Explainable machine learning for statistical prediction of polymer fiber properties using process parameters

Abstract

The modeling and optimization of electrospinning parameters are essential for controlling the fiber diameter and material properties. This study uses machine learning to examine the effects of multiple electrospinning parameters on fiber diameter. Ten regression models were evaluated, with hyperparameter optimization performed using grid search cross-validation and Bayesian optimization with multiple fold configurations. The Random Forest model demonstrated superior performance (root mean square error = 129.308, coefficient of determination = 0.542, mean absolute error = 104.014, mean absolute percentage error = 0.371). Further improvement was achieved through Bayesian optimization (root mean square error = 127.400, coefficient of determination = 0.555, mean absolute percentage error = 0.360). Extreme Gradient Boosting and Gradient Boosting also showed high accuracy, while linear models performed poorly. The Shapley Additive Explanations analysis identified rotational speed as the most influential parameter (value = 0.473), followed by flow rate (0.36), porosity (0.32) and needle diameter (0.27), all positively affecting fiber diameter. In contrast, voltage (-0.24), temperature (-0.19), towing (-0.14), and humidity (-0.13) showed negative impacts. Experimentally, Polycaprolactone (Molecular number = 80,000) nanofibers were manufactured at three rotation speeds (150, 450 and 750 revolutions per minute), resulting in fiber diameters of 100.09, 154.0, and 175.45 nanometers, respectively. These findings reveal complex interactions between the electrospinning parameters and the fiber morphology, demonstrating the potential of machine learning to optimize nanofiber production.

Keywords

• Electrospinning
• explainable machine learning
• machine learning
• polycaprolactone
• prediction
• shap

References

1. [1] J. A Ilemobayo, O. Durodola, O. Alade, O. J Awotunde, A. T Olanrewaju, O. Falana, A. Ogungbire, A. Osinuga, D. Ogunbiyi, A. Ifeanyi, I. E Odezuligbo and O. E Edu, Hyperparameter tuning in machine learning: a comprehensive review, Journal of Engineering Research and Reports 26 (6), 388-395, 2024.
2. [2] A. Al-Abduljabbar and I. Farooq, Electrospun polymer nanofibers: processing, properties, and applications, Polymers 15 (1), 2023.
3. [3] N. Alharbi, A. Daraei, H. Lee and M. Guthold, The effect of molecular weight and fiber diameter on the mechanical properties of single, electrospun pcl nanofibers, Materials Today Communications 35, 105773, 2023.
4. [4] E. Archer, M. Torretti and S. Madbouly, Biodegradable polycaprolactone (pcl) based polymer and composites, Physical Sciences Reviews 8 (11), 4391-4414, 2023.
5. [5] Z. Asvar, E. Mirzaei, N. Azarpira, B. Geramizadeh and M. Fadaie, Evaluation of electrospinning parameters on the tensile strength and suture retention strength of polycaprolactone nanofibrous scaffolds through surface response methodology, J Mech Behav Biomed Mater 75, 369-378, 2017.
6. [6] M. Bartnikowski, T.R. Dargaville, S. Ivanovski and D.W. Hutmacher, Degradation mechanisms of polycaprolactone in the context of chemistry, geometry and environment, Progress in Polymer Science 96, 1-20, 2019.
7. [7] D.M. Belete and M.D. Huchaiah, Grid search in hyperparameter optimization of machine learning models for prediction of hiv/aids test results, International Journal of Computers and Applications 44 (9), 875-886, 2022.
8. [8] O.O. Bifarin, Interpretable machine learning with tree-based shapley additive explanations: application to metabolomics datasets for binary classification, PLoS One 18 (5), e0284315, 2023.

9. [9] N.D. Bikiaris, I. Koumentakou, G. Michailidou, M. Kostoglou, M. Vlachou, P. Barmpalexis, E. Karavas and G.Z. Papageorgiou, Investigation of molecular weight, polymer concentration and process parameters factors on the sustained release of the antimultiple- sclerosis agent teriflunomide from poly("-caprolactone) electrospun nanofibrous matrices, Pharmaceutics 14 (8), 2022.
10. [10] B. Bischl, M. Binder, M. Lang, T. Pielok, J. Richter, S. Coors, J. Thomas, T. Ullmann, M. Becker, A. Boulesteix, D. Deng and M. Lindauer, Hyperparameter optimization: foundations, algorithms, best practices, and open challenges, WIREs Data Mining and Knowledge Discovery 13 (2), e1484, 2023.
11. [11] J. Boelrijk, B. Pirok, B. Ensing and P. Forre, Bayesian optimization of comprehensive two-dimensional liquid chromatography separations, J Chromatogr A 1659, 462628, 2021.
12. [12] A. Botchkarev, A new typology design of performance metrics to measure errors in machine learning regression algorithms, Interdisciplinary Journal of Information, Knowledge, and Management 14, 045076, 2019.
13. [13] M. Chen, H. Michaud and S. Bhowmick, Controlled vacuum seeding as a means of generating uniform cellular distribution in electrospun polycaprolactone (pcl) scaffolds, J Biomech Eng 131 (7), 074521, 2009.
14. [14] Z. Chen, Z. Zhang, Y. Ouyang, Y. Chen, X. Yin, Y. Liu, H. Ying and W. Yang, Electrospinning polycaprolactone/collagen fiber coatings for enhancing the corrosion resistance and biocompatibility of az31 mg alloys, Colloids and Surfaces A Physicochemical and Engineering Aspects 662, 2023.
15. [15] D. Chicco, M.J. Warrens and G. Jurman, The coefficient of determination r-squared is more informative than smape, mae, mape, mse and rmse in regression analysis evaluation, PeerJ Computer Science 7, e623, 2021.
16. [16] F. Croisier, A.S. Duwez, C. Jerome, A.F. Leonard, K.O. van der Werf, P.J. Dijkstra and M.L. Bennink, Mechanical testing of electrospun pcl fibers, Acta Biomater 8 (1), 218-24, 2012.
17. [17] J.R. Dias, A. Sousa, A. Augusto, P.J. Bartolo and P.L. Granja, Electrospun polycaprolactone (pcl) degradation: an in vitro and in vivo study, Polymers 14 (16), 2022.
18. [18] M.D. Edwards, G.R. Mitchell, S.D. Mohan and R.H. Olley, Development of orientation during electrospinning of fibres of poly($\varepsilon$-caprolactone), European Polymer Journal 46 (6), 1175-1183, 2010.
19. [19] S.J. Eichhorn and W.W. Sampson, Statistical geometry of pores and statistics of porous nanofibrous assemblies, Journal of the royal society Interface 2 (4), 309-318, 2005.
20. [20] B. Esteki, M. Masoomi, M. Moosazadeh and C. Yoo, Data-driven prediction of janus/coreshell morphology in polymer particles: a machine-learning approach, Langmuir 39 (14), 4943-4958, 2023.
21. [21] A.H. Etefagh and M.R. Razfar, Bayesian optimization of 3d bioprinted polycaprolactone/ magnesium oxide nanocomposite scaffold using a machine learning technique, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 238 (10), 1448-1462, 2024.
22. [22] Y. Fan, X. Miao, C. Hou, J. Wang, J. Lin and F. Bian, High tensile performance of pla fiber-reinforced pcl composite via a synergistic process of strain and crystallization, Polymer 270, 125778, 2023.
23. [23] P. Francavilla, D.P. Ferreira, J.C. Araujo and R. Fangueiro, Smart fibrous structures produced by electrospinning using the combined effect of pcl/graphene nanoplatelets, Applied Sciences 11 (3), 2021.
24. [24] Z. Fu, D. Li, J. Cui, H. Xu, C. Yuan, P. Wang, B. Zhao and K. Lin, Promoting bone regeneration via bioactive calcium silicate nanowires reinforced poly ($\varepsilon$-caprolactone) electrospun fibrous membranes, Materials & Design 226, 111671, 2023.
25. [25] K. Fujihara, M. Kotaki and S. Ramakrishna, Guided bone regeneration membrane made of polycaprolactone/calcium carbonate composite nano-fibers, Biomaterials 26 (19), 4139-47, 2005.
26. [26] S. Gautam, S.D. Purohit, H. Singh, A. Dinda, D.P. Potdar, C. Sharma, C. Chou and N. Mishra, Surface modification of pcl-gelatin-chitosan electrospun scaffold by nano-hydroxyapatite for bone tissue engineering, Materials Today Communications 34, 105237, 2022.
27. [27] D. Gupta, J. Venugopal, M.P. Prabhakaran, V.R. Dev, S. Low, A.T. Choon and S. Ramakrishna, Aligned and random nanofibrous substrate for the in vitro culture of schwann cells for neural tissue engineering, Acta Biomater 5 (7), 2560-9, 2009.
28. [28] O. Ishii, M. Shin, T. Sueda and J.P. Vacanti, In vitro tissue engineering of a cardiac graft using a degradable scaffold with an extracellular matrix-like topography, The Journal of Thoracic and Cardiovascular Surgery 130 (5), 1358-1363, 2005.
29. [29] B. Joseph, A.J. John, J. Glamolija, D. Stojkovi, M. Sokovi, S. Lazovi, J. Kochupurackal, N. Kalarikkal and S. Thomas, Processing and evaluation of the structureproperties of electrospun pcl/ zirconium nanoparticle scaffolds, Materials Today Communications 34, 104961, 2023.
30. [30] C. Kaliaperumal and A. Thulasisingh, Electrospun polycaprolactone/chitosan/pectin composite nanofibre: a novel wound dressing scaffold, Bulletin of Materials Science 46 (1), 23, 2023.
31. [31] L. Kalluri, M. Satpathy and Y. Duan, Effect of electrospinning parameters on the fiber diameter and morphology of plga nanofibers, Dent Oral Biol Craniofacial Res 4 (2), 2021.
32. [32] F. Kashani-Asadi-Jafari, A. Parhizgar and A. Hadjizadeh, Magnetic-field-assisted emulsion electrospinning system: designing, assembly, and testing for the production of pcl/gelatin coreshell nanofibers, Fibers and Polymers 24, 515-523, 2023.
33. [33] K.A.G. Katsogiannis, G.T. Vladisavljevi and S. Georgiadou, Porous electrospun polycaprolactone fibers: effect of process parameters, Journal of Polymer Science Part B: Polymer Physics 54 (18), 1878-1888, 2016.
34. [34] J.W. Kim, S. Park, K. Park and B. Kim, Non-toxic natural additives to improve the electrical conductivity and viscosity of polycaprolactone for melt electrospinning, Applied Sciences 13 (3), 2023.
35. [35] J. Ko, S. Jun, J. Lee, P. Lee and M. Jun, Effects of molecular weight and temperature on fiber diameter of poly($\varepsilon$-caprolactone) melt electrospun fiber, Journal of the Korean Society of Manufacturing Technology Engineers 24, 160-165, 2015.
36. [36] J. Lévesque, C. Gagné and R. Sabourin, Bayesian hyperparameter optimization for ensemble learning, Proceedings Of The Thirty-second Conference On Uncertainty In Artificial Intelligence, 437446, Arlington, Virginia, USA, 2016.
37. [37] W.J. Li, K.G. Danielson, P.G. Alexander and R.S. Tuan, Biological response of chondrocytes cultured in three-dimensional nanofibrous poly("-caprolactone) scaffolds, J Biomed Mater Res A 67 (4), 1105-14, 2003.
38. [38] M. Li, H. Sun, Y. Huang and H. Chen, Shapley value: from cooperative game to explainable artificial intelligence, Autonomous Intelligent Systems 4 (1), 2, 2024.
39. [39] W.J. Li, R. Tuli, C. Okafor, A. Derfoul, K.G. Danielson, D.J. Hall and R.S. Tuan, A three-dimensional nanofibrous scaffold for cartilage tissue engineering using human mesenchymal stem cells, Biomaterials 26 (6), 599-609, 2005.
40. [40] W.J. Li, R. Tuli, X. Huang, P. Laquerriere and R.S. Tuan, Multilineage differentiation of human mesenchymal stem cells in a three-dimensional nanofibrous scaffold, Biomaterials 26 (25), 5158-66, 2005.
41. [41] Q. Liang, A.E. Gongora, Z. Ren, A. Tiihonen, Z. Liu, S. Sun, J.R. Deneault, D. Bash, F. Mekki-Berrada, S.A. Khan, K. Hippalgaonkar, B. Maruyama, K.A. Brown, J. Fisher Iii and T. Buonassisi, Benchmarking the performance of bayesian optimization across multiple experimental materials science domains, npj Computational Materials 7 (1), 188, 2021.
42. [42] F.J. Lopez-Flores, J.A. Ornelas-Guillen, A. Perez-Nava, J.B. Gonzalez-Campos and J.M. Ponce-Ortega, Data-driven machine learning approach for modeling the production and predicting the characteristics of aligned electrospun nanofibers, Industrial & Engineering Chemistry Research 63 (22), 9904-9913, 2024.
43. [43] S.M. Lundberg, G. Erion, H. Chen, A. DeGrave, J.M. Prutkin, B. Nair, R. Katz, J. Himmelfarb, N. Bansal and S.I. Lee, From local explanations to global understanding with explainable ai for trees, Nat Mach Intell 2 (1), 56-67, 2020.
44. [44] M. Ma, H. Zhou, S. Gao, N. Li, W. Guo and Z. Dai, Analysis and prediction of electrospun nanofiber diameter based on artificial neural network, Polymers 15 (13), 2023.
45. [45] E. Malikmammadov, T.E. Tanir, A. Kiziltay, V. Hasirci and N. Hasirci, Pcl and pcl-based materials in biomedical applications, J Biomater Sci Polym Ed 29 (7-9), 863-893, 2018.
46. [46] T.B. Martin and D.J. Audus, Emerging trends in machine learning: a polymer perspective, ACS Polymers Au 3 (3), 239-258, 2023.
47. [47] A. Mishra, V.S. Jatti, E.M. Sefene and S. Paliwal, Explainable artificial intelligence (xai) and supervised machine learning-based algorithms for prediction of surface roughness of additively manufactured polylactic acid (pla) specimens, Applied Mechanics 4 (2), 668-698, 2023.
48. [48] R. Mitchell, E. Frank and G. Holmes, Gputreeshap: massively parallel exact calculation of shap scores for tree ensembles, PeerJ Comput Sci 8, e880, 2022.
49. [49] M. Nemeth, D. Borkin and G. Michalconok, The Comparison Of Machine-learning Methods Xgboost And Lightgbm To Predict Energy Development, 208-215, 2019.
50. [50] R.M. Nezarati, M.B. Eifert and E. Cosgriff-Hernandez, Effects of humidity and solution viscosity on electrospun fiber morphology, Tissue Eng Part C Methods 19 (10), 810-9, 2013.
51. [51] D.R. Nisbet, A.E. Rodda, M.K. Horne, J.S. Forsythe and D.I. Finkelstein, Neurite infiltration and cellular response to electrospun polycaprolactone scaffolds implanted into the brain, Biomaterials 30 (27), 4573-80, 2009.
52. [52] C. Nnaji and U. Nwodo, Predicting customer churn in the telecommunication industry using machine learning algorithms: performance comparison with logistic regression, random forest, and gradient boosting techniques., Machine Learning 22, 3-66, 2022.
53. [53] N. Obregon, V. Agubra, M. Pokhrel, H. Campos, D. Flores, D. De la Garza, Y. Mao, J. Macossay and M. Alcoutlabi, Effect of polymer concentration, rotational speed, and solvent mixture on fiber formation using forcespinningo, Fibers 4 (2), 2016.
54. [54] E. Pektok, B. Nottelet, J. Tille, R. Gurny, A. Kalangos, M. Moeller and B.H.Walpoth, Degradation and healing characteristics of small-diameter poly($\varepsilon$-caprolactone) vascular grafts in the rat systemic arterial circulation, Circulation 118 (24), 2563-2570, 2008.
55. [55] M.N. Pervez, W.S. Yeo, M.M.R. Mishu, M.E. Talukder, H. Roy, M.S. Islam, Y. Zhao, Y. Cai, G.K. Stylios and V. Naddeo, Electrospun nanofiber membrane diameter prediction using a combined response surface methodology and machine learning approach, Scientific Reports 13 (1), 9679, 2023.
56. [56] Q.P. Pham, U. Sharma and A.G. Mikos, Electrospun poly($\varepsilon$-caprolactone) microfiber and multilayer nanofiber/microfiber scaffolds: characterization of scaffolds and measurement of cellular infiltration, Biomacromolecules 7 (10), 2796-805, 2006.
57. [57] M.P. Prabhakaran, J. Venugopal, C.K. Chan and S. Ramakrishna, Surface modified electrospun nanofibrous scaffolds for nerve tissue engineering, Nanotechnology 19 (45), 455102, 2008.
58. [58] M. R and R. Rohini, Lasso: a feature selection technique in predictive modeling for machine learning, 18-20, 2016.
59. [59] O. Rainio, J. Teuho and R. Klen, Evaluation metrics and statistical tests for machine learning, Scientific Reports 14 (1), 6086, 2024.
60. [60] S. Ramazani and M. Karimi, Investigating the influence of temperature on electrospinning of polycaprolactone solutions, e-Polymers 14 (5), 323-333, 2014.
61. [61] R. Rodriguez-Perez and J. Bajorath, Interpretation of machine learning models using shapley values: application to compound potency and multi-target activity predictions, J Comput Aided Mol Des 34 (10), 1013-1026, 2020.
62. [62] K. Safjan, Explaining ai - the key differences between lime and shap methods, Krystian’s Safjan Blog, 2023.
63. [63] V. Salaris, A. Leones, D. Lopez, J.M. Kenny and L. Peponi, A comparative study on the addition of mgo and mg(oh)2 nanoparticles into pcl electrospun fibers, Macromolecular Chemistry and Physics 224 (1), 2200215, 2023.
64. [64] A.M. Salih, Z. Raisi-Estabragh, I.B. Galazzo, P. Radeva, S.E. Petersen, K. Lekadir and G. Menegaz, A perspective on explainable artificial intelligence methods: shap and lime, Advanced Intelligent Systems 7 (1), 2400304, 2025.
65. [65] S. Sarma, A.K. Verma, S.S. Phadkule and M. Saharia, Towards an interpretable machine learning model for electrospun polyvinylidene fluoride (pvdf) fiber properties, Computational Materials Science 213, 111661, 2022.
66. [66] R. Scaffaro, M. Gammino and A. Maio, Wet electrospinning-aided self-assembly of multifunctional go-cnt@pcl core-shell nanocomposites with spider leg bioinspired hierarchical architectures, Composites Science and Technology 221, 109363, 2022.
67. [67] R. Schofield, B. Maciejewska, S. Dong, G. Tebbutt, D. McGurty, R. Bonilla, H. Assender and N. Grobert, Driving fiber diameters to the limit: nanoparticle-induced diameter reductions in electrospun photoactive composite nanofibers for organic photovoltaics, Advanced Composites and Hybrid Materials 6, 2023.
68. [68] M. Shie Karizmeh, S.A. Poursamar, A. Kefayat, Z. Farahbakhsh and M. Rafienia, An in vitro and in vivo study of pcl/chitosan electrospun mat on polyurethane/propolis foam as a bilayer wound dressing, Mater Sci Eng C Mater Biol Appl 135, 112667, 2022.
69. [69] G. Simsek Gunduz, Investigation of the effect of needle diameter and the solution flow rate on fiber morphology in the electrospinning method, Fibres & Textiles in Eastern Europe 31, 2023.
70. [70] M. Sivan, D. Madheswaran, J. Valtera, E.K. Kostakova and D. Lukas, Alternating current electrospinning: the impacts of various high-voltage signal shapes and frequencies on the spinnability and productivity of polycaprolactone nanofibers, Materials & Design 213, 110308, 2022.
71. [71] T. Subbiah, G.S. Bhat, R.W. Tock, S. Parameswaran and S.S. Ramkumar, Electrospinning of nanofibers, Journal of Applied Polymer Science 96 (2), 557-569, 2005.
72. [72] B. Subeshan, A. Atayo and E. Asmatulu, Machine learning applications for electrospun nanofibers: a review, Journal of Materials Science 59 (31), 14095-14140, 2024.
73. [73] S. Sukpancharoen, T. Wijakmatee, T. Katongtung, K. Ponhan, N. Rattanachoung and S. Khojitmate, Data-driven prediction of electrospun nanofiber diameter using machine learning: a comprehensive study and web-based tool development, Results in Engineering 24, 102826, 2024.
74. [74] R.S. Tigli, N.M. Kazaroglu, B. Mavis and M. Gumusderelioglu, Cellular behavior on epidermal growth factor (egf)-immobilized pcl/gelatin nanofibrous scaffolds, J Biomater Sci Polym Ed 22 (1-3), 207-23, 2011.
75. [75] A.D. Tsareva, V.S. Shtol, D.V. Klinov and D.A. Ivanov, Electrospinning for biomedical applications: an overview of material fabrication techniques, Surfaces 8 (1), 2025.
76. [76] J. Ukwaththa, S. Herath and D. Meddage, A review of machine learning (ml) and explainable artificial intelligence (xai) methods in additive manufacturing (3d printing), Materials Today Communications 41, 110294, 2024.
77. [77] J. Venugopal, L.L. Ma, T. Yong and S. Ramakrishna, In vitro study of smooth muscle cells on polycaprolactone and collagen nanofibrous matrices, Cell Biol Int 29 (10), 861-7, 2005.
78. [78] J. Venugopal, Y.Z. Zhang and S. Ramakrishna, Fabrication of modified and functionalized polycaprolactone nanofibre scaffolds for vascular tissue engineering, Nanotechnology 16 (10), 2138-42, 2005.
79. [79] S. Vinay, Standardization in machine learning, 2021.
80. [80] E. Vivas, H. Allende-Cid and R. Salas, A systematic review of statistical and machine learning methods for electrical power forecasting with reported mape score, Entropy 22 (12), 1412, 2020.
81. [81] C.Wan and B. Chen, Poly($\varepsilon$-caprolactone)/graphene oxide biocomposites: mechanical properties and bioactivity, Biomed Mater 6 (5), 055010, 2011.
82. [82] C. Wongoutong, The impact of neglecting feature scaling in k-means clustering, PLoS One 19 (12), e0310839, 2024.
83. [83] Y. Xie, Q. Fang, H. Zhao, Y. Li, Z. Lin and J. Chen, Effects of six processing parameters on the size of pcl fibers prepared by melt electrospinning writing, Micromachines 14 (7), 2023.
84. [84] S. Xie and R.T. Ogden, Functional support vector machine, Biostatistics 25 (4), 1178- 1194, 2024.
85. [85] S. Yadav and S. Shukla, Analysis of k-fold cross-validation over hold-out validation on colossal datasets for quality classification, 2016 Ieee 6th International Conference On Advanced Computing (iacc), 78-83, 2016.
86. [86] J. Yang, Fast treeshap: accelerating shap value computation for trees, 2022.
87. [87] H. Yildirim and M.. Ozkale, The performance of elm based ridge regression via the regularization parameters, Expert Systems with Applications 134, 225-233, 2019.
88. [88] H. Yoshimoto, Y.M. Shin, H. Terai and J.P. Vacanti, A biodegradable nanofiber scaffold by electrospinning and its potential for bone tissue engineering, Biomaterials 24 (12), 2077-82, 2003.
89. [89] H. Yu, J. Jang, T. Kim, H. Lee and H. Kim, Apatite-mineralized polycaprolactone nanofibrous web as a bone tissue regeneration substrate, Journal of Biomedical Materials Research Part A 88A (3), 747-754, 2009.
90. [90] Z. Zhang, Introduction to machine learning: k-nearest neighbors, Ann Transl Med 4 (11), 218, 2016.
91. [91] H. Zou and T. Hastie, Regularization and variable selection via the elastic net, Journal of the Royal Statistical Society Series B: Statistical Methodology 67 (2), 301-320, 2005.