Data-driven optimization of biaxial shrinkage and stability in electrospun membranes via machine learning and Monte Carlo simulation

Abstract

Controlling shrinkage behavior in electrospun membranes is critical for applications that require precise dimensional or mechanical performance. However, experimental variability and limited datasets often hinder the development of robust process models. This study introduces a data-driven framework that combines machine learning with Monte Carlo simulation to enable both accurate and stable shrinkage control in electrospinning using a small experimental dataset. Multiple regression models were trained to predict biaxial shrinkage ratios and their variability, with support vector regression and extreme gradient boosting showing the best performance for accuracy and stability prediction, respectively. Feature importance analysis revealed applied voltage and thermoplastic polyurethane concentration as the dominant parameters. A Monte Carlo-based optimization strategy was employed to identify process parameter sets that achieve target shrinkage ratios while minimizing output variability. The proposed approach enables multi-objective optimization in low-data, high-variability manufacturing environments, offering practical insights into precision fabrication of stimulus-responsive membranes.

Keywords

Electrospinning / Shrinkage stability / Machine learning / Monte Carlo simulation / Process parameter optimization

Acknowledgments

None.

Funding

This work was funded by the National Natural Science Foundation of China (grant no.: 52031005, 52571227), Natural Science Foundation of Shanghai (grant no.: 24ZR1438200), Shanghai Academy of Spaceflight Technology Joint Research Fund (grant no.: USCAST2023-19), Equipment Development Department Huiyan Action (grant no.: 5D3D1365), and China Scholarship Council (grant no.:202406230025).

Conflict of interest

The authors declare they have no competing interests.

Author contributions

Conceptualization: Wei Min Huang, Shiyu He

Formal analysis: Shiyu He, Li Cong Huang

Investigation: Shiyu He, Wei Min Huang, Fei Xiao

Methodology: Shiyu He, Chentong Gao, Runzhi Lu

Writing-original draft: Shiyu He, Wei Min Huang

Writing-review & editing: Shiyu He, Wei Min Huang, Fei Xiao

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Availability of data

Data are available from the corresponding author upon reasonable request.

References

[1] Cheng F, Song D, Li H, Ravi SK, Tan SC. Recent progress in biomedical scaffold fabricated via electrospinning: Design, fabrication and tissue engineering application. Adv Funct Mater. 2025; 35(1):2406950. doi: 10.1002/adfm.202406950

[2] Cho Y, Beak JW, Sagong M, Ahn S, Nam JS, Kim ID. Electrospinning and nanofiber technology: Fundamentals, innovations, and applications. Adv Mater. 2025; 37:2500162. doi: 10.1002/adma.202570190

[3] Wang C, Su Y, Xie J. Advances in electrospun nanofibers: Versatile materials and diverse biomedical applications. Acc Mater Res. 2024; 5(8):987-999. doi: 10.1021/accountsmr.4c00145

[4] Yadav S, Sharma A, Kurmi BD, et al. Nanofiber drug delivery systems: Recent advances in nanofabrication and their role in targeted therapy in cancer, neurodegenerative, and cardiovascular diseases. Polym Adv Technol. 2025; 36(5):e70198. doi: 10.1002/pat.70198

[5] Wang Z, Gao C, Yang R, Xiong F. The interface effect of electrospun fiber promotes wound healing. Macromol Rapid Commun. 2025:2500038. doi: 10.1002/marc.202500038

[6] Wang J, You C, Xu Y, Xie T, Wang Y. Research advances in electrospun nanofiber membranes for non-invasive medical applications. Micromachines. 2024; 15(10):1226. doi: 10.3390/mi15101226

[7] Wu H, Zheng Y, Zeng Y. Fabrication of helical nanofibers via co-electrospinning. Ind Eng Chem Res. 2015; 54(3):987-993. doi: 10.1021/ie504305s

[8] Zhao Y, Miao X, Lin J, et al. Coiled plant tendril bioinspired fabrication of helical porous microfibers for crude oil cleanup. Glob Challenges. 2017; 1(3):1600021. doi: 10.1002/gch2.201600021

[9] Wang M, Li W, Tang G, Garciamendez Mijares CE, Zhang YS. Engineering (bio) materials through shrinkage and expansion. Adv Healthc Mater. 2021; 10(14):2100380. doi: 10.1002/adhm.202100380

[10] Mandal A, Chatterjee K. 4D printing for biomedical applications. J Mater Chem B. 2024; 12(12):2985-3005. doi: 10.1039/D4TB00006D

[11] Fang F, Wang H, Wang H, et al. Stimulus-responsive shrinkage in electrospun membranes: Fundamentals and control. Micromachines. 2021; 12(8):920. doi: 10.3390/mi12080920

[12] Zaarour B, Liu W, Omran W, et al. A mini-review on wrinkled nanofibers: Preparation principles via electrospinning and potential applications. J Ind Text. 2024; 54:15280837241255396. doi: 10.1177/15280837241255396

[13] Wang CC, Zhao Y, Purnawali H, Huang WM, Sun L. Chemically induced morphing in polyurethane shape memory polymer micro fibers/springs. React Funct Polym. 2012; 72:757-764. doi: 10.1016/j.reactfunctpolym.2012.07.013

[14] Aadithiya D, Fang FY, Wang H, Huang WM. Stimulus-induced shrinkage in electrospun polymeric fibres: An investigation on thickness of prestretched shell and prestrain via finite element analysis. Fibers Polym. 2023; 24(2):525-536. doi: 10.1007/s12221-023-00133-8

[15] Ahmadi Bonakdar M, Rodrigue D. Electrospinning: Processes, structures, and materials. Macromol. 2024; 4(1):58-103. doi: 10.3390/macromol4010004

[16] El Ferik S, Adeniran AA. Modeling and identification of nonlinear systems: A review of the multimodel approach-Part 2. IEEE Trans Syst Man Cybern Syst. 2016; 47(7):1160-1168. doi: 10.1109/TSMC.2016.2560129

[17] Subeshan B, Atayo A, Asmatulu E. Machine learning applications for electrospun nanofibers: A review. J Mater Sci. 2024; 59(31):14095-14140. doi: 10.1007/s10853-024-09994-7

[18] Shastry T, Basdogan Y, Wang ZG, Kunmar SK, Carbone MR. Machine learning-based discovery of molecular descriptors that control polymer gas permeation. J Membr Sci. 2024; 697:122563. doi: 10.1016/j.memsci.2024.122563

[19] Ignacz G, Beke AK, Toth V, Szekely G. A hybrid modelling approach to compare chemical separation technologies in terms of energy consumption and carbon dioxide emissions. Nat Energy. 2025; 10(3):308-317. doi: 10.1038/s41560-024-01668-7

[20] Lee S, Shirts MR, Straub AP. Molecular fingerprint-aided prediction of organic solute rejection in reverse osmosis and nanofiltration. J Membr Sci. 2024; 705:122927. doi: 10.1016/j.memsci.2024.122927

[21] He S, Wang Y, Zhang Z, et al. Interpretable machine learning workflow for evaluation of the transformation temperatures of TiZrHfNiCoCu high entropy shape memory alloys. Mater Des. 2023; 225:111513. doi: 10.1016/j.matdes.2022.111513

[22] He SY, Xiao F, Hou RH, et al. Accelerated learning and co-optimization of elastocaloric effect and stress hysteresis of elastocaloric alloys. Rare Met. 2024; 43(12):6606-6624. doi: 10.1007/s12598-024-02827-1

[23] Rigatti SJ. Random forest. J Insur Med. 2017; 47(1):31-39. doi: 10.17849/insm-47-01-31-39.1

[24] Osman AIA, Ahmed AN, Chow MF, Huang YF, EI-Shafle A. Extreme gradient boosting (Xgboost) model to predict the groundwater levels in Selangor Malaysia. Ain Shams Eng J. 2021; 12(2):1545-1556. doi: 10.1016/j.asej.2020.11.011

[25] Zou J, Han Y, So SS. Overview of artificial neural networks. In: Artificial Neural Networks: Methods and Applications. Springer; 2009. doi: 10.1007/978-1-60327-101-1_2

[26] Su X, Yan X, Tsai CL. Linear regression. Wiley Interdiscip Rev Comput Stat. 2012; 4(3):275-294. doi: 10.1002/wics.1198

[27] Mosca E, Szigeti F, Tragianni S, Gallagher D, Groh G. SHAP-based explanation methods: A review for NLP interpretability. In: Proceedings of the 29th International Conference on Computational Linguistics; 2022. doi: 2022.coling-1.406

[28] Antwarg L, Miller R M, Shapira B, Rokach L. Explaining anomalies detected by autoencoders using Shapley Additive Explanations. Expert Syst Appl. 2021; 186:115736. doi: 10.1016/j.eswa.2021.115736

[29] Van den Broeck G, Lykov A, Schleich M, Suciu D. On the tractability of SHAP explanations. J Artif Intell Res. 2022; 74:851-886. doi: 10.1613/jair.1.13283

[30] Li Z. Extracting spatial effects from machine learning model using local interpretation method: An example of SHAP and XGBoost. Comput Environ Urban Syst. 2022; 96:101845. doi: 10.1016/j.compenvurbsys.2022.101845

[31] Zhang J, Ma X, Zhang J, et al. Insights into geospatial heterogeneity of landslide susceptibility based on the SHAP XGBoost model. J Environ Manag. 2023; 332:117357. doi: 10.1016/j.jenvman.2023.117357

[32] Wang H, Liang Q, Hancock JT, Khoshgoftaar TM. Feature selection strategies: A comparative analysis of SHAP value and importance based methods. J Big Data. 2024; 11(1):44. doi: 10.1186/s40537-024-00905-w

[33] Harrison RL.Introduction to monte carlo simulation. AIP Conf Proc. 2010; 1204:17. doi: 10.1063/1.3295638

[34] Metropolis N, Ulam S.The monte carlo method. J Am Stat Assoc. 1949; 44(247):335-341. doi: 10.2307/2280232

[35] Raychaudhuri S. Introduction to monte carlo simulation. In: Proceedings of the 2008 Winter Simulation Conference; 2008. doi: 10.1109/WSC.2008.4736059

[36] Kroese DP, Rubinstein RY.Monte carlo methods. Wiley Interdiscip Rev Comput Stat. 2012; 4(1):48-58. doi: 10.3390/nano15020117

[37] Kroese DP, Brereton T, Taimre T, et al. Why the Monte Carlo method is so important today. Wiley Interdiscip Rev Comput Stat. 2014; 6(6):386-392. doi: 10.1002/wics.1314

[38] Gao H, He W, Zhao YB, Opris DM, Xu G, Wang J. Electret mechanisms and kinetics of electrospun nanofiber membranes and lifetime in filtration applications in comparison with corona charged membranes. J Membr Sci. 2020; 600:117879. doi: 10.1016/j.memsci.2020.117879

[39] Tong HW, Wang M. Electrospinning of fibrous polymer scaffolds using positive voltage or negative voltage: A comparative study. Biomed Mater. 2010; 5(5):054110. doi: 10.1088/1748-6041/5/5/054110

[40] Liao Y, Wang R, Tian M, Qiu C, Fane AG. Fabrication of polyvinylidene fluoride (PVDF) nanofiber membranes by electro spinning for direct contact membrane distillation. J Membr Sci. 2013; 425:30-39. doi: 10.1016/j.memsci.2012.09.023

[41] Mi HY, Jing X, Jacques BR, Turng LS, Peng XF. Characterization and properties of electrospun thermoplastic polyurethane blend fibers: Effect of solution rheological properties on fiber formation. J Mater Res. 2013; 28(17):2339-2350. doi: 10.1016/j.memsci.2012.09.023

[42] Lem KW, Haw JR, Curran S, et al. Effect of hard segment molecular weight on dilute solution properties of ether based thermoplastic polyurethanes. Spectroscopy. 2013; 1:11-18. doi: 10.13189/nn.2013.01030

[43] Awad M, Khanna R.Support vector regression. In: Efficient Learning Machines: Theories, Concepts, and Applications for Engineers and System Designers. Springer; 2015. doi: 10.1007/978-1-4302-5990-9