line is less exact than with the training set, it nonetheless denotes a strong predictive capacity. This is evidenced by a test (RMSE) of 0.43 and an R² of 0.84. The (RMSE) indicates the average deviation of predicted values from actual data points is relatively low, and the R² value reflects that a substantial proportion of the variance in the actual values is accounted for by the model. Notably, the consistency between the training and testing performance suggests the model has generalized well, avoiding overfitting, which is a common concern in machine learning where a model performs exceptionally on the training data but poorly on unseen data. The test (RMSE), being higher than the training (RMSE), does point to some loss in predictive accuracy, which is common when generalizing from training data to testing data. However, the test R² of 0.84 indicates that the model still maintains a robust predictive quality. The SHAP summary plot and the top 10 feature importance chart in Fig. 4 and Fig. 5, respectively provide a comprehensive view of the impact each feature has on the model's predictions. It indicates the distribution of the impacts each feature has on the model's output. For each feature, a SHAP value is calculated, with positive values indicating an increase in the likelihood of a higher prediction outcome and negative values indicating a decrease. 'Pressure' has a wide range of effects, with a cluster of high positive impact values, suggesting that higher pressure values are strongly associated with higher predictions. 'Surface Area' and 'Temperature' also appear to have a mixture of positive and negative impacts, though 'Surface Area' seems to have a more consistent positive influence on the predictions. 'Pore Volume' presents a similar but less pronounced distribution. The top 10 feature importance chart, derived from the mean absolute SHAP values, ranks the features by their overall impact on the model's predictions. 'Pressure' seems to be the most influential feature, followed by 'Surface Area', 'Temperature', and 'Pore Volume'. The presence of molecular descriptors such as 'PEOE_VSA7' and 'FpDensityMorgan1' among the top influencers points to their significant roles in the model's decision process. PEOE_VSA7 (Partial Equalization of Orbital Electronegativities Van der Waals Surface Area) relates to the electrostatic environment of the molecule, which can influence interactions with CO 2 . FpDensityMorgan1 reflects the presence of certain atomic environments within a molecule, indicating that specific structural motifs are important for CO 2 uptake. High average localized polarizability (AvgLpc) suggests that linkers with the ability to polarize under an electric field might interact more effectively with CO 2 molecules. EState_VSA3 indicates the steric and electronic features that can affect the binding and adsorption process. For organic chemists, these insights point towards designing linkers with specific electrostatic and steric properties, potentially favoring those that can induce polarization and possess certain atomic environments conducive to CO 2 adsorption. These findings can direct the synthesis of novel linkers that enhance MOF performance for CO 2 capture. The SHAP dependence plots provided in Fig. S5-S7 showcase the relationship between individual features — Pore Volume, Pressure, and Surface Area — and their SHAP values, which represent the impact of each feature on the model's output. The color gradient represents the value of another feature, which can help to identify interaction effects between features. In the Pore Volume dependence plot, the SHAP values suggest that changes in pore volume can have both positive and negative impacts on the model's predictions, with a cluster of higher SHAP values at certain levels of pore volume. This implies that there is a specific range of pore volume where changes are most influential in affecting the model's output. The feature represented by the color gradient could be showing that the impact of pore volume on the prediction changes depending on the value of another feature, indicating a possible interaction effect. For the Pressure dependence plot, the SHAP values show variability in their impact on the model's output across different pressure levels. If the color represents a feature like temperature, for example, we might infer that at different temperatures, the influence of pressure on the model's predictions varies. Some clusters of points suggest that there are specific pressure ranges where the impact on the model's prediction is more pronounced. The Surface Area dependence plot indicates that as the surface area increases, its impact on the model's predictions also generally increases, evidenced by the upward trend in SHAP values. The interaction effect, as denoted by the color gradient, again suggests that the impact of surface area is not uniform across all levels of another feature, which might be indicative of complex behavior that the model is capturing. In the comparative analysis of machine learning models for CO 2 uptake prediction in MOFs, we assessed the performance of five different algorithms: Random Forest, XGBoost, Support Vector Machine, LightGBM, and CATBoost Regression. The Random Forest algorithm demonstrates remarkable training accuracy, evidenced by its high R² value, suggesting a strong ability to capture the underlying patterns in the training dataset. However, the performance on the test set, while still robust, indicates a slight overfitting, as the R² and (RMSE) values drop when generalizing to new data. XGBoost showcases excellent training performance with the lowest (RMSE) and highest R² across the models, confirming its efficiency in handling tabular data and complex relationships. On the test data, it maintains a high level of accuracy, although a slight decrease in performance compared to the training set is observed, implying potential overfitting. The Support Vector Machine, known for its effectiveness in high-dimensional spaces, shows commendable predictive power. It maintains a relatively consistent performance from training to testing, indicating good generalization capabilities. Nevertheless, it falls short compared to ensemble methods like Random Forest and XGBoost in terms of both (RMSE) and R². LightGBM, another gradient boosting framework, presents a competitive performance with a balance between training and testing results. It slightly underperforms compared to XGBoost but displays a similar trend of reduced accuracy on the test set, which could be attributed to model complexity and overfitting. CATBoost Regression emerges as a strong contender, with its performance on the training set being close to perfect. However, it experiences a significant reduction in test R², the largest among the models, highlighting a pronounced overfitting issue. In brief, while all models exhibit a high level of predictive accuracy on the training data, their performance on the test set reveals varying degrees of overfitting. XGBoost stands out with the best overall performance, maintaining high accuracy on unseen data. These insights suggest that while ensemble methods have superior predictive power for this dataset, careful tuning and regularization are necessary to improve their generalizability. The results underscore the importance of model selection and hyperparameter optimization in the development of predictive models for material science applications. The last three models—Neural Networks (NN), Gaussian Processes (GPR), and Symbolic Regression—underperformed in the CO 2 uptake prediction task, as evidenced by their higher (RMSE) and lower R² values. Neural Networks, with an (RMSE) of 0.76 and an R² of 0.27, likely suffered from insufficient training data and overfitting, lacking the depth of architecture optimization necessary for the complexity at hand. Gaussian Processes, showing an (RMSE) of 0.67 and an R² of 0.61, may have been hindered by the high dimensionality and computational limits. Symbolic Regression, with (RMSE) and R² values of 0.70 and 0.43 respectively, might not have effectively captured intricate data patterns, often requiring a more nuanced approach to model nonlinear relationships inherent in the data. The exploration and analysis of the dataset concerning CO 2 uptake in MOFs provide a nuanced understanding of the factors influencing adsorption efficiency. The preprocessing steps, which involve feature scaling, contribute to the enhancement of model performance by focusing on representative data trends and minimizing the impact of extremities. The pair plot and correlation heatmap offer a granular view of the relationships between different variables. A notable positive correlation between surface area, pore volume, and CO 2 uptake indicates that these features are potentially predictive of MOFs’ adsorption capabilities. Conversely, the lack of a strong correlation with temperature and pressure hints at the complexity of adsorption dynamics, which may not be linearly dependent on these conditions. The SHAP summary plot, alongside the top feature importance chart, elucidates the underlying influences of each feature on the model's output. The SHAP values suggest that pressure and surface area have a significant impact on the predictions, aligning with the initial correlation observations. Interestingly, other descriptors with notable SHAP values may reflect more subtle and complex interactions within the MOF structures that affect CO 2 uptake. The comparison across five regression models – Random Forest, XGBoost, SVM, LightGBM, and CATBoost – in the context of model performance reveals that while all models exhibit strengths, the CATBoost model achieves the best performance post-preprocessing. Its superiority could be attributed to its ability to handle categorical features and its robustness against overfitting, which is particularly beneficial in datasets with complex and non-linear patterns. Therefore, the scientific inquiry into MOFs for enhanced CO 2 uptake is significantly advanced by machine learning models capable of decoding the intricate patterns of molecular structures. The superior performance of the CATBoost model in this study not only underscores the potential of advanced ensemble learning techniques in materials science but also paves the way for the discovery and design of MOFs with optimized adsorption properties. This, in turn, contributes to the broader goal of developing efficient materials for carbon capture and storage, an essential endeavor in the Fig.ht against climate change. The feature importance evaluation via SHAP values reveals that 'Pressure' and 'Surface Area' are pivotal in influencing CO 2 uptake predictions (Fig. 4 and Fig. 5). This is consistent with literature where such features have been highlighted as significant in the adsorption process.[24] However, Zheng et al.[23] posits the efficacy of Quantum-informed machine-learning force fields (QMLFFs) in simulating CO 2 within MOFs, emphasizing the potential of quantum mechanics in enhancing model accuracy, which could provide a more granular understanding of adsorption phenomena beyond the scope of the current model. The SHAP dependence plots further elucidate the nuanced relationships between features such as 'Pore Volume' and 'Pressure,' and their respective impacts on CO 2 uptake predictions. The interaction effects denoted may indicate complex, non-linear relationships that are not fully captured by the current model, suggesting an area for improvement. In a similar vein, studies employing graph-based convolutional neural networks, like the work by Cong et al.[41], have shown the ability to predict adsorption properties with fewer features, which could streamline the feature selection process and potentially enhance model performance. The bar chart comparison of (RMSE) and R² across different machine learning models (Fig. 6) is a testament to the robustness of the CATBoost model. However, when contextualized with the literature, it becomes apparent that each model's performance has idiosyncrasies that must be considered. For instance, the deep reinforcement learning framework for inverse design of MOFs,[42] has shown promising results in material design, which may suggest avenues for predictive model application beyond mere uptake prediction. In the realm of advancing CO 2 capture technologies through the predictive modeling of CO 2 adsorption capacities in Metal-Organic Frameworks (MOFs), our study delineates a methodological leap forward, particularly when viewed in conjunction with the work by Abdi et al. Our research, meticulously focused on the CATBoost algorithm, outshines the broader, albeit comprehensive, analysis presented by Abdi et al.[43], which comparatively assessed multiple decision tree-based models including XGBoost, LightGBM, CatBoost, and Random Forest. The linchpin of our study’s superiority lies in the in-depth feature importance analysis utilizing SHAP values, providing a granular understanding of MOF structural attributes' impact on CO 2 adsorption. This approach not only unveils the complex interrelations influencing CO 2 uptake but also underscores the methodological sophistication in assessing model reliability and mitigating overfitting. Our quantitative analysis further establishes this edge, showcasing the CATBoost model’s predictive performance superiority, with an up to 15% improvement in root mean square error (RMSE) over the best model identified by Abdi et al. This advancement is not just numerical but also conceptual, as we emphasize the criticality of 'Pressure' and 'Surface Area' in CO 2 uptake predictions, refining both the accuracy and the theoretical underpinnings for MOF design tailored to carbon capture. By addressing the challenge of overfitting head-on through dataset diversification and validation, our study not only ensures the robustness of our predictive models but also enhances their generalizability across different MOF structures. Consequently, our paper not only sets a new benchmark in the predictive modeling for CO 2 capture using MOFs but also significantly contributes to the ongoing dialogue initiated by Abdi et al., pushing the boundaries of machine learning applications in environmental sustainability. Consequently, while the CATBoost model's performance is impressive, it is essential to recognize that machine learning in the context of MOF research for CO 2 uptake is an ever-evolving field. The potential overfitting indicated by the higher test (RMSE) relative to the training (RMSE) necessitates a vigilant approach to model tuning. This aligns with the limitations presented by Huang et al., where the model's performance is dependent on the original data, underscoring the need for comprehensive datasets for training. Despite these strengths, the disparity between the training and testing (RMSE) values hints at potential overfitting—a caveat echoed by Huang et al.,[44] who also caution against models' dependence on the original datasets used for training. This highlights the necessity for diverse and extensive datasets for model training to avoid overfitting and ensure generalizability. The culmination of this extensive data-driven analysis yields profound implications for the design and synthesis of MOFs with superior CO 2 uptake capabilities. The insights gleaned from the predictive modeling, particularly the CATBoost Gradient Boosting Machine's (CATBoost) exemplary performance, demonstrate the potential of utilizing machine learning algorithms to discern and predict the efficiency of MOFs in carbon capture. The strong correlations between CO 2 uptake and specific features such as surface area and pore volume, which emerged as significant predictors in the SHAP value analysis, indicate key structural properties that can be targeted in the design phase. By focusing on optimizing these attributes, materials scientists can engineer MOFs with expansive surface areas and optimal pore volumes, thus enhancing their capacity for gas adsorption. The identification of specific molecular descriptors that heavily influence CO 2 uptake performance points to the nuanced interplay of factors that govern adsorption. These findings suggest that an intricate balance of structural integrity, chemical functionality, and physical properties must be achieved to enhance MOF performance. In practical terms, this could involve the strategic selection of metal nodes and organic linkers, as well as the fine-tuning of synthesis conditions to tailor the porosity and surface characteristics of the MOFs. Furthermore, the application of advanced machine learning techniques like CATBoost provides a pathway to expedite the iterative process of MOF development. By predicting the adsorption performance of hypothetical MOFs before their synthesis, researchers can prioritize the most promising candidates, thereby saving significant time and resources. Conclusion We presented application of machine learning-enhanced Quantitative Structure-Property Relationship (QSPR) models for predicting CO 2 uptake in MOFs. It is underlined the CATBoost Gradient Boosting Machine (CATBoost) model has a superior performance, highlighting its robust predictive power. This underscores the potential of machine learning algorithms to accurately predict the gas adsorption properties of MOFs based on their molecular and structural characteristics. The study's comprehensive approach, employing a range of machine learning techniques, has demonstrated that certain features—particularly surface area, pore volume, and specific molecular descriptors—are highly influential in determining CO 2 uptake. These insights can direct the strategic design of MOFs to tailor their properties towards improved carbon capture performance. The best ML model reveals, in addition, that 'Surface Area' and 'CO 2 Uptake' exhibit a pronounced right-skewness, suggesting a subset of MOFs with higher porosity and superior adsorption capacities. Uniform distributions for 'Pressure' and 'Temperature' across a wide operational range suggest MOF performance resilience under varying conditions. Notably, increased surface area correlates positively with CO 2 uptake, underlining its significance in MOF design for enhanced gas adsorption. The type of metal used in MOFs also influences CO 2 uptake, indicating that specific metal-MOF interactions can be critical for adsorption efficacy. Despite these advancements, the study is not without limitations. The dataset used, while substantial, could benefit from greater diversity to capture a broader spectrum of MOFs and adsorption behaviors. Future research could consider incorporating datasets with a wider range of chemical functionalities and structural varieties to refine the models further. Additionally, exploring other advanced machine learning techniques, such as deep learning or ensemble methods that combine multiple models, could unveil more intricate relationships within the data and potentially yield even more accurate predictions. This application exemplifies the transformative role of computational approaches in material science. By leveraging the predictive power of machine learning-enhanced QSPR models, the pace of MOF development for CO 2 capture can be significantly accelerated. This computational foresight allows for a more efficient allocation of resources, focusing experimental efforts on the most promising MOF candidates predicted by the models. It sets a precedent for a more informed and strategic pathway to material discovery, one that is crucial for meeting the urgent demands of environmental sustainability and the global challenge of CO 2 emissions mitigation. Declarations Funding Statement This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Author Contributions Sofiene Achour designed the experiments and led the writing of the original draft, also contributing to review and editing. Zied Hosni assisted in conceptualizing the research approach and contributed to both the writing and the review and editing of the manuscript. 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In: Deep Learning with Python de Franca FO, Aldeia GSI (2021) Interaction–transformation evolutionary algorithm for symbolic regression. Evol Comput. https://doi.org/10.1162/evco_a_00285 Schulz E, Speekenbrink M, Krause A (2018) A tutorial on Gaussian process regression: Modelling, exploring, and exploiting functions. J Math Psychol. https://doi.org/10.1016/j.jmp.2018.03.001 Hancock JT, Khoshgoftaar TM (2020) CatBoost for big data: an interdisciplinary review. J Big Data. https://doi.org/10.1186/s40537-020-00369-8 Zhang J, Ma X, Zhang J, et al (2023) Insights into geospatial heterogeneity of landslide susceptibility based on the SHAP-XGBoost model. J Environ Manage 332:117357 Keller JU, Staudt R (2005) Gas adsorption equilibria: experimental methods and adsorptive isotherms. Springer Science \& Business Media Bonjour J, Chalfen J-B, Meunier F (2002) Temperature swing adsorption process with indirect cooling and heating. 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Supplementary Files SIMOFsSofiene.docx Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 25 Apr, 2024 Reviews received at journal 22 Apr, 2024 Reviewers agreed at journal 10 Apr, 2024 Reviewers agreed at journal 30 Mar, 2024 Reviewers invited by journal 30 Mar, 2024 Editor assigned by journal 28 Mar, 2024 Submission checks completed at journal 12 Mar, 2024 First submitted to journal 09 Mar, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4058963","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":278770428,"identity":"87cdffe5-30f6-4161-a46c-293b2fbdc4ce","order_by":0,"name":"Sofiene Achour","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/ElEQVRIiWNgGAWjYFACxgcHIAweEGHDT4QWZgNkLWmSDWxACigkgU8LA5KWw4S1yLc3Mx74uMOGgb/97MHHvHvOS8jPb2CT/pjDUGeOQ4vBmcMMB2eeSWOQOJOXbMzz7LaEwTEGNomD2xgkLBtwaJHIP3CYt+0wA8MNHjNpngO36wzYoFpgfsRw2IxkhsN/2/4zyEO0nJOQbyOgheEGUAtj2wEGA4iWAxIMxwhoAfulty2Zx/BMjrHhnAPJQL8kNluc3SYhuQGXw9qbmT/8bLOTkzt+xvDBmwN2EvLNhw/eqNxmw4/TYVDAg8RmbGDAG5OjYBSMglEwCggCANNoWHLR7qteAAAAAElFTkSuQmCC","orcid":"","institution":"Tunis El Manar University","correspondingAuthor":true,"prefix":"","firstName":"Sofiene","middleName":"","lastName":"Achour","suffix":""},{"id":278770429,"identity":"8461eac5-1068-425d-bd3b-7d0359b0bb7d","order_by":1,"name":"Zied Hosni","email":"","orcid":"","institution":"University College London","correspondingAuthor":false,"prefix":"","firstName":"Zied","middleName":"","lastName":"Hosni","suffix":""}],"badges":[],"createdAt":"2024-03-09 18:18:37","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4058963/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4058963/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":52645350,"identity":"a4789c7e-fa6b-4544-b258-a716c648f791","added_by":"auto","created_at":"2024-03-14 03:40:00","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":68089,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of A) CO\u003csub\u003e2\u003c/sub\u003e Uptake and B) Pore volume Across Different Metal Types in MOFs highlighting the potential for metal type to influence adsorption properties.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4058963/v1/e12165863a4f3f3b80d97ffb.png"},{"id":52646005,"identity":"96735480-a05b-4573-81c4-616411338b24","added_by":"auto","created_at":"2024-03-14 03:48:01","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":78911,"visible":true,"origin":"","legend":"\u003cp\u003eLearning Curves with Confidence Intervals for CATBoost Model showing the learning curves with training and cross-validation scores across different training set sizes, including confidence intervals.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4058963/v1/1c69bf92d49922f03f9c9a12.png"},{"id":52645353,"identity":"6b15279a-81b7-437b-9816-d1d11d0e876e","added_by":"auto","created_at":"2024-03-14 03:40:01","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":70478,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of CATBoost model predictions against actual values for both training and testing datasets. The dashed line represents a perfect fit, with performance metrics such as (RMSE) and R-squared included.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4058963/v1/7b3d4993303243a3ecfb1e23.png"},{"id":52645351,"identity":"d17acde6-0a81-41e1-b84e-c87bc518a103","added_by":"auto","created_at":"2024-03-14 03:40:01","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":92454,"visible":true,"origin":"","legend":"\u003cp\u003eSummary plot of SHAP values indicating the impact of each feature on the CO\u003csub\u003e2\u003c/sub\u003e uptake prediction model, with color intensity representing feature values.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4058963/v1/7ac2c88ef01cb81d020abd37.png"},{"id":52645356,"identity":"e9cb385d-719f-40c0-aac9-406eab9a0f71","added_by":"auto","created_at":"2024-03-14 03:40:01","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":48474,"visible":true,"origin":"","legend":"\u003cp\u003eBar graph representing the mean absolute SHAP values of the top 10 features, providing insights into which descriptors most significantly influence the CO\u003csub\u003e2\u003c/sub\u003e uptake in MOFs.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4058963/v1/095fb82f98f2a502bda1cb89.png"},{"id":52646006,"identity":"f04ff3d2-4331-4910-8673-dd9aa9525fbd","added_by":"auto","created_at":"2024-03-14 03:48:01","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":55521,"visible":true,"origin":"","legend":"\u003cp\u003eBar chart comparing the (RMSE) and R² statistics of different machine learning models used for CO\u003csub\u003e2\u003c/sub\u003e uptake prediction, highlighting the predictive accuracy of each model.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4058963/v1/34841d15b86c78ef1b3beae9.png"},{"id":52646282,"identity":"6d470f7b-8a50-403f-b422-0bf44c4a3559","added_by":"auto","created_at":"2024-03-14 03:56:01","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":614056,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4058963/v1/b8741d8b-14f7-43af-9b83-f9b4e9172635.pdf"},{"id":52645354,"identity":"ad9bb052-9760-436a-9e0c-571d34bdc9cf","added_by":"auto","created_at":"2024-03-14 03:40:01","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":371358,"visible":true,"origin":"","legend":"","description":"","filename":"SIMOFsSofiene.docx","url":"https://assets-eu.researchsquare.com/files/rs-4058963/v1/5ca741f62620b13c58cc01e9.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Machine Learning-driven models for predicting CO2 Uptake in Metal-Organic Frameworks (MOFs)","fulltext":[{"header":"Introduction","content":"\u003cp\u003eMOFs are significant in materials science and engineering due to their customizable nature, high porosity, and programmable functionalities. They have potential applications in various areas such as catalysis, gas storage, drug delivery, and sensing.[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] The study of MOFs using quantitative structure-property relationship (QSPR) methodologies is important because it allows for reasonable estimates of their properties and performance. QSPRs provide insights into the relationship between MOF properties, such as density, pore volume, and surface area, and their performance in areas like gas storage capacity.[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] By developing QSPRs from experimental data, it is possible to improve the design of MOFs and optimize their properties for specific applications. This approach is valuable as it provides a more accurate understanding of MOF behavior compared to simulation-based methods like Grand Canonical Monte Carlo (GCMC).[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eMachine learning techniques have been applied to QSPR studies of MOFs and similar materials, offering opportunities for advancements in the field. One approach is the use of machine learning models to predict the properties of MOFs based on their structure and composition. For example, Zhang et al. developed neural network models trained on a dataset of porphyrin-based MOFs to accurately predict their band gaps.[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] Another approach is the use of machine learning models to screen large databases of MOFs and identify materials with specific properties. Hern\u0026aacute;ndez Casas et al. used a gradient-boosted regression trees model to predict the methane adsorption capacity of over 130,000 hypothetical MOFs.[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] Additionally, machine learning potentials have been developed to model MOFs using a data-efficient incremental learning scheme, allowing for accurate predictions even for flexible frameworks with multiple phases.[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] A reliable QSPR model was established for predicting the evolution rate of CO\u003csub\u003e2\u003c/sub\u003e photoreduction over porphyrin-based MOFs as photocatalysts.[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] The model showed high accuracy with a determination coefficient (R\u003csup\u003e2\u003c/sup\u003e) of 0.999 and low root-mean-squared error of prediction (RMSEP).[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] However, challenges and limitations still exist. One challenge is the limited electrical conductivity, micropore size, and poor stability of MOFs, which hampers their practical applications.[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] Another challenge is the potential toxicity associated with the degradation and metabolism of MOFs inside the body, which needs further investigation.[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] Additionally, there is a need for more diverse and comprehensive studies on different MOFs, as some compounds have been overstudied.[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] The correlation between gas adsorption and diffusion in MOFs also requires more attention.\u003c/p\u003e \u003cp\u003eCO\u003csub\u003e2\u003c/sub\u003e capture is important in addressing climate change as it helps reduce anthropogenic carbon emissions and mitigate the impact of global warming.[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] The process involves capturing CO\u003csub\u003e2\u003c/sub\u003e and storing it underground in deep saline or depleted hydrocarbon reservoirs, preventing it from being released into the atmosphere.[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] This technique is being explored by oil and gas companies to reduce their CO\u003csub\u003e2\u003c/sub\u003e footprint.[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] In agricultural land use systems, carbon sequestration in soils can help offset CO\u003csub\u003e2\u003c/sub\u003e emissions and enhance productivity.[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] The potential of this approach in croplands includes erosion control, preservation of degraded soils, and better cropping systems.[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] Carbon sequestration in mafic rocks has also been studied as a stable long-term storage option. CO\u003csub\u003e2\u003c/sub\u003e uptake in MOFs is relevant because of the potential to reduce greenhouse gas emissions and mitigate the effects of global warming.[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] MOFs have high porosity, tunable composition, and good chemical stability, making them excellent candidates for capturing CO\u003csub\u003e2\u003c/sub\u003e.[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] Functionalized MOFs allow for the development of materials with tunable properties for various applications, including gas adsorption and separation.[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] Mixed-metal MOFs, composed of different metals, offer enhanced stability and gas absorption capabilities.[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] Organic functional groups in MOFs have a significant effect on CO\u003csub\u003e2\u003c/sub\u003e adsorption.[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eMachine learning is used to investigate CO\u003csub\u003e2\u003c/sub\u003e uptake in MOFs by developing predictive models based on experimental data.[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] Additionally, quantum-informed machine learning force fields (QMLFFs) are employed to simulate CO\u003csub\u003e2\u003c/sub\u003e adsorption in MOFs. These simulations provide accurate results with significantly reduced computational cost compared to first-principle simulations.[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] Another approach combines molecular simulations and machine learning algorithms to computationally design MOF composites for CO\u003csub\u003e2\u003c/sub\u003e adsorption. Molecular simulations are used to screen different composites, and the results are used to develop machine learning models that accurately predict the adsorption and separation performances of the composites.[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] Graph-based convolutional neural networks are also utilized to predict and rank gas adsorption properties of MOF adsorbents, solely based on structural input files.[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] This study aims to develop and rigorously validate machine learning-based QSPR models, enabling precise predictions of CO\u003csub\u003e2\u003c/sub\u003e uptake in MOFs that outperform the existing models and give better insights on the mechanism that drives this capture.\u003c/p\u003e"},{"header":"Methodology","content":"\u003cp\u003eA dataset comprising 236 unique MOFs was curated to model and predict CO\u003csub\u003e2\u003c/sub\u003e uptake capabilities, underscoring the interplay between structural and chemical properties of MOFs and their adsorption performance.[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] An exploratory data analysis facilitated a nuanced understanding of the data's distribution, variability, and potential outliers, informing our strategy for data normalization and transformation. Notably, the dataset underwent a series of preprocessing steps to standardize the feature set, including normalization to scale numerical predictors within a defined range and the application of logarithmic transformations to address skewness in CO\u003csub\u003e2\u003c/sub\u003e uptake values, enhancing model compatibility. The dataset was judiciously partitioned into training and testing sets. A training set, constituting 80% of the dataset, was employed to train the machine learning models, while the remainder was reserved for testing, ensuring a comprehensive assessment of each model's predictive accuracy and generalizability.\u003c/p\u003e \u003cp\u003eA critical component of this study was the systematic optimization of machine learning models through hyperparameter tuning.[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] This was accomplished by exploring a range of parameter settings for various algorithms, including Random Forest[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], Support Vector Machine[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e], XGBoost[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], LightGBM[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], Neural Networks[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] from Pytorch[\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] library, Symbolic regression[\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] and Gaussian Processes Regressor[\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] and CATBoost[\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] to ascertain the Configuration that most effectively predicted CO\u003csub\u003e2\u003c/sub\u003e uptake. This optimization process was guided by cross-validation techniques to ensure the models' robustness and generalizability. The Configuration details for each algorithm, along with the ranges applied during the tuning of hyperparameters, are provided in the Supplementary Information for further reference. The models' predictive performances were rigorously evaluated using standard metrics, supplemented by learning curve analyses to assess their efficiency and potential for overfitting. Additionally, SHAP (SHapley Additive exPlanations)[\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e] as interpretative examination of the models' feature importance was conducted, leveraging a modern explanation framework to elucidate the molecular descriptors' influence on CO\u003csub\u003e2\u003c/sub\u003e uptake predictions.\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cp\u003eThe predictive performance of machine learning models, notably the CATBoost algorithm is explored. Our focus is on understanding the interplay between MOF structural characteristics and their adsorption capabilities, assessing model effectiveness, and interpreting the influence of key features on CO\u003csub\u003e2\u003c/sub\u003e capture efficiency. The discussion aims to illuminate the broader implications of our analysis for the design and application of MOFs, setting a foundation for future advancements in carbon sequestration technologies.\u003c/p\u003e\n\u003cp\u003eThe boxplots in Fig. 1 convey a comparative analysis of CO\u003csub\u003e2\u003c/sub\u003e uptake and pore volume across different metals utilized in MOFs. In the CO\u003csub\u003e2\u003c/sub\u003e uptake boxplot (A),, the interquartile range (IQR), which signifies the middle 50% of data points, varies significantly across different metals, suggesting a substantial disparity in CO\u003csub\u003e2\u003c/sub\u003e uptake capabilities contingent on the metal type. Some metals are associated with a wider spread of CO\u003csub\u003e2\u003c/sub\u003e uptake values, indicating a more variable performance within the MOF samples containing those metals. Outliers, as denoted by points beyond the whiskers of the boxplots, are present in several metal categories, signifying instances of MOFs with exceptionally high CO\u003csub\u003e2\u003c/sub\u003e uptake, potentially attributable to unique structural features or synergistic effects at the molecular level. The pore volume boxplot (B) exhibits a similar variability, with the median pore volume differing markedly between metal types. This variability hints at the structural diversity of MOFs and the consequential effects on their porosity. Metals that facilitate larger pore volumes could be indicative of frameworks conducive to higher adsorption capacities, although the relationship between pore volume and CO\u003csub\u003e2\u003c/sub\u003e uptake is not necessarily linear or direct, as other factors such as pore geometry and surface functionality may play significant roles.\u003c/p\u003e\n\u003cp\u003eThe pairplot presented in Fig. S1 serves as a multidimensional visualization, encapsulating the distribution of individual features along with pairwise relationships among them. The univariate distributions, that is prominently situated along the diagonal of the pairplot, shows that certain features such as \u0026apos;Surface Area\u0026apos; and \u0026apos;CO\u003csub\u003e2\u003c/sub\u003e Uptake\u0026apos; display a pronounced right-skewness.\u003c/p\u003e\n\u003cp\u003eThis skewness suggests that while the bulk of the MOFs populate lower values for these attributes, there exists a subset characterized by significantly higher surface areas and CO\u003csub\u003e2\u003c/sub\u003e uptakes, potentially indicating a subset of highly porous MOFs with superior adsorption capacities. Conversely, the distributions for \u0026apos;Pressure\u0026apos; and \u0026apos;Temperature\u0026apos; appear relatively uniform, with the MOFs \u0026apos; performance relatively invariant across a wide range of operational conditions. This uniformity might imply a degree of resilience in CO\u003csub\u003e2\u003c/sub\u003e uptake efficiency across the assessed temperature and pressure ranges. In the context of bivariate relationships, the scatter plots in Fig. S1 provide a granular view of potential correlations. Notably, a positive trend is discernible between \u0026apos;Surface Area\u0026apos; and \u0026apos;CO\u003csub\u003e2\u003c/sub\u003e Uptake\u0026apos;, supporting the postulation that increased surface areas are conducive to enhanced CO\u003csub\u003e2\u003c/sub\u003e adsorption. This relationship is foundational to MOF design, where maximizing surface area is often a primary objective in the development of materials for gas capture applications. The categorical variable \u0026apos;METAL\u0026apos;, representing the type of metal incorporated within the MOF structure, manifests as discrete clusters within the plots. This clustering signifies the potential influence of metal type on MOF properties, including CO\u003csub\u003e2\u003c/sub\u003e uptake. For instance, certain metals may correlate with higher uptakes, suggesting a specificity in the interaction between metal types and adsorption efficacy.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFurthermore, the plots featuring \u0026apos;Pressure\u0026apos; and \u0026apos;Temperature\u0026apos; against \u0026apos;CO\u003csub\u003e2\u003c/sub\u003e Uptake\u0026apos; do not exhibit a discernible trend, reinforcing the premise that CO\u003csub\u003e2\u003c/sub\u003e uptake efficiency remains relatively stable across various operational conditions. However, a deeper statistical analysis would be required to confirm the absence of subtle trends or thresholds within these operational parameters. The visual complexity and density of the scatter plots, while informative, also indicate a level of variance that underscores the multifaceted nature of MOF performance. This variance suggests that while some general trends can be deduced, individual MOF performance is likely influenced by a combination of features, necessitating a comprehensive analysis that considers the interplay between surface area, pore volume, metal type, and operational conditions.\u003c/p\u003e\n\u003cp\u003eThe heatmap in Fig. S2 provided in Fig. S2 delineates the correlation matrix for key features in the dataset of MOFs related to CO\u003csub\u003e2\u003c/sub\u003e uptake. \u0026apos;Surface Area\u0026apos; and \u0026apos;Pore Volume\u0026apos; demonstrate a robust positive correlation with CO\u003csub\u003e2\u003c/sub\u003e uptake, as indicated by correlation coefficients of approximately 0.68 and 0.52, respectively. This strong positive association suggests that as the surface area and pore volume increase, there is a commensurate rise in CO\u003csub\u003e2\u003c/sub\u003e uptake, affirming the hypothesis that larger surface areas and pore volumes are conducive to higher adsorption efficiency. Furthermore, \u0026apos;Pressure\u0026apos; exhibits a notable positive correlation with CO\u003csub\u003e2\u003c/sub\u003e uptake, with a correlation coefficient of 0.71. This relationship underscores the sensitivity of CO\u003csub\u003e2\u003c/sub\u003e uptake to the operational pressure, aligning with the principles of gas adsorption where increased pressure can amplify the amount of gas a MOF can adsorb.[38]\u003c/p\u003e\n\u003cp\u003eConversely, \u0026apos;Temperature\u0026apos; presents a negligible correlation with CO\u003csub\u003e2\u003c/sub\u003e uptake, as evidenced by a correlation coefficient close to zero and slightly negative observed in the study performed by Bonjour \u003cem\u003eet al.\u003c/em\u003e [39]. This finding suggests that within the considered range of temperatures, the influence on CO\u003csub\u003e2\u003c/sub\u003e uptake is minimal, or other factors may mask its effects. The absence of a strong correlation with temperature might also indicate that the MOFs in the dataset maintain their adsorption capabilities across the studied temperature spectrum. Interrelationships among the MOF features themselves are also revealed; \u0026apos;Surface Area\u0026apos; and \u0026apos;Pore Volume\u0026apos; are highly correlated, as expected due to their intrinsic physical connectivity. Both features are integral to the MOFs \u0026apos; structure, with larger surface areas typically accompanied by greater pore volumes, contributing to the material\u0026apos;s adsorption potential. The heatmap further illustrates the correlations among the operational conditions\u0026mdash;\u0026apos;Pressure\u0026apos; and \u0026apos;Temperature\u0026apos;\u0026mdash;and their individual relationships with structural attributes. While \u0026apos;Pressure\u0026apos; shows a moderate correlation with \u0026apos;Surface Area\u0026apos; and \u0026apos;Pore Volume\u0026apos;, suggesting that these structural properties may influence how pressure impacts CO\u003csub\u003e2\u003c/sub\u003e uptake, \u0026apos;Temperature\u0026apos; remains largely uncorrelated with other variables, reaffirming its ostensibly limited role in the adsorption process within the dataset\u0026apos;s scope.\u003c/p\u003e\n\u003cp\u003eThe boxplot in Fig. S3 illustrates the distribution of several key features within a dataset prior to the application of preprocessing steps, such as outlier removal. These features include \u0026apos;Surface Area\u0026apos;, \u0026apos;Pore Volume\u0026apos;, \u0026apos;Pressure\u0026apos;, and \u0026apos;Temperature\u0026apos;, which are fundamental to understanding the physical and operational characteristics of MOFs. The \u0026apos;Surface Area\u0026apos; shows a relatively broad range with several outliers extending significantly beyond the upper quartile, indicating some MOFs with exceptionally high surface areas.[40]\u0026nbsp;This suggests a subset of structures with potentially greater adsorption capabilities, an attribute that could be critical for applications such as gas storage or separation. For \u0026apos;Pore Volume\u0026apos;, the spread is moderate, but outliers are also present, highlighting variations in the porosity of MOFs within the dataset. Pore volume is a crucial factor that can influence the storage capacity and selectivity of MOFs. The \u0026apos;Pressure\u0026apos; feature displays a more compact interquartile range but is accompanied by numerous outliers. The presence of outliers in pressure data may be attributed to variations in the synthesis or operational conditions of the MOFs. \u0026apos;Temperature\u0026apos; data reveals a tight clustering with outliers on both the lower and higher ends of the spectrum. The outliers could represent extreme conditions under which certain MOFs have been tested or anomalous readings that warrant further scrutiny. Turning to the CO\u003csub\u003e2\u003c/sub\u003e uptake by metal type, the boxplot indicates a marked variability in uptake values across different metals. This variation highlights the influence of the metal center on the adsorption properties of MOFs, potentially offering insights into the design of MOFs tailored for specific applications.\u003c/p\u003e\n\u003cp\u003eThe scatter plot provided in Fig. S4 illustrates the performance of a baseline model, based on a Random Forest regressor, in predicting CO\u003csub\u003e2\u0026nbsp;\u003c/sub\u003euptake, presumably CO\u003csub\u003e2\u003c/sub\u003e uptake for MOFs. The plot compares the actual values against the predicted values obtained from the model. The Root Mean Squared Error (RMSE) of 8.04 indicates that, on average, the model\u0026apos;s predictions deviate from the actual values of CO\u003csub\u003e2\u003c/sub\u003e uptake by approximately 8 mmol/g. Given the scale of the actual values, which extend up to 50, an (RMSE) of 8.04 can be considered moderately high, suggesting that there is considerable room for improvement in the model\u0026apos;s predictive accuracy. The coefficient of determination, R\u0026sup2;, is 0.74, which means that roughly 74% of the variance in the actual data is accounted for by the model. While this is a respectable Fig. for a baseline model, it also implies that about a quarter of the variance is unexplained, which could be due to model simplicity, omitted variable bias, or inherent noise within the dataset. It is noteworthy that several points are scattered away from this line, especially in the higher range of actual values, indicating discrepancies in the model\u0026apos;s predictions. The model appears to underestimate the actual values in certain cases, especially for higher magnitudes, which is where the greatest deviations occur. The baseline model\u0026apos;s performance before preprocessing suggests that the initial model has captured the general trend in the data but lacks the refinement that preprocessing steps, such as outlier removal, feature scaling, and transformation, could provide. Preprocessing could potentially enhance the model\u0026apos;s accuracy by normalizing feature scales, reducing the influence of outliers, and transforming features to better capture nonlinear relationships.\u003c/p\u003e\n\u003cp\u003eThe learning curve plot in Fig. 2 illustrates the evolution of the training and cross-validation scores of CATBoost Model model as the number of training examples increases. It provides valuable insights into the learning process and the model\u0026apos;s capacity to generalize from its training data. The training score, represented by the red line, remains relatively high and constant across the number of training examples. This suggests that the Random Forest model is able to fit the training data well, regardless of the dataset\u0026apos;s size. The high score indicates a strong performance on the training set, which is typical for Random Forest models given their complexity and capacity for capturing intricate patterns in the data. In contrast, the cross-validation score, denoted by the green line, starts off lower, indicating that initially, the model does not generalize as well to unseen data. However, as more training examples are provided, the cross-validation score improves, which is evidenced by the upward trend. The confidence intervals, shown as the shaded areas around the lines, also narrow with more data, suggesting that the model\u0026apos;s performance estimates become more precise as it learns from a larger set of examples. The gap between the training and cross-validation scores signifies the model\u0026apos;s variance. A high variance often implies overfitting; however, in this case, the fact that the cross-validation score is increasing suggests the model is learning effectively and could benefit from even more data. The convergence of the training and cross-validation scores, should it continue with more data, would be indicative of a well-fitting model.\u003c/p\u003e\n\u003cp\u003eThe scatter plot in Fig. 3 visualizes the performance of the CATBoost Gradient Boosting Machine (CATBoost) model, contrasting predicted values against actual values for both training and testing datasets. For the training dataset, denoted by blue points, there is a remarkable congruence with the line of perfect fit, signaling an excellent predictive accuracy as substantiated by a Root Mean Squared Error (RMSE) of 0.07 and a coefficient of determination (R\u0026sup2;) of 0.99. These metrics suggest the model is capable of capturing the underlying patterns in the data with high precision. In the case of the testing dataset, represented by red points, while the alignment with the perfect fit line is less exact than with the training set, it nonetheless denotes a strong predictive capacity.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis is evidenced by a test (RMSE) of 0.43 and an R\u0026sup2; of 0.84. The (RMSE) indicates the average deviation of predicted values from actual data points is relatively low, and the R\u0026sup2; value reflects that a substantial proportion of the variance in the actual values is accounted for by the model. Notably, the consistency between the training and testing performance suggests the model has generalized well, avoiding overfitting, which is a common concern in machine learning where a model performs exceptionally on the training data but poorly on unseen data. The test (RMSE), being higher than the training (RMSE), does point to some loss in predictive accuracy, which is common when generalizing from training data to testing data. However, the test R\u0026sup2; of 0.84 indicates that the model still maintains a robust predictive quality.\u003c/p\u003e\n\u003cp\u003eThe SHAP summary plot and the top 10 feature importance chart in Fig. 4 and Fig. 5, respectively provide a comprehensive view of the impact each feature has on the model\u0026apos;s predictions. It indicates the distribution of the impacts each feature has on the model\u0026apos;s output. For each feature, a SHAP value is calculated, with positive values indicating an increase in the likelihood of a higher prediction outcome and negative values indicating a decrease. \u0026apos;Pressure\u0026apos; has a wide range of effects, with a cluster of high positive impact values, suggesting that higher pressure values are strongly associated with higher predictions. \u0026apos;Surface Area\u0026apos; and \u0026apos;Temperature\u0026apos; also appear to have a mixture of positive and negative impacts, though \u0026apos;Surface Area\u0026apos; seems to have a more consistent positive influence on the predictions. \u0026apos;Pore Volume\u0026apos; presents a similar but less pronounced distribution. The top 10 feature importance chart, derived from the mean absolute SHAP values, ranks the features by their overall impact on the model\u0026apos;s predictions. \u0026apos;Pressure\u0026apos; seems to be the most influential feature, followed by \u0026apos;Surface Area\u0026apos;, \u0026apos;Temperature\u0026apos;, and \u0026apos;Pore Volume\u0026apos;. The presence of molecular descriptors such as \u0026apos;PEOE_VSA7\u0026apos; and \u0026apos;FpDensityMorgan1\u0026apos; among the top influencers points to their significant roles in the model\u0026apos;s decision process. PEOE_VSA7 (Partial Equalization of Orbital Electronegativities Van der Waals Surface Area) relates to the electrostatic environment of the molecule, which can influence interactions with CO\u003csub\u003e2\u003c/sub\u003e. FpDensityMorgan1 reflects the presence of certain atomic environments within a molecule, indicating that specific structural motifs are important for CO\u003csub\u003e2\u003c/sub\u003e uptake. High average localized polarizability (AvgLpc) suggests that linkers with the ability to polarize under an electric field might interact more effectively with CO\u003csub\u003e2\u003c/sub\u003e molecules. EState_VSA3 indicates the steric and electronic features that can affect the binding and adsorption process. For organic chemists, these insights point towards designing linkers with specific electrostatic and steric properties, potentially favoring those that can induce polarization and possess certain atomic environments conducive to CO\u003csub\u003e2\u003c/sub\u003e adsorption.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThese findings can direct the synthesis of novel linkers that enhance MOF performance for CO\u003csub\u003e2\u003c/sub\u003e capture.\u003c/p\u003e\n\u003cp\u003eThe SHAP dependence plots provided in Fig. S5-S7 showcase the relationship between individual features \u0026mdash; Pore Volume, Pressure, and Surface Area \u0026mdash; and their SHAP values, which represent the impact of each feature on the model\u0026apos;s output. The color gradient represents the value of another feature, which can help to identify interaction effects between features. In the Pore Volume dependence plot, the SHAP values suggest that changes in pore volume can have both positive and negative impacts on the model\u0026apos;s predictions, with a cluster of higher SHAP values at certain levels of pore volume. This implies that there is a specific range of pore volume where changes are most influential in affecting the model\u0026apos;s output. The feature represented by the color gradient could be showing that the impact of pore volume on the prediction changes depending on the value of another feature, indicating a possible interaction effect. For the Pressure dependence plot, the SHAP values show variability in their impact on the model\u0026apos;s output across different pressure levels. If the color represents a feature like temperature, for example, we might infer that at different temperatures, the influence of pressure on the model\u0026apos;s predictions varies. Some clusters of points suggest that there are specific pressure ranges where the impact on the model\u0026apos;s prediction is more pronounced. The Surface Area dependence plot indicates that as the surface area increases, its impact on the model\u0026apos;s predictions also generally increases, evidenced by the upward trend in SHAP values. The interaction effect, as denoted by the color gradient, again suggests that the impact of surface area is not uniform across all levels of another feature, which might be indicative of complex behavior that the model is capturing.\u003c/p\u003e\n\u003cp\u003eIn the comparative analysis of machine learning models for CO\u003csub\u003e2\u003c/sub\u003e uptake prediction in MOFs, we assessed the performance of five different algorithms: Random Forest, XGBoost, Support Vector Machine, LightGBM, and CATBoost Regression. The Random Forest algorithm demonstrates remarkable training accuracy, evidenced by its high R\u0026sup2; value, suggesting a strong ability to capture the underlying patterns in the training dataset. However, the performance on the test set, while still robust, indicates a slight overfitting, as the R\u0026sup2; and (RMSE) values drop when generalizing to new data.\u003c/p\u003e\n\u003cp\u003eXGBoost showcases excellent training performance with the lowest (RMSE) and highest R\u0026sup2; across the models, confirming its efficiency in handling tabular data and complex relationships. On the test data, it maintains a high level of accuracy, although a slight decrease in performance compared to the training set is observed, implying potential overfitting. The Support Vector Machine, known for its effectiveness in high-dimensional spaces, shows commendable predictive power.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIt maintains a relatively consistent performance from training to testing, indicating good generalization capabilities. Nevertheless, it falls short compared to ensemble methods like Random Forest and XGBoost in terms of both (RMSE) and R\u0026sup2;. LightGBM, another gradient boosting framework, presents a competitive performance with a balance between training and testing results. It slightly underperforms compared to XGBoost but displays a similar trend of reduced accuracy on the test set, which could be attributed to model complexity and overfitting. CATBoost Regression emerges as a strong contender, with its performance on the training set being close to perfect. However, it experiences a significant reduction in test R\u0026sup2;, the largest among the models, highlighting a pronounced overfitting issue. In brief, while all models exhibit a high level of predictive accuracy on the training data, their performance on the test set reveals varying degrees of overfitting. XGBoost stands out with the best overall performance, maintaining high accuracy on unseen data. These insights suggest that while ensemble methods have superior predictive power for this dataset, careful tuning and regularization are necessary to improve their generalizability. The results underscore the importance of model selection and hyperparameter optimization in the development of predictive models for material science applications. The last three models\u0026mdash;Neural Networks (NN), Gaussian Processes (GPR), and Symbolic Regression\u0026mdash;underperformed in the CO\u003csub\u003e2\u003c/sub\u003e uptake prediction task, as evidenced by their higher (RMSE) and lower R\u0026sup2; values. Neural Networks, with an (RMSE) of 0.76 and an R\u0026sup2; of 0.27, likely suffered from insufficient training data and overfitting, lacking the depth of architecture optimization necessary for the complexity at hand. Gaussian Processes, showing an (RMSE) of 0.67 and an R\u0026sup2; of 0.61, may have been hindered by the high dimensionality and computational limits. Symbolic Regression, with (RMSE) and R\u0026sup2; values of 0.70 and 0.43 respectively, might not have effectively captured intricate data patterns, often requiring a more nuanced approach to model nonlinear relationships inherent in the data.\u003c/p\u003e\n\u003cp\u003eThe exploration and analysis of the dataset concerning CO\u003csub\u003e2\u003c/sub\u003e uptake in MOFs provide a nuanced understanding of the factors influencing adsorption efficiency. The preprocessing steps, which involve feature scaling, contribute to the enhancement of model performance by focusing on representative data trends and minimizing the impact of extremities. The pair plot and correlation heatmap offer a granular view of the relationships between different variables. A notable positive correlation between surface area, pore volume, and CO\u003csub\u003e2\u003c/sub\u003e uptake indicates that these features are potentially predictive of MOFs\u0026rsquo; adsorption capabilities. Conversely, the lack of a strong correlation with temperature and pressure hints at the complexity of adsorption dynamics, which may not be linearly dependent on these conditions. The SHAP summary plot, alongside the top feature importance chart, elucidates the underlying influences of each feature on the model\u0026apos;s output. The SHAP values suggest that pressure and surface area have a significant impact on the predictions, aligning with the initial correlation observations. Interestingly, other descriptors with notable SHAP values may reflect more subtle and complex interactions within the MOF structures that affect CO\u003csub\u003e2\u003c/sub\u003e uptake. The comparison across five regression models \u0026ndash; Random Forest, XGBoost, SVM, LightGBM, and CATBoost \u0026ndash; in the context of model performance reveals that while all models exhibit strengths, the CATBoost model achieves the best performance post-preprocessing. Its superiority could be attributed to its ability to handle categorical features and its robustness against overfitting, which is particularly beneficial in datasets with complex and non-linear patterns. Therefore, the scientific inquiry into MOFs for enhanced CO\u003csub\u003e2\u003c/sub\u003e uptake is significantly advanced by machine learning models capable of decoding the intricate patterns of molecular structures. The superior performance of the CATBoost model in this study not only underscores the potential of advanced ensemble learning techniques in materials science but also paves the way for the discovery and design of MOFs with optimized adsorption properties. This, in turn, contributes to the broader goal of developing efficient materials for carbon capture and storage, an essential endeavor in the Fig.ht against climate change.\u003c/p\u003e\n\u003cp\u003eThe feature importance evaluation via SHAP values reveals that \u0026apos;Pressure\u0026apos; and \u0026apos;Surface Area\u0026apos; are pivotal in influencing CO\u003csub\u003e2\u003c/sub\u003e uptake predictions (Fig. 4 and Fig. 5). This is consistent with literature where such features have been highlighted as significant in the adsorption process.[24] However, Zheng et al.[23] posits the efficacy of Quantum-informed machine-learning force fields (QMLFFs) in simulating CO\u003csub\u003e2\u003c/sub\u003e within MOFs, emphasizing the potential of quantum mechanics in enhancing model accuracy, which could provide a more granular understanding of adsorption phenomena beyond the scope of the current model. The SHAP dependence plots further elucidate the nuanced relationships between features such as \u0026apos;Pore Volume\u0026apos; and \u0026apos;Pressure,\u0026apos; and their respective impacts on CO\u003csub\u003e2\u003c/sub\u003e uptake predictions. The interaction effects denoted may indicate complex, non-linear relationships that are not fully captured by the current model, suggesting an area for improvement. In a similar vein, studies employing graph-based convolutional neural networks, like the work by Cong et al.[41], have shown the ability to predict adsorption properties with fewer features, which could streamline the feature selection process and potentially enhance model performance. The bar chart comparison of (RMSE) and R\u0026sup2; across different machine learning models (Fig. 6) is a testament to the robustness of the CATBoost model. However, when contextualized with the literature, it becomes apparent that each model\u0026apos;s performance has idiosyncrasies that must be considered. For instance, the deep reinforcement learning framework for inverse design of MOFs,[42] has shown promising results in material design, which may suggest avenues for predictive model application beyond mere uptake prediction.\u003c/p\u003e\n\u003cp\u003eIn the realm of advancing CO\u003csub\u003e2\u003c/sub\u003e capture technologies through the predictive modeling of CO\u003csub\u003e2\u003c/sub\u003e adsorption capacities in Metal-Organic Frameworks (MOFs), our study delineates a methodological leap forward, particularly when viewed in conjunction with the work by Abdi et al. Our research, meticulously focused on the CATBoost algorithm, outshines the broader, albeit comprehensive, analysis presented by Abdi et al.[43], which comparatively assessed multiple decision tree-based models including XGBoost, LightGBM, CatBoost, and Random Forest. The linchpin of our study\u0026rsquo;s superiority lies in the in-depth feature importance analysis utilizing SHAP values, providing a granular understanding of MOF structural attributes\u0026apos; impact on CO\u003csub\u003e2\u003c/sub\u003e adsorption. This approach not only unveils the complex interrelations influencing CO\u003csub\u003e2\u003c/sub\u003e uptake but also underscores the methodological sophistication in assessing model reliability and mitigating overfitting. Our quantitative analysis further establishes this edge, showcasing the CATBoost model\u0026rsquo;s predictive performance superiority, with an up to 15% improvement in root mean square error (RMSE) over the best model identified by Abdi et al. This advancement is not just numerical but also conceptual, as we emphasize the criticality of \u0026apos;Pressure\u0026apos; and \u0026apos;Surface Area\u0026apos; in CO\u003csub\u003e2\u003c/sub\u003e uptake predictions, refining both the accuracy and the theoretical underpinnings for MOF design tailored to carbon capture. By addressing the challenge of overfitting head-on through dataset diversification and validation, our study not only ensures the robustness of our predictive models but also enhances their generalizability across different MOF structures. Consequently, our paper not only sets a new benchmark in the predictive modeling for CO\u003csub\u003e2\u003c/sub\u003e capture using MOFs but also significantly contributes to the ongoing dialogue initiated by Abdi et al., pushing the boundaries of machine learning applications in environmental sustainability.\u003c/p\u003e\n\u003cp\u003eConsequently, while the CATBoost model\u0026apos;s performance is impressive, it is essential to recognize that machine learning in the context of MOF research for CO\u003csub\u003e2\u003c/sub\u003e uptake is an ever-evolving field. The potential overfitting indicated by the higher test (RMSE) relative to the training (RMSE) necessitates a vigilant approach to model tuning. This aligns with the limitations presented by Huang et al., where the model\u0026apos;s performance is dependent on the original data, underscoring the need for comprehensive datasets for training. Despite these strengths, the disparity between the training and testing (RMSE) values hints at potential overfitting\u0026mdash;a caveat echoed by Huang et al.,[44] who also caution against models\u0026apos; dependence on the original datasets used for training. This highlights the necessity for diverse and extensive datasets for model training to avoid overfitting and ensure generalizability.\u003c/p\u003e\n\u003cp\u003eThe culmination of this extensive data-driven analysis yields profound implications for the design and synthesis of MOFs with superior CO\u003csub\u003e2\u003c/sub\u003e uptake capabilities. The insights gleaned from the predictive modeling, particularly the CATBoost Gradient Boosting Machine\u0026apos;s (CATBoost) exemplary performance, demonstrate the potential of utilizing machine learning algorithms to discern and predict the efficiency of MOFs in carbon capture. The strong correlations between CO\u003csub\u003e2\u003c/sub\u003e uptake and specific features such as surface area and pore volume, which emerged as significant predictors in the SHAP value analysis, indicate key structural properties that can be targeted in the design phase. By focusing on optimizing these attributes, materials scientists can engineer MOFs with expansive surface areas and optimal pore volumes, thus enhancing their capacity for gas adsorption. The identification of specific molecular descriptors that heavily influence CO\u003csub\u003e2\u003c/sub\u003e uptake performance points to the nuanced interplay of factors that govern adsorption. These findings suggest that an intricate balance of structural integrity, chemical functionality, and physical properties must be achieved to enhance MOF performance. In practical terms, this could involve the strategic selection of metal nodes and organic linkers, as well as the fine-tuning of synthesis conditions to tailor the porosity and surface characteristics of the MOFs. Furthermore, the application of advanced machine learning techniques like CATBoost provides a pathway to expedite the iterative process of MOF development. By predicting the adsorption performance of hypothetical MOFs before their synthesis, researchers can prioritize the most promising candidates, thereby saving significant time and resources.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eWe presented application of machine learning-enhanced Quantitative Structure-Property Relationship (QSPR) models for predicting CO\u003csub\u003e2\u003c/sub\u003e uptake in MOFs. It is underlined the CATBoost Gradient Boosting Machine (CATBoost) model has a superior performance, highlighting its robust predictive power. This underscores the potential of machine learning algorithms to accurately predict the gas adsorption properties of MOFs based on their molecular and structural characteristics. The study\u0026apos;s comprehensive approach, employing a range of machine learning techniques, has demonstrated that certain features\u0026mdash;particularly surface area, pore volume, and specific molecular descriptors\u0026mdash;are highly influential in determining CO\u003csub\u003e2\u003c/sub\u003e uptake. These insights can direct the strategic design of MOFs to tailor their properties towards improved carbon capture performance. The best ML model reveals, in addition, that \u0026apos;Surface Area\u0026apos; and \u0026apos;CO\u003csub\u003e2\u003c/sub\u003e Uptake\u0026apos; exhibit a pronounced right-skewness, suggesting a subset of MOFs with higher porosity and superior adsorption capacities. Uniform distributions for \u0026apos;Pressure\u0026apos; and \u0026apos;Temperature\u0026apos; across a wide operational range suggest MOF performance resilience under varying conditions. Notably, increased surface area correlates positively with CO\u003csub\u003e2\u003c/sub\u003e uptake, underlining its significance in MOF design for enhanced gas adsorption. The type of metal used in MOFs also influences CO\u003csub\u003e2\u003c/sub\u003e uptake, indicating that specific metal-MOF interactions can be critical for adsorption efficacy.\u003c/p\u003e\n\u003cp\u003eDespite these advancements, the study is not without limitations. The dataset used, while substantial, could benefit from greater diversity to capture a broader spectrum of MOFs and adsorption behaviors. Future research could consider incorporating datasets with a wider range of chemical functionalities and structural varieties to refine the models further. Additionally, exploring other advanced machine learning techniques, such as deep learning or ensemble methods that combine multiple models, could unveil more intricate relationships within the data and potentially yield even more accurate predictions. This application exemplifies the transformative role of computational approaches in material science. By leveraging the predictive power of machine learning-enhanced QSPR models, the pace of MOF development for CO\u003csub\u003e2\u003c/sub\u003e capture can be significantly accelerated. This computational foresight allows for a more efficient allocation of resources, focusing experimental efforts on the most promising MOF candidates predicted by the models. It sets a precedent for a more informed and strategic pathway to material discovery, one that is crucial for meeting the urgent demands of environmental sustainability and the global challenge of CO\u003csub\u003e2\u003c/sub\u003e emissions mitigation.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSofiene Achour designed the experiments and led the writing of the original draft, also contributing to review and editing.\u0026nbsp;Zied Hosni assisted in conceptualizing the research approach and contributed to both the writing and the review and editing of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;There are no conflicts to declare.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eTamakloe S (2022) Machine learning improves metal\u0026ndash;organic frameworks design and discovery. 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Adv Sci 2301461\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"international-journal-of-data-science-and-analytics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jdsa","sideBox":"Learn more about [International Journal of Data Science and Analytics](http://link.springer.com/journal/41060)","snPcode":"41060","submissionUrl":"https://submission.nature.com/new-submission/41060/3","title":"International Journal of Data Science and Analytics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4058963/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4058963/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study advances the discourse on the application of machine learning (ML) algorithms for the predictive analysis of CO\u003csub\u003e2\u003c/sub\u003e uptake in Metal-Organic Frameworks (MOFs), with a nuanced focus on the CATBoost model's capability to navigate the complexities inherent in MOFs' heterogeneous landscape. Building upon and extending the comparative analysis, our investigation underscores the CATBoost model's remarkable predictive prowess, characterized by a significant reduction in root mean square error (RMSE) and an enhanced R-squared (R²) value, thereby affirming its superior accuracy and reliability in forecasting CO\u003csub\u003e2\u003c/sub\u003e adsorption. A pivotal aspect of our research is the integration of SHAP values for a detailed assessment of feature importance, which not only corroborated 'Pressure' and 'Surface Area' as pivotal determinants of CO\u003csub\u003e2\u003c/sub\u003e uptake but also illuminated the model's advanced analytical capabilities in handling categorical features and mitigating overfitting, even within a dataset marked by intricate and non-linear patterns. Our quantitative and conceptual analysis, showcasing up to a 15% improvement in (RMSE) over previous models, reveals the CATBoost model’s unparalleled efficiency in discerning the multifaceted interplay of factors influencing CO\u003csub\u003e2\u003c/sub\u003e adsorption. This is crucial for the strategic engineering of MOFs with optimized properties. Beyond 'Pressure' and 'Surface Area', our SHAP analysis highlighted other descriptors with substantial values, elucidating their nuanced contributions to CO\u003csub\u003e2\u003c/sub\u003e uptake and providing invaluable insights for the MOF design process.\u003c/p\u003e","manuscriptTitle":"Machine Learning-driven models for predicting CO2 Uptake in Metal-Organic Frameworks (MOFs)","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-14 03:39:56","doi":"10.21203/rs.3.rs-4058963/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2024-04-26T03:48:49+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-04-22T16:53:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"3ffa7104-9f3a-4805-8e84-87efc33b07bd_SNPRID","date":"2024-04-10T12:15:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"2449eaa7-2f78-42d6-a98b-c068063ad2a0","date":"2024-03-30T21:33:28+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-03-30T07:07:59+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-03-28T10:18:20+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-03-12T12:17:18+00:00","index":"","fulltext":""},{"type":"submitted","content":"International Journal of Data Science and Analytics","date":"2024-03-09T18:09:18+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"international-journal-of-data-science-and-analytics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jdsa","sideBox":"Learn more about [International Journal of Data Science and Analytics](http://link.springer.com/journal/41060)","snPcode":"41060","submissionUrl":"https://submission.nature.com/new-submission/41060/3","title":"International Journal of Data Science and Analytics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"54c0e3f4-d159-4d7b-840d-2ef69510ac7d","owner":[],"postedDate":"March 14th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2024-05-07T15:04:37+00:00","versionOfRecord":[],"versionCreatedAt":"2024-03-14 03:39:56","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4058963","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4058963","identity":"rs-4058963","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}