Modeling CO₂ solubility in polyethylene glycol polymer using data driven methods

The solubility of CO₂ in polyethylene glycol (PEG) polymer is a critical parameter for optimizing its use in various industrial processes, underscoring the need for precise predictive models. In this research, a Random Forest (RF) machine learning model is meticulously tuned through four sophisticated optimization algorithms: Batch Bayesian Optimization (BBO), Self-Adaptive Differential Evolution (SADE), Bayesian Probability Improvement (BPI), and Gaussian Processes Optimization (GPO). The model leverages a dataset of 164 experimental samples, incorporating essential input parameters such as pressure, PEG molar mass, and temperature to predict CO₂ solubility. To prevent overfitting, K-fold cross-validation is applied throughout model training. The efficacy of each optimization method is evaluated using computational runtime and performance metrics, including R-squared (R²), mean squared error (MSE), and average absolute relative error (AARE%). Correlation analysis indicates that pressure has a moderate positive relationship with CO₂ solubility (correlation coefficient: 0.58), while PEG molar mass and temperature exhibit weaker associations (0.2 and 0.05, respectively). Among the optimization techniques, RF-BPI proves to be the most effective, delivering superior predictive performance. The results show RF-BPI achieves an R² of 0.9625 for the training set and 0.9307 for the test set, surpassing other methods. For benchmarking, a conventional multiple linear regression (LR) model was tested, demonstrating significantly lower accuracy (R² notably inferior to RF-BPI’s 0.9307 on the test set). In terms of computational efficiency, BPI records the shortest runtime (63.9 seconds), while SADE is the least efficient, requiring 2370.2 seconds. Sensitivity analysis further clarifies the relative impact of each input variable on CO₂ solubility, affirming the power of data-driven approaches in modeling complex systems. The created models can be seen as promising predictive tools to predict CO2 solubility in PEG in the absence of requiring physical measurements that are often labor-intensive, costly, and laborious.二氧化碳（CO₂）在聚乙二醇（polyethylene glycol, PEG）聚合物中的溶解度是优化其在各类工业应用中使用的关键参数，凸显了构建精准预测模型的迫切需求。本研究针对随机森林（Random Forest, RF）机器学习模型，通过四种先进的优化算法进行精细调参：批量贝叶斯优化（Batch Bayesian Optimization, BBO）、自适应差分进化（Self-Adaptive Differential Evolution, SADE）、贝叶斯概率提升（Bayesian Probability Improvement, BPI）以及高斯过程优化（Gaussian Processes Optimization, GPO）。该模型基于包含164组实验样本的数据集，纳入压力、PEG摩尔质量与温度等核心输入参数，以预测CO₂的溶解度。为防止模型过拟合，模型训练全程采用K折交叉验证。通过计算运行时长与性能指标对各优化方法的有效性进行评估，性能指标包括决定系数（R-squared, R²）、均方误差（mean squared error, MSE）以及平均绝对相对误差（average absolute relative error, AARE%）。相关性分析显示，压力与CO₂溶解度呈中等程度正相关（相关系数为0.58），而PEG摩尔质量与温度的相关性则较弱（分别为0.2与0.05）。在所有优化技术中，RF-BPI表现最优，具备更优异的预测性能。结果表明，RF-BPI在训练集上的R²可达0.9625，测试集上为0.9307，优于其他所有方法。为进行基准对比，本研究同时测试了传统多元线性回归（multiple linear regression, LR）模型，其精度显著偏低（测试集上的R²明显低于RF-BPI的0.9307）。在计算效率方面，BPI的运行时长最短（63.9秒），而SADE的效率最低，耗时达2370.2秒。敏感性分析进一步明确了各输入变量对CO₂溶解度的相对影响，证实了数据驱动方法在复杂系统建模中的有效性。本研究构建的模型可作为极具前景的预测工具，在无需开展通常耗时费力、成本高昂的物理测量的前提下，实现PEG介质中CO₂溶解度的精准预测。