Enabling Ultrastable Microbubbles With Graphene Aerogel Enrichment and Machine Learning for Highly Efficient Carbon Storage

Mohammad Hossein Akhlaghi , Malek Naderi , Ali Pilehvar Meibody , Shurui Yang , Mojtaba Abdi-Jalebi

Electron ›› 2026, Vol. 4 ›› Issue (3) : e70048

PDF (6700KB)
Electron ›› 2026, Vol. 4 ›› Issue (3) :e70048 DOI: 10.1002/elt2.70048
RESEARCH ARTICLE
Enabling Ultrastable Microbubbles With Graphene Aerogel Enrichment and Machine Learning for Highly Efficient Carbon Storage
Author information +
History +
PDF (6700KB)

Abstract

Microbubbles (MBs) have garnered significant attention across various scientific disciplines, including medical imaging, drug delivery, materials science, and environmental engineering due to their unique properties and versatile utility. However, their inherent limitations regarding stability and pressure resilience have impeded their potential application in demanding conditions. Here, an innovative paradigm is presented for next-generation CO2-filled ultrastable microbubbles (UMBs) by incorporating hydrophobic graphene aerogel microparticles (HAG-MPs) into the aphron MB shells, resulting in MBs with exceptional resilience and longevity. The findings demonstrate that the reinforced UMBs, enhanced with 0.16 wt% HAG-MPs, display a significantly improved elastic response and mechanical stiffness so that these UMBs exhibit remarkable bubble survival rates of approximately 71% and exhibit an amazing 490% increase in cyclic pressure stability (about 6 times) under a high-pressurizing cycle up to 400 bar. This research serves as a catalyst for the creation of advanced UMB systems capable of revolutionizing diverse applications in carbon capture, storage, and utilization. Furthermore, a multi-output machine learning (ML) framework based on multi-target regressor stacking (MTRS) is developed to predict key UMB performance parameters, achieving prediction errors as low as 3% for half-life time, approximately 4% for shell thickness-to-diameter ratio, and 3% for cyclic pressure stability, representing up to an 82% reduction in prediction error compared to classical single-output ML methods.

Keywords

aerographene microparticle / colloidal aphron microbubble / high pressure cycle / machine learning / multi-output regression / robust shell / ultrastability

Cite this article

Download citation ▾
Mohammad Hossein Akhlaghi, Malek Naderi, Ali Pilehvar Meibody, Shurui Yang, Mojtaba Abdi-Jalebi. Enabling Ultrastable Microbubbles With Graphene Aerogel Enrichment and Machine Learning for Highly Efficient Carbon Storage. Electron, 2026, 4 (3) : e70048 DOI:10.1002/elt2.70048

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

J. R. Lindner, “Microbubbles in Medical Imaging: Current Applications and Future Directions,” Nature Reviews Drug Discovery 3, no. 6 (2004): 527–533, https://doi.org/10.1038/nrd1417.

[2]

J. Rodriguez-Rodriguez, A. Sevilla, C. Martinez-Bazan, and J. M. Gordillo, “Generation of Microbubbles With Applications to Industry and Medicine,” Annual Review of Fluid Mechanics 47, no. 1 (2015): 405–429, https://doi.org/10.1146/annurev-fluid-010814-014658.

[3]

S. Sirsi and M. Borden, “Microbubble Compositions, Properties and Biomedical Applications,” Bubble Science, Engineering and Technology 1, no. 1–2 (2009): 3–17, https://doi.org/10.1179/175889709x446507.

[4]

N. V. Lebedeva, S. N. Sanders, M. Ina, et al., “Multicore Expandable Microbubbles: Controlling Density and Expansion Temperature,” Polymer 90 (2016): 45–52, https://doi.org/10.1016/j.polymer.2016.02.050.

[5]

Y. Peng, R. P. Seekell, A. R. Cole, et al., “Interfacial Nanoprecipitation Toward Stable and Responsive Microbubbles and Their Use as a Resuscitative Fluid,” Angewandte Chemie 130, no. 5 (2018): 1285–1290, https://doi.org/10.1002/ange.201711839.

[6]

R. A. Barmin, A. Dasgupta, C. Bastard, et al., “Engineering the Acoustic Response and Drug Loading Capacity of PBCA-Based Polymeric Microbubbles With Surfactants,” Molecular Pharmaceutics 19, no. 9 (2022): 3256–3266, https://doi.org/10.1021/acs.molpharmaceut.2c00416.

[7]

M. A. Nakatsuka, M. J. Hsu, S. C. Esener, J. N. Cha, and A. P. Goodwin, “DNA-Coated Microbubbles With Biochemically Tunable Ultrasound Contrast Activity,” Advanced Materials 23, no. 42 (2011): 4908–4912, https://doi.org/10.1002/adma.201102677.

[8]

M. A. Nakatsuka, R. F. Mattrey, S. C. Esener, J. N. Cha, and A. P. Goodwin, “Aptamer-Crosslinked Microbubbles: Smart Contrast Agents for Thrombin-Activated Ultrasound Imaging,” Advanced Materials 24, no. 45 (2012): 6010–6016, https://doi.org/10.1002/adma.201201484.

[9]

A. Molaei and K. Waters, “Aphron Applications—A Review of Recent and Current Research,” Advances in Colloid and Interface Science 216 (2015): 36–54, https://doi.org/10.1016/j.cis.2014.12.001.

[10]

M. Zhang and P. Guiraud, “Surface-Modified Microbubbles (Colloidal Gas Aphrons) for Nanoparticle Removal in a Continuous Bubble Generation-Flotation Separation System,” Water Research 126 (2017): 399–410, https://doi.org/10.1016/j.watres.2017.09.051.

[11]

M. Zhang, B. Yu, T. Xu, D. Zhang, Z. Qiang, and X. Pan, “Insights Into Capture-Inactivation/Oxidation of Antibiotic Resistance Bacteria and Cell-Free Antibiotic Resistance Genes From Waters Using Flexibly-Functionalized Microbubbles,” Journal of Hazardous Materials 428 (2022): 128249, https://doi.org/10.1016/j.jhazmat.2022.128249.

[12]

M. Zhang, Y. Feng, D. Zhang, L. Dong, and X. Pan, “Ozone-Encapsulated Colloidal Gas Aphrons for in Situ and Targeting Remediation of Phenanthrene-Contaminated Sediment-Aquifer,” Water Research 160 (2019): 29–38, https://doi.org/10.1016/j.watres.2019.05.043.

[13]

P. Pal, S. W. Hasan, M. Abu Haija, M. Sillanpää, and F. Banat, “Colloidal Gas Aphrons for Biotechnology Applications: A Mini Review,” Critical Reviews in Biotechnology 43, no. 7 (2022): 1–11, https://doi.org/10.1080/07388551.2022.2092716.

[14]

K. Ward, A. Taylor, A. Mohammed, and D. C. Stuckey, “Current Applications of Colloidal Liquid Aphrons: Predispersed Solvent Extraction, Enzyme Immobilization and Drug Delivery,” Advances in Colloid and Interface Science 275 (2020): 102079, https://doi.org/10.1016/j.cis.2019.102079.

[15]

M. H. Akhlaghi and M. Naderi, Stabilized Colloidal aphron/graphene Derivatives Hybrid Fluids (Google Patents, 2022).

[16]

M. Dermiki, I. J. Garrard, and P. Jauregi, “Selective Separation of Dyes by Colloidal Gas Aphrons: Conventional Flotation vs Countercurrent Chromatography,” Separation and Purification Technology 279 (2021): 119770, https://doi.org/10.1016/j.seppur.2021.119770.

[17]

P. Pal, A. G. Corpuz, S. W. Hasan, M. Sillanpää, and F. Banat, “Simultaneous Removal of Single and Mixed Cationic/Anionic Dyes From Aqueous Solutions Using Flotation by Colloidal Gas Aphrons,” Separation and Purification Technology 255 (2021): 117684, https://doi.org/10.1016/j.seppur.2020.117684.

[18]

M. Priyanka and M. Saravanakumar, “A Sustainable Approach for Removal of Microplastics From Water Matrix Using Colloidal Gas Aphrons: New Insights on Flotation Potential and Interfacial Mechanism,” Journal of Cleaner Production 334 (2022): 130198, https://doi.org/10.1016/j.jclepro.2021.130198.

[19]

S. Banifatemi, H. Mohammadifard, and M. Amiri, “A Novel Method to Synthesize Copper Oxide Nanoparticles by Using Colloidal Gas Aphrons,” Colloids and Surfaces A: Physicochemical and Engineering Aspects 497 (2016): 35–40, https://doi.org/10.1016/j.colsurfa.2016.02.025.

[20]

H. Ghaedamini and M. Amiri, “Effects of Temperature and Surfactant Concentration on the Structure and Morphology of Calcium Carbonate Nanoparticles Synthesized in a Colloidal Gas Aphrons System,” Journal of Molecular Liquids 282 (2019): 213–220, https://doi.org/10.1016/j.molliq.2019.02.119.

[21]

T. Buapuean and S. Jarudilokkul, “Synthesis of Mesoporous TiO2 With Colloidal Gas Aphrons, Colloidal Liquid Aphrons, and Colloidal Emulsion Aphrons for Dye-Sensitized Solar Cells,” Materials Today Chemistry 16 (2020): 100235, https://doi.org/10.1016/j.mtchem.2019.100235.

[22]

L. S. Spinelli, G. R. Neto, L. F. Freire, et al., “Synthetic-Based Aphrons: Correlation Between Properties and Filtrate Reduction Performance,” Colloids and Surfaces A: Physicochemical and Engineering Aspects 353, no. 1 (2010): 57–63, https://doi.org/10.1016/j.colsurfa.2009.10.017.

[23]

B. Keshavarzi, A. Javadi, A. Bahramian, and R. Miller, “Formation and Stability of Colloidal Gas Aphron Based Drilling Fluid Considering Dynamic Surface Properties,” Journal of Petroleum Science and Engineering 174 (2019): 468–475, https://doi.org/10.1016/j.petrol.2018.11.057.

[24]

W. Zhu, X. Zheng, and G. Li, “Micro-Bubbles Size, Rheological and Filtration Characteristics of Colloidal Gas Aphron (CGA) Drilling Fluids for High Temperature Well: Role of Attapulgite,” Journal of Petroleum Science and Engineering 186 (2020): 106683, https://doi.org/10.1016/j.petrol.2019.106683.

[25]

W. Zhu, X. Zheng, J. Shi, and Y. Wang, “A High-Temperature Resistant Colloid Gas Aphron Drilling Fluid System Prepared by Using a Novel Graft Copolymer Xanthan Gum-AA/AM/AMPS,” Journal of Petroleum Science and Engineering 205 (2021): 108821, https://doi.org/10.1016/j.petrol.2021.108821.

[26]

M. H. Akhlaghi, M. Naderi, and M. Abdi-Jalebi, “Graphene-Loaded Aphron Microbubbles for Enhanced Drilling Fluid Performance and Carbon Capture and Storage,” ACS Applied Nano Materials 7, no. 22 (2024): 26187–26201, https://doi.org/10.1021/acsanm.4c05693.

[27]

X. Li, B. Peng, Q. Liu, J. Liu, and L. Shang, “Micro and Nanobubbles Technologies as a New Horizon for CO2-EOR and CO2 Geological Storage Techniques: A Review,” Fuel 341 (2023): 127661, https://doi.org/10.1016/j.fuel.2023.127661.

[28]

O. Zozulya and V. Pletneva, “Influence of Thermobaric Conditions on Size Distribution of Colloidal Gas Aphrons,” Colloids and Surfaces A: Physicochemical and Engineering Aspects 483 (2015): 232–238, https://doi.org/10.1016/j.colsurfa.2015.05.039.

[29]

A. Belkin, M. Irving, B. O’Connor, M. Fosdick, T. L. Hoff, and F. B. Growcock, “How Aphron Drilling Fluids Work,” in SPE Annual Technical Conference and Exhibition (OnePetro, 2005), https://doi.org/10.2523/96145-MS.

[30]

F. B. Growcock, A. Belkin, M. Fosdick, M. Irving, B. O’Connor, and T. Brookey, “Recent Advances in Aphron Drilling-Fluid Technology,” SPE Drilling and Completion 22, no. 2 (2007): 74–80, https://doi.org/10.2118/97982-pa.

[31]

M. Pasdar, E. Kazemzadeh, E. Kamari, M. H. Ghazanfari, and M. Soleymani, “Insight into the Behavior of Colloidal Gas Aphron (CGA) Fluids at Elevated Pressures: An Experimental Study,” Colloids and Surfaces A: Physicochemical and Engineering Aspects 537 (2018): 250–258, https://doi.org/10.1016/j.colsurfa.2017.10.001.

[32]

A. C. Martinez, E. Rio, G. Delon, A. Saint-Jalmes, D. Langevin, and B. P. Binks, “On the Origin of the Remarkable Stability of Aqueous Foams Stabilised by Nanoparticles: Link With Microscopic Surface Properties,” Soft Matter 4, no. 7 (2008): 1531–1535, https://doi.org/10.1039/b804177f.

[33]

E. Rio, W. Drenckhan, A. Salonen, and D. Langevin, “Unusually Stable Liquid Foams,” Advances in Colloid and Interface Science 205 (2014): 74–86, https://doi.org/10.1016/j.cis.2013.10.023.

[34]

L. R. Arriaga, W. Drenckhan, A. Salonen, et al., “On the Long-Term Stability of Foams Stabilised by Mixtures of Nano-Particles and Oppositely Charged Short Chain Surfactants,” Soft Matter 8, no. 43 (2012): 11085–11097, https://doi.org/10.1039/c2sm26461g.

[35]

M. Abkarian, A. B. Subramaniam, S.-H. Kim, R. J. Larsen, S.-M. Yang, and H. A. Stone, “Dissolution Arrest and Stability of Particle-Covered Bubbles,” Physical Review Letters 99, no. 18 (2007): 188301, https://doi.org/10.1103/physrevlett.99.188301.

[36]

T. Ramanathan, A. Abdala, S. Stankovich, et al., “Functionalized Graphene Sheets for Polymer Nanocomposites,” Nature Nanotechnology 3, no. 6 (2008): 327–331, https://doi.org/10.1038/nnano.2008.96.

[37]

V. Palermo, I. A. Kinloch, S. Ligi, and N. M. Pugno, “Nanoscale Mechanics of Graphene and Graphene Oxide in Composites: A Scientific and Technological Perspective,” Advanced Materials 28, no. 29 (2016): 6232–6238, https://doi.org/10.1002/adma.201505469.

[38]

M. Wang, X. Duan, Y. Xu, and X. Duan, “Functional Three-Dimensional Graphene/Polymer Composites,” ACS Nano 10, no. 8 (2016): 7231–7247, https://doi.org/10.1021/acsnano.6b03349.

[39]

B. Wang, Z. Li, C. Wang, et al., “Folding Large Graphene-on-Polymer Films Yields Laminated Composites With Enhanced Mechanical Performance,” Advanced Materials 30, no. 35 (2018): 1707449, https://doi.org/10.1002/adma.201707449.

[40]

M. Šilhavík, P. Kumar, Z. A. Zafar, et al., “Anomalous Elasticity and Damping in Covalently Cross-Linked Graphene Aerogels,” Communications Physics 5, no. 1 (2022): 1–8, https://doi.org/10.1038/s42005-022-00806-5.

[41]

M. Wu, H. Geng, Y. Hu, et al., “Superelastic Graphene Aerogel-Based Metamaterials,” Nature Communications 13, no. 1 (2022): 4561, https://doi.org/10.1038/s41467-022-32200-8.

[42]

J. Lei and Z. Liu, “The Structural and Mechanical Properties of Graphene Aerogels Based on Schwarz-Surface-Like Graphene Models,” Carbon 130 (2018): 741–748, https://doi.org/10.1016/j.carbon.2018.01.061.

[43]

H. Hu, Z. Zhao, W. Wan, Y. Gogotsi, and J. Qiu, “Ultralight and Highly Compressible Graphene Aerogels,” Advanced Materials 25, no. 15 (2013): 2219–2223, https://doi.org/10.1002/adma.201204530.

[44]

J. Hu, J. Zhu, S. Ge, et al., “Hydrophobic and Resilience Graphene/Chitosan Composite Aerogel for Efficient Oil−Water Separation,” Surface and Coatings Technology 385 (2020): 125361, https://doi.org/10.1016/j.surfcoat.2020.125361.

[45]

L. Qiu, D. Liu, Y. Wang, et al., “Mechanically Robust, Electrically Conductive and Stimuli-Responsive Binary Network Hydrogels Enabled by Superelastic Graphene Aerogels,” Advanced Materials 26, no. 20 (2014): 3333–3337, https://doi.org/10.1002/adma.201305359.

[46]

S. Wu, R. B. Ladani, J. Zhang, et al., “Strain Sensors With Adjustable Sensitivity by Tailoring the Microstructure of Graphene Aerogel/PDMS Nanocomposites,” ACS Applied Materials and Interfaces 8, no. 37 (2016): 24853–24861, https://doi.org/10.1021/acsami.6b06012.

[47]

P. Liu, X. Li, P. Min, et al., “3D Lamellar-Structured Graphene Aerogels for Thermal Interface Composites With High Through-Plane Thermal Conductivity and Fracture Toughness,” Nano-Micro Letters 13, no. 1 (2021): 1–15, https://doi.org/10.1007/s40820-020-00548-5.

[48]

N. M. Han, Z. Wang, X. Shen, et al., “Graphene Size-Dependent Multifunctional Properties of Unidirectional Graphene Aerogel/Epoxy Nanocomposites,” ACS Applied Materials and Interfaces 10, no. 7 (2018): 6580–6592, https://doi.org/10.1021/acsami.7b19069.

[49]

S. Yan, G. Zhang, X. Jin, et al., “Rapid Room-Temperature Self-Healing Conductive Nanocomposites Based on Naturally Dried Graphene Aerogels,” Journal of Materials Chemistry C 6, no. 38 (2018): 10184–10191, https://doi.org/10.1039/c8tc03692f.

[50]

Y. Lin, J. Chen, S. Dong, G. Wu, P. Jiang, and X. Huang, “Wet-Resilient Graphene Aerogel for Thermal Conductivity Enhancement in Polymer Nanocomposites,” Journal of Materials Science & Technology 83 (2021): 219–227, https://doi.org/10.1016/j.jmst.2020.12.051.

[51]

C. Zhu, T. Han, E. B. Duoss, et al., “Highly Compressible 3D Periodic Graphene Aerogel Microlattices,” Nature Communications 6, no. 1 (2015): 1–8, https://doi.org/10.1038/ncomms7962.

[52]

A. Upadhyay and S. V. Dalvi, “Microbubble Formulations: Synthesis, Stability, Modeling and Biomedical Applications,” Ultrasound in Medicine and Biology 45, no. 2 (2019): 301–343, https://doi.org/10.1016/j.ultrasmedbio.2018.09.022.

[53]

H. Zhai, Q. Zhou, and G. Hu, “Predicting Micro-Bubble Dynamics With Semi-Physics-Informed Deep Learning,” AIP Advances 12, no. 3 (2022): 035153, https://doi.org/10.1063/5.0079602.

[54]

A. S. Qaddoori, J. H. Saud, and F. Hamad, “A Classifier Design for Micro Bubble Generators Based on Deep Learning Technique,” Materials Today: Proceedings 80 (2023): 2684–2696, https://doi.org/10.1016/j.matpr.2021.07.013.

[55]

X. Wang, Z. Ning, M. Lv, and C. Sun, “Machine Learning for Predicting the Bubble-Collapse Strength as Affected by Physical Conditions,” Results in Physics 25 (2021): 104226, https://doi.org/10.1016/j.rinp.2021.104226.

[56]

G. Besagni, P. Brazzale, A. Fiocca, and F. Inzoli, “Estimation of Bubble Size Distributions and Shapes in Two-phase Bubble Column Using Image Analysis and Optical Probes,” Flow Measurement and Instrumentation 52 (2016): 190–207, https://doi.org/10.1016/j.flowmeasinst.2016.10.008.

[57]

E. Spyromitros-Xioufis, G. Tsoumakas, W. Groves, and I. Vlahavas, “Multi-Label Classification Methods for Multi-Target Regression,” preprint, arXiv:1211.6581 (2012): 1159–1168.

[58]

E. Spyromitros-Xioufis, G. Tsoumakas, W. Groves, and I. Vlahavas, “Multi-Target Regression via Input Space Expansion: Treating Targets as Inputs,” Machine Learning 104, no. 1 (2016): 55–98, https://doi.org/10.1007/s10994-016-5546-z.

[59]

B. P. Binks and S. Lumsdon, “Influence of Particle Wettability on the Type and Stability of Surfactant-Free Emulsions,” Langmuir 16, no. 23 (2000): 8622–8631, https://doi.org/10.1021/la000189s.

[60]

M. B. Meinders and T. van Vliet, “The Role of Interfacial Rheological Properties on Ostwald Ripening in Emulsions,” Advances in Colloid and Interface Science 108 (2004): 119–126, https://doi.org/10.1016/j.cis.2003.10.005.

[61]

T. A. Rovers, G. Sala, E. Van Der Linden, and M. B. Meinders, “Effect of Temperature and Pressure on the Stability of Protein Microbubbles,” ACS Applied Materials and Interfaces 8, no. 1 (2016): 333–340, https://doi.org/10.1021/acsami.5b08527.

[62]

P. Chu, J. Finch, G. Bournival, S. Ata, C. Hamlett, and R. J. Pugh, “A Review of Bubble Break-Up,” Advances in Colloid and Interface Science 270 (2019): 108–122, https://doi.org/10.1016/j.cis.2019.05.010.

[63]

S. Tcholakova, Z. Mitrinova, K. Golemanov, N. D. Denkov, M. Vethamuthu, and K. Ananthapadmanabhan, “Control of Ostwald Ripening by Using Surfactants With High Surface Modulus,” Langmuir 27, no. 24 (2011): 14807–14819, https://doi.org/10.1021/la203952p.

[64]

S. Tcholakova, F. Mustan, N. Pagureva, et al., “Role of Surface Properties for the Kinetics of Bubble Ostwald Ripening in Saponin-Stabilized Foams,” Colloids and Surfaces A: Physicochemical and Engineering Aspects 534 (2017): 16–25, https://doi.org/10.1016/j.colsurfa.2017.04.055.

[65]

O. J. Fisher, N. J. Watson, L. Porcu, D. Bacon, M. Rigley, and R. L. Gomes, “Multiple Target Data-Driven Models to Enable Sustainable Process Manufacturing: An Industrial Bioprocess Case Study,” Journal of Cleaner Production 296 (2021): 126242, https://doi.org/10.1016/j.jclepro.2021.126242.

[66]

A. Korotcov, V. Tkachenko, D. P. Russo, and S. Ekins, “Comparison of Deep Learning With Multiple Machine Learning Methods and Metrics Using Diverse Drug Discovery Data Sets,” Molecular Pharmaceutics 14, no. 12 (2017): 4462–4475, https://doi.org/10.1021/acs.molpharmaceut.7b00578.

[67]

G. J. Aguiar, E. J. Santana, S. M. Mastelini, R. G. Mantovani, and S. B. Júnior, “Towards Meta-Learning for Multi-Target Regression Problems,” in 2019 8th Brazilian Conference on Intelligent Systems (BRACIS) (IEEE, 2019), 377–382, https://doi.org/10.1109/BRACIS.2019.00073.

[68]

D. C. Marcano, D. V. Kosynkin, J. M. Berlin, et al., “Improved Synthesis of Graphene Oxide,” ACS Nano 4, no. 8 (2010): 4806–4814, https://doi.org/10.1021/nn1006368.

[69]

T. Soltani and B.-K. Lee, “Low Intensity-Ultrasonic Irradiation for Highly Efficient, Eco-Friendly and Fast Synthesis of Graphene Oxide,” Ultrasonics Sonochemistry 38 (2017): 693–703, https://doi.org/10.1016/j.ultsonch.2016.08.010.

[70]

R. Shadkam, M. Naderi, A. Ghazitabar, A. Asghari-Alamdari, and S. Shateri, “Enhanced Electrochemical Performance of Graphene Aerogels by Using Combined Reducing Agents Based on Mild Chemical Reduction Method,” Ceramics International 46, no. 14 (2020): 22197–22207, https://doi.org/10.1016/j.ceramint.2020.05.297.

[71]

A. Ghazitabar, M. Naderi, and D. F. Haghshenas, “A Facile Chemical Route for Synthesis of Nitrogen-Doped Graphene Aerogel Decorated by Co3O4 Nanoparticles,” Ceramics International 44, no. 18 (2018): 23162–23171, https://doi.org/10.1016/j.ceramint.2018.09.126.

[72]

G. Van Rossum and F. L. Drake Jr., Python Tutorial (Centrum voor Wiskunde en Informatica, 1995).

[73]

C. R. Harris, K. J. Millman, S. J. Van Der Walt, et al., “Array Programming With NumPy,” Nature 585, no. 7825 (2020): 357–362, https://doi.org/10.1038/s41586-020-2649-2.

[74]

W. McKinney, “Data Structures for Statistical Computing in Python,” in Proceedings of the 9th Python in Science Conference Vol. 445 (2010), 51–56, https://doi.org/10.25080/Majora-92bf1922-00a.

[75]

J. D. Hunter, “Matplotlib: A 2D Graphics Environment,” Computing in Science & Engineering 9, no. 3 (2007): 90–95, https://doi.org/10.1109/mcse.2007.55.

[76]

M. L. Waskom, “Seaborn: Statistical Data Visualization,” Journal of Open Source Software 6, no. 60 (2021): 3021, https://doi.org/10.21105/joss.03021.

[77]

F. Pedregosa, G. Varoquaux, A. Gramfort, et al., “Scikit-Learn: Machine Learning in Python,” Journal of Machine Learning Research 12 (2011): 2825–2830, https://doi.org/10.48550/arXiv.1201.0490.

Rights & permissions

2026 The Author(s). Electron published by Harbin Institute of Technology and John Wiley & Sons Australia, Ltd.

PDF (6700KB)

0

Accesses

0

Citation

Detail

Sections
Recommended

/

〈 〉