Accuracy Techniques for Announcement of Hydrogen Solubility in Vines through Data-Driven Modeling

This paper conducted a comprehensive evaluation of data-driven algorithms to estimate hydrogen solubility in aqueous systems using a variety of ML algorithms. These algorithms included CNN, Ridge regression, Linear regression, ANN, Elastic net, GP, Lasso regression, SVR, GBM, RF, KNN, DT, XGBoost, LightGBM, and CatBoost.

To rigorously assess the effectiveness of the algorithm, multiple evaluation metrics were applied, including:

1. a.

   R-squared (R²): Calculates the percentage of variation in dependent parameters affected by independent parameters.

2. b.

   Mean Square Error (MSE): Determines the mean square imbalance between the estimated and actual values.

3. c.

   Mean relative deviation rate (MRD%): Indicates the typical percentage deviation of the estimated parameters from the actual measurement.

4. d.

   Residual Standard Deviation (σ): Evaluates the variance of the algorithm's estimates on the mean.

These metrics provide a comprehensive framework for assessing the performance and predictive capabilities of developed ML models in estimating hydrogen solubility^67,68. These metrics are defined as follows:

here, \(\:{\varvec {y}}_{\varvec {i}}^{\varvec {p}\varvec {r}\varvec {e}\varvec {d}\varvec {i}\varvec {c}\varvec {t}\varvec {e}\varvec {d}}\) and \(\:{\varvec {y}}_{\varvec {i}}^{\varvec {r}\varvec {e}\varvec {a}\varvec {l}}}\) n means the total count of data in the data bank, but it represents the predicted and actual target values.

Figure 16 shows the Taylor Diagram, a sophisticated visual tool for comparing the performance of regression models in predicting hydrogen solubility. This diagram simultaneously represents the correlation coefficients and standard deviations of multiple ML algorithms. These algorithms include Ridge regression, Lasso regression, Linear regression, SVR, Gradient boost, RF, XGBoost, KNN, LightGBM, DT, CatBoost, ANN, GP, and CNN. All algorithms are plotted as points, close to the reference data point, with improved accuracy and enhanced agreement with experimental hydrogen solubility data. The Taylor diagram provides a thorough glass-enhanced comparison of model performance, allowing researchers to quickly assess the effectiveness of various ML approaches in capturing trends in hydrogen solubility in water systems.

According to Taylor diagrams and evaluation tables, the algorithms that stand out as top performers are cat boost, SVR, gradient boost, and RF. These algorithms demonstrate robust execution across all evaluation criteria, including high R² scores, MSE, and relatively minor MRD%. Table 1 emphasizes their exceptional results, with CatBoost leading the way through attaining the top R² values ​​(training: 0.9984, validation: 0.9888, and testing: 0.9756), the lowest MSE (training: 0.0001, validation: 0.0005, testing: 0.0012), and relatively low MRD% (training: 26.84%, validation: 28.44%, and testing: 57.35%). Similarly, gradient boost, SVR, and RF provide amazing performance featuring high R² values, minimum MSE, and relatively low MRD%.

On the other hand, simpler models such as linear regression, lasso regression, and DT show relatively weaker runs. These algorithms achieve lower R² values ​​(range 0.1215-0.8659), higher MSE values ​​(range 0.0366-0.0430), and significantly larger average relative deviation rate (MRD%) (range 85.28-1362.02%). The limited ability to capture the variance of data and their larger prediction errors make them less reliable for accuracy estimation. Notably, the DT model reaches an ideal R² score of 1.0000 in training data, but very high MRD% (1362.02% and 2636.74%, respectively) in the test and validation set reveals significant overfitting and inadequate generalizations to previously unabsorbed data, making predictions unreliable.

Advanced ML models CatBoost, SVR, Gradient Boosting, and RF showed exceptional performance in predicting hydrogen solubility. These algorithms showed increased accuracy, minimum estimation errors, and robust executions through various evaluation criteria. In the opposite, linear regression, Lasso regression, and DT models were found to have low effects, indicating substantial deviations between reduced predictive power and real values. The complex and nonlinear nature of hydrogen solubility appears to be better captured by more sophisticated ensemble and ML techniques.

This study employs graphical techniques such as relative deviation values ​​and cross-plotting to evaluate ML models for estimating hydrogen solubility in aqueous systems. These visualization methods allow for a comprehensive model performance assessment by comparing predicted and actual values. The graphical approach provides intuitive insight into model accuracy and reveals potential inconsistencies and error patterns. By juxtapping predicted and actual hydrogen solubility data, scientists can critically examine the robustness and reliability of different prediction algorithms. These visual tools are essential to enhance the evaluation process and provide a clear and immediate understanding of the predictive capabilities of each model when representing complex hydrogen dissolution relationships.

Figure 17 compares actual points with predictive values ​​generated by all developed algorithms charted in relation to data point indexes for all phases of hydrosolution estimation of aqueous systems. As shown in the diagram, predicted values ​​from CatBoost, SVR, Gradient Boosting, and RF are closely matched with actual data points, and are often roughly intersected. This strong agreement between the actual and modeled values ​​suggests that these ML methods outweigh the other methods used in this study, indicating excellent accuracy and reliability in predicting hydrogen solubility.

Furthermore, Figure 18 shows a cross-plot comparing actual and predicted values ​​for all ML algorithms. A significant concentration of points near line y = x was observed in catboost, gradient boost, SVR, and RF, highlighting exceptional prediction accuracy. Furthermore, the trend lines applied to the cross-plot points of these algorithms are closely aligned with rows y = x. These observations show a strong relationship between actual hydrogen solubility values ​​and the predictions generated by these methods, further verifying the excellent effects in assessing hydrogen solubility in aqueous systems.

Figure 19 shows a scatter plot showing the associated inaccuracies of the developed models in predicting hydrogen solubility. For CatBoost, Gradient Boost, SVR, and RF, the error values ​​are closely distributed around the X-axis, minimizing deviations from the actual values. This analysis highlights the strong alignment of the predicted and actual hydrogen solubility criteria for these models, with error patterns indicating high reliability of predation.

Figure 20 shows the predictive distribution capabilities of all ML methods developed in all phases. An overview of estimate frequency for CatBoost, Gradient Boosting, SVR, and RF shows greater consistency across all databanks compared to other methods. This regularity confirms that these models are the most robust and reliable for estimating hydrogen solubility in aqueous systems, as demonstrated in this study.

Evaluating the importance of features is an important step in understanding the influence of input parameters on prediction of hydrogen solubility in aqueous systems using ML algorithms. In this study, the importance of features is analyzed using the Shapley Additive Description (SHAP) method, which provides a powerful way to interpret the complexity of high-performance models. The game theory-based SHAP method provides a reliable foundation for measuring the effects of all input functions into model estimation. SHAP increases the explanability of the model at the global level and at the individual by assigning a specific allocation value to all points according to the input function. This allows for a more clear understanding of how input parameters affect the target output. In this case, it is the hydrogen solubility in the water system. Figure 21 shows the SHAP values ​​of input properties and their importance as assessed by the random forest, gradient boost, and cat boost models in estimating hydrogen solubility. The attributes are listed in order from highest to lowest depending on the SHAP value, with higher rank features having a strong influence on model estimation. SHAP analysis determines pressure and salinity as one of the most influential and top-level factors affecting the hydrogen solubility of water systems, highlighting important functions in the prediction procedure.