ISSN print edition: 0366-6352 ISSN electronic edition: 1336-9075 Registr. No.: MK SR 9/7 Published monthly

Development of hybrid smart models to accurately model nano-polyethylene glycol composite viscosity

Tianxiang Li, Ayat Hussein Adhab, Vicky Jain, Anupam Yadav, R. Roopashree, Aditya Kashyap, Suman Saini, Pushpa Negi Bhakuni, Shaxnoza Saydaxmetova, Morug Salih Mahdi, Aseel Salah Mansoor, Usama Kadem Radi, Nasr Saadoun Abd, and Hojjat Abbasi

School of Information Engineering, Chengdu Industry and Trade College, Chengdu, China

E-mail: litx2006@163.com

Received: 19 December 2024  Accepted: 14 October 2025

Abstract:

The viscosity of nano-polyethylene glycol (PEG) composites, shaped by molecular and environmental factors, is critical for optimizing their performance in various industrial applications, demanding precise predictive models. This research develops a refined Gradient Boosting Decision Tree (GBDT) model, enhanced through four sophisticated optimization techniques: Batch Bayesian Optimization (BBO), Evolution Strategies (ES), Bayesian Probability Improvement (BPI), and Gaussian Processes Optimization (GPO). The model utilizes a dataset of 229 experimental data points, with 90% allocated for training and 10% for testing, incorporating input parameters such as shear rate, temperature, nano concentration, PEG molecular weight, and nano type index to forecast the viscosity of nano-PEG composites. To mitigate overfitting, k-fold cross-validation is applied during the training phase. The efficacy of each optimization method is evaluated using execution time and performance metrics, including R-squared (R²), mean squared error (MSE), and average absolute relative error (AARE%). Correlation analysis indicates that temperature has the strongest influence on viscosity with a correlation coefficient of  −0.22, followed by shear rate and PEG molecular weight (both  −0.14), nano concentration ( −0.03), and nano type index ( −0.03). Among the optimization techniques, GBDT-BPI stands out as the most accurate, achieving an R² of 0.988202 for training and 0.985078 for the total dataset, with an AARE% of 8.851454 for the total dataset, while GBDT-GPO offers the fastest computation time at 235.72 s compared to BPI’s 373.58 s. Sensitivity analysis verifies that all input features contribute to the viscosity prediction, with SHAP analysis identifying shear rate as the most impactful parameter, followed by nano concentration, temperature, nano type index, and PEG molecular weight. These models provide robust tools for predicting nano-PEG composite viscosity, minimizing the need for costly and time-intensive experimental approaches.

Keywords: Machine learning modeling; Nano-polyethylene glycol composite viscosity; Predictive analytics; Gradient boosting decision tree; Optimization algorithms

Full paper is available at www.springerlink.com.

DOI: 10.1007/s11696-025-04512-8

Chemical Papers 80 (3) 2209–2227 (2026)