Introduction

Electrospinning has gained significant interest within the scientific research and industrial sectors since the latter part of the twentieth century, emerging as a critical scientific and commercial endeavor with widespread global economic implications. This technique has become increasingly important due to advancing insights into nanotechnology, particularly concerning nanoparticles and nanostructures [1]. Electrospun nanofibrous materials have garnered considerable interest in various scientific and industrial domains due to their remarkable flexibility, thus fulfilling stringent mechanical property prerequisites while offering an extensive surface area, rendering them versatile for different applications [2, 3]. Furthermore, the nanofibers fabricated through electrospinning exhibit cross-sectional diameters ranging from tens to hundreds of nanometers, thereby providing them with enhanced surface energy, primarily due to their extensive surface area. Additionally, these electrospun nanofibers possess the ability to interconnect and create intricate networks of highly porous mesh structures, making them versatile candidates for numerous applications [4]. The remarkable attributes of electrospun nanofibers include their exceptional extensibility, high mechanical strength, substantial porosity, large surface area, as well as the capacity for adjusting fiber diameter. Furthermore, they exhibit thin layering, high permeability, low basis weight, customizable wettability, retention of electrostatic charges, and mechanical flexibility [5]. In addition to these characteristics, electrospinning possesses the added advantage of a user-friendly application. An essential aspect of electrospun nanofibers is their diameter, which directly governs their mechanical and functional attributes [6]. Through meticulous manipulation of electrospinning process parameters, the precise control of nanofiber diameter and morphology can be achieved, thereby tailoring their properties to suit specific applications across diverse fields.

A standard electrospinning process commences with the activation of a high-voltage power source, which prompts the generation of an electric field among two main electrodes—the needle and the collector—which elevate the electrostatic potential of a polymer droplet ejected from a needle tip. As the electrostatic potential increases, so does the surface charge carried by the solution. In general, a fluid’s shape is governed by its inherent surface tension. However, when the fluid bears an electric charge, this surface charge creates a counteractive force, opposing the conventional effects of surface tension and causing a shift in the fluid’s shape, initiating the characteristic formation known as the Taylor cone. At the apex of the Taylor cone, the convergence of electric stresses acts as a critical catalyst for the fluid jet ejection, which, imbued with an electric charge, experiences a directional attraction toward the local electrostatic field. As the jet progresses through a designated period of flight time, it reaches a critical point where it becomes susceptible to various instabilities. One prominent instability is bending, which largely influences the resultant fiber diameter produced through the electrospinning process. The high surface area inherent in this narrow fluid jet facilitates a quick loss of solvent, thereby accelerating the transformation of the fluid jet into a solidified fiber [7]. Electrospinning possesses the remarkable ability to fabricate nanostructures from a wide variety of raw materials, including natural and synthetic polymers, as well as composite materials. In order to effectively carry out the electrospinning process, it is crucial to define and configure a specific set of process parameters, which ensures the successful production of nanostructures, maintaining the integrity and quality of the resulting nanofibers.

According to several prior studies, several process parameters have been recalled as crucial influencers in the electrospinning process. These crucial parameters include the applied voltage, the solution feed (flow) rate, the solution concentration, the molecular weight of the polymer, and the needle-to-collector distance. Each of these parameters plays a significant role in determining the quality and characteristics of the resulting nanofibers. These process parameters must be precisely controlled to achieve optimal nanofiber properties for various polymers, such as polyacrylonitrile (PAN), polyvinyl alcohol (PVA), polycaprolactone (PCL), polyethylene oxide (PEO), polylactic acid (PLA), polyurethane (PU), and polyacrylic acid (PAA) [8,9,10,11,12].

Controlling the diameter of electrospun nanofibers has been shown to be an essential strategy for achieving specific targeted properties tailored to various vital applications. This precise control is essential for optimizing the functionality and effectiveness of nanofibers in fields such as tissue engineering, bone regeneration, wound dressing, drug delivery, and cancer therapy [13,14,15]. This precision in controlling nanofiber characteristics has garnered attention among scientists and researchers as a competent technique for fabricating particular types of electrospun nanofibers with predefined diameters and morphology for various applications. For instance, Acatay et al. [16] investigated the influence of the morphology of PAN electrospun nanofibers on their hydrophobic properties. Similarly, Wu et al. [17] provided theoretical insights demonstrating that the performance of true axial tensile stress in solid nanofibers can be adjusted by manipulating the nanofiber diameter relative to the axial tensile stretch. He et al. [18] documented that electrospun nanofibers with diameters below 100 nm exhibit exceptional strength, elevated surface energy, heightened surface reactivity, and enhanced thermal and electrical conductivity, which are all attributed to nanoscale effects. Noriega et al. [19] conducted a study to investigate the effect of fiber diameter on the behavior of chondrocytes, which are cartilage-forming cells when cultured on electrospun chitosan scaffolds. Their research focused on understanding how variations in fiber diameter influenced the spreading, proliferation, and differentiation of these chondrocytes. The findings from this study revealed an interrelationship between the electrospun fiber diameter and the activation of gene expression in the chondrocytes. In another study, Chen et al. [20] explored the relationship between the electrospun fiber diameter and the adhesion and proliferation activities of NIH 3T3 fibroblast cells. The study intended to determine how variations in fiber diameter could influence the ability of these cells to attach to and grow on the scaffolds. The results of their investigation revealed that scaffolds composed of smaller-diameter fibers, which lacked any bead formation, were more effective in promoting cell attachment and proliferation. Hodgkinson et al. [21] conducted a study to examine how the diameter of fibers in an electrospun silk fibroin scaffold influences the proliferation and gene expression of primary human dermal fibroblast cells. Their research revealed a correlation between fiber diameter and cellular activities. Specifically, they found that fibers with diameters ranging from 250 to 300 nm significantly promoted more significant cell proliferation and spreading. In contrast, as the fiber diameter increased beyond this optimal range, both cell proliferation and spreading activities tended to decrease. Furthermore, in addition to examining the effects of fiber diameter on cellular activities, other researchers have expanded their studies by incorporating conductive fillers into electrospun fibers. These conductive fillers are added to the fiber matrix to enhance the electrical properties of the scaffolds [22, 23].

As previously mentioned, the fiber diameter of electrospun nanofibers can vary significantly in response to the various process parameters involved in the electrospinning technique. Even when dealing with polymers and solvents that share similar characteristics, understanding and predicting the nonlinear relationships between these process parameters can be quite challenging. Hence, determining a clear correlation between these process parameters and the target fiber diameter of electrospun nanofibers is crucial for any application. In the past, numerous studies have been conducted to optimize the process parameters of electrospinning through experimental intuition and further developed through trial-and-error approaches, including the utilization of computational simulation techniques and the integration of advanced sensor technologies [24, 25]. These conventional methods employed to determine the relationship between process parameters and target fiber diameter of electrospun nanofibers have their inherent drawbacks, including being time-intensive processes, incurring substantial costs, being resource-intensive (with the significant usage of polymers and solvents), and exhibiting a deficiency in precision control for effectively addressing the challenges, which makes it difficult to attain the target fiber diameter of electrospun nanofibers.

In addition, some authors have explored the use of various mathematical models to predict the fiber diameter of electrospun nanofibers based on process parameters. These models include techniques such as response surface methodology, linearization of equations derived from experimental data, and the development of empirical equations. These models were aimed to establish a relationship between process parameters and fiber diameter to achieve more precise control over the electrospinning process. However, despite these efforts, the error percentage in these predictions remains significant, which is because the experimental data used to develop these mathematical models involve a wide range of variables, including differences in viscosity, conductivity, flow rate, applied voltage, and resulting fiber diameters [26, 27]. Consequently, in recent times, paradigm shifts in machine learning (ML) have introduced innovative approaches to overcoming these obstacles. ML has emerged as a promising method for identifying patterns within complex data sets and predicting outcomes with a high degree of accuracy. By leveraging ML algorithms, scientists and researchers can analyze vast amounts of experimental data to discern intricate relationships between process parameters and fiber diameters. This capability significantly accelerates the fabrication process of electrospun nanofibers, enabling the production of fibers with precise, specified diameters tailored to meet the requirements of various applications. As a result, ML not only enhances the efficiency and reliability of electrospun nanofiber production but also opens new possibilities for customizing nanofiber properties for specific biomedical, environmental, and industrial uses. This method of computation holds great potential as the most accurate approach for predicting the physical properties of electrospun nanofibers, thereby saving time, cost, and material.

ML, which falls under the area of artificial intelligence (AI), stands out as an effective tool employed for prediction, optimization, and pattern identification, primarily leveraging extensive datasets. ML models can be employed to comprehend and build the intricate relationships between input and output results. Typically, ML has three predominant algorithmic categories: supervised learning, unsupervised learning, and reinforcement learning. Supervised learning employs models from predefined training datasets (labeled datasets) to predict the anticipated output. Standard methodologies of supervised learning involve support vector machine (SVM) and decision tree (DT), which have proven to be instrumental in addressing classification and regression challenges. Unsupervised learning methodologies, exemplified by clustering and dimensionality reduction analysis, have proven beneficial to problems without predefined labels within their datasets. Reinforcement learning is a specialized ML algorithm that centers around the acquisition of knowledge through the evaluation of consequences, whether in the form of rewards or punishments, resulting from specific actions taken within a given environment [28]. In addition to the SVM and DT ML models, other widely used models are artificial neural networks (ANNs), which emulate the principles of biological neural networks and feature trainable network parameters set through iterative training procedures. The iterative nature of this training approach facilitates the refinement and optimization of the parameters, allowing the ANNs to enhance their ability to capture intricate patterns within data progressively. The capability of ANNs to construct intricate patterns has led to their widespread integration throughout several domains, such as image recognition, natural language processing, and others [29, 30].

To date, several studies have focused on modeling and optimizing the structure of electrospun nanofibers using these advanced computational techniques. Sarkar et al. [31] utilized ANNs to develop control techniques to manipulate the diameter of nanofibers in the electrospinning process, specifically focusing on electrospun PEO nanofibers. Their work demonstrated the potential of ANNs in adjusting the electrospinning parameters to achieve targeted fiber diameters. Similarly, Nasouri et al. [32] conducted a study between ANNs technique and response surface methodology to predict the production rate of PAN nanofibers fabricated through electrospinning. Their research highlighted the strengths and weaknesses of each approach, providing valuable insights into the effectiveness of these predictive models. Faridi-Majidi et al. [33] employed the ANNs to predict the impact of various electrospinning parameters on the diameter of PAN nanofibers. They focused on key parameters such as polymer solution concentration, applied voltage, and nozzle-to-collector distance to understand how these factors influence the fiber diameter. In another study, Premasudha et al. [34] developed ANNs and trained them using the backpropagation algorithm to predict fiber diameter. Their model achieved average prediction errors of 0.05% for the training data and 2.6% for the testing data.

Karimi et al. [35] demonstrated the efficacy of the ANNs technique in predicting the diameter of nanofibers made from polymers such as PAN and chitosan at various ratios. In a related study, Abdelhady et al. [36] highlighted the accuracy of ANNs compared to multiple regression analysis for predicting the diameter of electrospun nanofibers. Their findings showed that ANNs delivered more precise and reliable predictions with greater accuracy. Nasouri et al. [37] presented the ANNs model for predicting the diameter of nanofibers produced from PVP solutions. This study highlighted the model’s accuracy, reporting a correlation coefficient (R) of 0.98. Such a high R-value indicates a robust predictive capability of the model, demonstrating that it can reliably predict the average diameter of electrospun nanofibers based on the input parameters. The study concluded that the process parameters selected for designing the ANNs model had a significant impact on the average diameter of the electrospun nanofibers produced. Maurya et al. [38] emphasized the vital relationship between the electrospinning process parameters and the resulting diameter of magnetic nanofibers composed of ferrofluid and PVA. They utilized ANNs to analyze and predict this relationship, demonstrating the effectiveness of ANNs in optimizing the electrospinning parameters to achieve desired fiber diameters. Similarly, Lakshmi Narayana et al. [39] developed the ANNs model to predict and analyze the diameter of PCL fibers.

The specialized focus on ML models is attributed to their strengthened proficiency in uncovering rules and comprehending features embedded in data, making them a powerful tool for enhancing the efficiency of solving materials science problems [40,41,42]. Similarly, the utilization of ML models offers scientists and researchers the opportunity to optimize electrospinning process parameters to achieve the target fiber diameter range, elevating both the reproducibility and accuracy of the process. Furthermore, the intricacies of the electrospinning process, starting from the variables involved in the process parameters, contribute to the generation of noisy experimental data. This highlights yet another justification for favoring ML over traditional optimization tools [43]. It is hypothesized that ML models have the transformative potential to develop smart, economically viable, and highly efficient electrospun nanofibers with the target diameter for any intended application.

This review highlights the developing body of research that leverages the capabilities of ML to predict the target diameter of electrospun nanofibers precisely. The focus is mainly on optimizing the configuration of process parameters to ensure accurate and consistent nanofiber diameters. The following sections delve deeply into the electrospinning technique, exploring its critical process parameters and illustrating how this nanofiber fabrication method has evolved into contemporary innovations driven by ML. This review highlights critical studies and significant breakthroughs that have paved the way for fabricating electrospun nanofibers with greater precision, efficiency, and cost-effectiveness. It also focuses on the customization of electrospun nanofiber properties to meet specific application requirements. By leveraging ML, scientists and researchers can optimize the electrospinning process, ensuring the fabrication of high-quality electrospun nanofibers with targeted properties. Furthermore, this assessment delves into the prevailing challenges, future opportunities, and potential prospects in the intersection of various ML algorithms and electrospinning processes. This review aims to keep scientists and researchers mindful of the latest advancements and breakthroughs in utilizing ML models to enhance the electrospinning process. Additionally, it serves as a momentum for further research and exploration, encouraging continued investigation and development within this captivating area of study.

Electrospinning technique principles and applications

Electrospinning prevails as a method of substantial importance due to its dynamic evolution in the field of fiber preparation. This versatile technique plays a vital role in the transformation of solutions or melts into continuous fibers characterized by nano/microscale diameters and its unique capability as the exclusive method of mass-producing continuous fibers within the nano/microscale size range. Electrospinning is a preeminent technique in continuous fiber synthesis, leveraging electrostatic forces to facilitate the formation and elongation of fibers from the polymer solutions. Electrospinning harnesses electrostatic forces adeptly, resulting in the production and extension of fibers with diameters varying from the diminutive scale of tens of nanometers to micrometers [44]. In the electrospinning process, high voltage is utilized to impart an electric charge onto a liquid solution or molten substance by positioning it between two conductors that have persistently contrasting electromagnetic charge polarities, which causes the polymer to stretch, ultimately forming fibers. A typical laboratory-scale configuration comprises four essential components: high-voltage DC or AC power supply, syringe pump, needle typically fashioned from metallic capillary material and collector. Figure 1 demonstrates the simple concept of the electrospinning process [45].

Figure 1
figure 1

Reproduced from reference [45]. Copyright 2023, John Wiley and Sons.

Schematic representation of the electrospinning process [45].

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The electrostatic force generated by the high-voltage source is utilized to apply a charge to the polymer solution or molten substance, a procedure facilitated by its controlled dispensing through the fine needle at a consistent pace. During the electrospinning, the precursor solution that emanates from the needle tip goes through a transformative phase, wherein it coalesces into a diminutive droplet that is subject to charge accumulation due to the electric field. The electrical discharge emanating from the polymer droplet causes a distinct conical-shaped configuration known as the Taylor cone [46]. Achieving a well-formed Taylor cone is essential in ensuring the stability of the electrospinning process, which exerts control over the diameter and morphology of the nanofibers. The jet emerging from the Taylor cone initially follows a predominantly linear trajectory. This particular section, typically characterized by its short length, is commonly referred to as the near-field region, as illustrated in Figure 2a [47]. Zheng et al. [48] conducted a study on the impact of the jet trajectory on polystyrene (PS) fibers, explaining that elongating the linear segment led to a corresponding augmentation in fiber diameter. As the intensity of the electric field is increased, there is a corresponding elevation in the accrual of charges along the polymer bud surface. Subsequently, the repulsive electric forces exert their dominance, overpowering the surface tension exhibited by the polymer solution, which triggers a sequence of whipping and splitting moves because of the emergence of bending instabilities, as shown in Figure 2b, thereby, through the effort of mechanical force, instigating the elongation of the fiber. At this stage, the arrangement of the asymmetrically electrospun fibers is determined by electrostatic repulsion, colloidal strength, the surface-to-volume ratio, and the influence of gravity [49]. The transition phase from a liquid to solid state in the solution is achieved by defining a region that propels the charged molecules, thereby facilitating a continuous process of solvent evaporation. Concurrently, the drawn polymer threads undergo elongation as they progress toward the collector. The transition phase from a liquid to solid state is instigated due to the predominant transition of the Ohmic current into a convective flow, consequently intensifying its rate of acceleration.

Figure 2
figure 2

Reproduced with permission from reference [49]. Copyright 2007, Elsevier.

Electrospinning jet: a Portrait of jet’s whipping motion and b Linear portion of electrified jet [49].

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The resultant electrospun mats manifest a distinctive fibrous structure reminiscent of a web, and bending instability occurs from the plastic deformation induced by the increased charge density of the jet and the concurrent unstable whipping motion. The formation of random and non-aligned orientation fibrous mats exhibits distinctive physical and chemical properties that are not observed in their macroscopic counterparts, thereby creating numerous traits among materials operating within the nanoscale [50,51,52]. Through detailed optimization of electrospinning process parameters, scientists and researchers have achieved the production of nanofibers exhibiting diverse sizes and morphologies, including aligned, core–shell, hollow, porous, and others [53,54,55,56,57]. Currently, electrospinning has facilitated the successful fabrication of thousands of types of nanofibers derived from diverse polymers, exhibiting diameters that range from several nanometers to hundreds of microns. Among the various applications of electrospun nanofibers, their role in the biomedical field stands out prominently, especially in areas such as tissue engineering, bone regeneration, and drug delivery, thereby showcasing their versatility and potential for advancing medical science. Considering the comparable sizes of biological molecules and nanofibers, nanofibers exhibit promising potential in emulating biological environments and natural extracellular matrices with remarkable reliability [58, 59].

Ribeiro et al. [60] demonstrated the creation of nanocomposite scaffolds made of collagen/nano-hydroxyapatite (nHA) through electrospinning, with the objective of mimicking the complex structure of the bone extracellular matrix. The findings indicated that these scaffolds had elastic moduli ranging from 0.3 to 2 GPa and a fiber diameter of 30 nm. Furthermore, both collagen and the bio-composite mats showed no cytotoxic effects and promoted osteoblast adhesion efficiently. In a related study, Zhang et al. [61] developed composite nanofibers incorporating polydopamine (PDA)-modified hydroxyapatite (HA) nanoparticles and PLA through electrospinning. These composite nanofibers possessed enhanced mechanical properties, hydrophilicity, and cellular activity, rendering them promising candidates for utilization in tissue engineering scaffolds. In a separate study, researchers integrated calcium oxide (CaO) nanoparticles derived from eggshell waste into PLA and subjected them to electrospinning, resulting in the fabrication of PLA/CaO scaffolds with promising prospects for bone tissue regeneration. Notably, the inclusion of CaO imparted substantial improvement in the mechanical integrity of the scaffolds, manifested in the enhancement of Young’s modulus relative to pristine PLA fibers. Furthermore, the inclusion of CaO not only conferred bioactivity but also endowed antimicrobial characteristics to the PLA matrix, thereby enhancing its overall biological functionality [62].

Liu et al. [63] formulated a method wherein cinnamaldehyde (CA) was encapsulated within cyclodextrin (CD) and subsequently added into PLA composite fibers via electrospinning. This approach resulted in significant enhancements in the mechanical properties, hydrophilicity, and antibacterial efficacy of the nanofibers while simultaneously mitigating their cytotoxicity. These electrospun nanofibers hold promise for wound dressings. Within the field of drug delivery, Mao et al. [64] conducted a study focusing on the development of electrospun PLA/graphene oxide (GO) nanofiber membranes, aiming to facilitate controlled drug release. An organic dye, rhodamine B (RhB), was employed as a drug to evaluate the drug-release capabilities. Their findings showed a notable enhancement in the release of RhB from the nanofibers with the inclusion of GO. Table 1 provides a collection of electrospun nanofibers, delineating the polymers employed alongside their corresponding solvents utilized in formulating the electrospinning solutions. Furthermore, Table 1 offers an overview of the applications associated with each of the produced electrospun nanofibers.

Table 1 A summary of the studies on electrospun nanofiber fabrications
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Process parameters of electrospinning technique

The factors influencing the electrospinning process can be organized into three primary categories: solution and solvent parameters, operating parameters, and ambient conditions. Solution and solvent parameters indicate polymer concentration, solvent volatility, solution viscosity, surface tension, and solution conductivity. Operating parameters include the applied voltage, solution flow rate, needle diameter, type of collector, and needle-to-collector distance. Additionally, ambient conditions involve chamber and solution temperature, humidity, air velocity, and atmospheric composition [95]. The ongoing exploration and advancement of the basic principles associated with the manipulation of traditional electrospinning equipment and the successful generation of unique morphologies and structures have been produced over the past two decades.

Numerous research teams have dedicated their efforts to investigating the influence of electrospinning process parameters on fiber properties, aiming to optimize them for particular applications. Several studies have systematically analyzed parameter variations across diverse polymer–solvent systems [96, 97]. Choosing the optimal operating range for each electrospinning requirement poses a considerable challenge during the experimental design phase, attributable to the various sets of polymers and their associated solvents. Furthermore, the interdependence of most parameters, engendering a nonlinear causality, represents a notable hurdle in this field. Also, variations in the process parameter will impact the advancement of the electrospinning process, consequently leading to variations in the attributes of the resultant fibers. Hence, the comprehension of parameters governing the electrospinability of a solution is crucial to forming electrospun nanofibers with the target fiber diameter.

A crucial factor in achieving an electrospinnable solution is the degree of polymer chain entanglement, which is influenced by the polymer concentration within the solution. For facilitating chain entanglement, the polymer concentration should remain within the optimal range—neither excessively low nor excessively high. In instances of low concentration, indicated by diluted solutions, the polymer chains exhibit a lack of overlap, and shorter polymer chains predominantly influence the viscoelastic properties of the solution. Also, a decrease in polymer concentration within the solution induces alterations in surface tension, thereby resulting in the formation of beads rather than continuous fibers. However, as the concentration of the polymer is elevated, entanglement appears as the polymeric chain commences overlapping. The critical concentration in an electrospinnable solution is conventionally understood to exhibit proportionality to the molecular weight of the polymer and the adequate volume of the solvent. When the polymer concentration falls below this critical threshold, insufficient chain entanglement becomes a concern, leading to the wobbliness of the jet due to Rayleigh instabilities. Consequently, to ensure a stable electrospinning process, the polymer concentration must exceed this critical threshold [98].

Under certain circumstances, the exploration of various molecular weights within the same polymer involves a strategy that can ultimately prove instrumental in attaining the necessary concentration for an effective and stable electrospinning process. In addition, elevating the polymer concentration can impede the solution feed rate at the needle tip due to excessive viscosity, thereby disrupting the electrospinning process [99]. Moreover, empirical evidence suggests that enhancing the polymer concentration tends to yield fibers with larger diameters. It was evident that the electrospun polyimide nanofibers exhibit increased coarseness with increasing polymer concentration. Bosworth et al. [100] conducted an extensive study to explore the impact of varying PCL concentrations in an acetone solution, revealing that higher concentrations, precisely at 10% w/v, not only yielded bead-free fibers but also resulted in a notable increase in fiber diameter.

Furthermore, the selection of a suitable solvent for solution preparation stands as a critical determinant of its spinnability. The chosen solvent must possess specific properties, including an optimal evaporation rate, boiling point, and vapor pressure. During the journey of the polymer jet from the needle tip to the collector, solvent evaporation and phase separation coincide, leading to the deposition of solid polymer fibers. This phenomenon is closely linked to the rate at which the solvent evaporates [95]. An increased solvent evaporation rate can be obtainable by utilizing solvents with lower volatility and elevating the temperature within the chamber. Inadequate solvent volatility and lower temperatures may direct wet fiber fusion during the deposition process. A quick evaporation process can lead to the formation of flattened fibers, which occurs when residual solvent becomes trapped within the fibers, prompting them to flatten out during solvent evaporation. The choice of solvent impacts the diameter of the fibers. For instance, utilizing a solution of dimethylformamide (DMF) alone or a blend of tetrahydrofuran and DMF results in electrospun polyvinyl chloride fibers with a smaller diameter compared to using a pure tetrahydrofuran solution [101]. Doshi et al. [102] demonstrated that lower surface tension of the solvent does not consistently yield optimal results in electrospinning.

Extensive research suggests that solution viscosity plays a pivotal role in determining the diameter and morphology of the resulting fibers. Elevating the solution viscosity, whether through higher molecular weight or increased polymer concentration, tends to promote electrospun nanofibers with larger diameters. It has been illustrated that extremely low solution viscosities, attributed to insufficient chain entanglement, prevent the formation of continuous fibers, causing the fiber jet to disintegrate into droplets instead. Conversely, when the solution viscosity is extremely high, it becomes challenging to expel a jet from the solution, as the flow of polymer is blocked at the needle tip. The solution viscosity is directly linked to the polymer concentration. Additionally, elevating the solution viscosity through an increase in polymer concentration leads to the production of larger and more uniformly structured fibers. Solutions characterized by lower viscosity and surface tension serve as noticeable indicators for the formation of fibers with beads. The morphologies of the beads exhibit a fascinating transformation, transitioning from a spherical droplet-like shape, characteristic of low-viscosity solutions, to elongated droplets or ellipses and eventually to smooth fibers as the solution viscosity varies [103]. Fong et al. [104] also observed a comparable phenomenon while electrospinning PEO with varying viscosity, resulting in similar morphological changes.

Also, in the electrospinning process, the electrical conductivity of the solution plays a crucial role because it is influenced by both the polymer type and the solvent employed in the solution formulation process. In comparison, it is evident that conductive solutions exhibit a more significant charge density than solutions with lower conductivity. Consequently, when subjected to an electric field, a highly conductive fiber jet undergoes increased tensile force compared to one with lower conductivity. Scientists and researchers have observed that increasing the electrical conductivity of the solution results in a significant reduction in fiber diameter [105]. By contrast, in a scenario of low conductivity, the electric field fails to induce sufficient jet elongation required to produce uniform fibers, resulting in the formation of beads. As noted by Abbasi et al. [106], solutions with high conductivity exhibit increased instability in the presence of a strong electric field, potentially leading to pronounced bending instability and broader fiber diameters.

In addition, the rate at which the solution is delivered plays a crucial role, a factor intricately tied to the solution feed rate, thereby exerting influence over both the diameter and morphology of the resultant fibers. Factors such as pumping pressure, gravity, and electric field intensity collectively determine the speed at which the solution flows during electrospinning. Notably, increasing the solution feed rate yields an increase in fiber diameter, whereas a slower solution feed rate can be employed to produce thinner fibers. A greater solution feed rate is considered advantageous due to the ample time it allows for solvent evaporation. Conversely, a greater solution feed rate often leads to the formation of beaded fibers, primarily because the solvent lacks sufficient time to evaporate before reaching the collector. In one study, Megelski et al. [107] investigated the impact of the solution feed rate on the structure of electrospun fibers derived from PS and tetrahydrofuran. Their findings revealed that an increase in solution feed rate corresponded to a rise in fiber diameter.

Furthermore, the applied voltage stands out as a pivotal process parameter in electrospinning, primarily owing to its profound impact on various aspects, such as the initial droplet shapes, formation of the Taylor cone, and ejection of the solution. It has been hypothesized that elevated applied voltages tend to result in the production of thicker fibers. Moreover, the size and morphology of electrospun nanofibers have been observed to be significantly affected by the applied voltage. The assertion has been made that as the applied voltage increases, thinner fibers tend to be generated due to the application of electrostatic repulsion forces on the polymer jet. However, in many instances, the heightened electric forces exerted on the jet result in rapid solvent evaporation and, consequently, reduced fiber diameter. Therefore, under high applied voltages, there is an increased likelihood of bead production occurring. Yuan et al. [108] reported that doubling the applied voltage results in approximately halving the fiber diameter. Deitzel et al. [109], in their investigation of PEO/water systems, revealed that increasing the applied voltage alters the shape of the surface where the Taylor cone and jet fiber are formed. With low applied voltage, a droplet forms at the tip of the needle, eventually giving rise to a Taylor cone at the droplet’s apex. Conversely, as the applied voltage rises, a Taylor cone forms directly at the needle tip, leading to the ejection of the fiber jet through the needle.

The distance between the needle and the collector impacts both the morphology and diameter of the fibers. Typically, the generation of finer fibers in the electrospinning process can be facilitated through the extension of fiber elongation or flight duration, which can be attainable by increasing the needle-to-collector distance [110]. Nevertheless, it is imperative to note that exceeding the threshold in the needle-to-collector distance, defined as the point where the stability of the Taylor cone is impaired, entails a lengthier flight time, which has the potential to induce inhomogeneous fiber formation, thereby introducing variations in the resulting structure. Additionally, some researchers have noted that altering the needle-to-collector distance may not result in significant changes in fiber size, but there is a possibility of bead formation when the needle-to-collector distance is too small. Lee et al. [111] demonstrated that the diameter of electrospun polyvinyl alcohol nanofiber exhibits an increase with an extended needle-to-collector distance, which is attributed to the reduced stretching experienced by the resultant fibers due to diminished electrostatic force. Moreover, it has been observed that augmenting the needle-to-collector distance leads to the formation of more rounded fibers, whereas decreasing this distance results in the production of flatter fibers.

Finally, environmental factors such as chamber temperature, humidity, atmospheric composition, and air flow velocity play a crucial role in determining the quality of electrospun nanofibers. As reported by Vrieze et al. [112], smaller polyvinylpyrrolidone (PVP) nanofibers were produced at both the lowest (283 K) and highest (303 K) temperatures. At the lowest temperature, the main factor influencing this outcome was the rate of solvent evaporation, which decreases as the temperature decreases, thereby encouraging greater elongation of the jet. Conversely, viscosity emerged as the dominant factor at the highest temperature. Specifically, elevating the temperature heightened the mobility of polymer chains, causing a reduction in viscosity. As a result, the rate of stretching increased, leading to the formation of thinner fibers. A few studies have demonstrated that manipulating humidity levels plays a crucial role in the development of electrospun nanofibers. Research findings indicate that increasing humidity levels trigger the formation of minuscule spherical pores on the surface of the fibers, with a further elevation in humidity, resulting in the gradual interconnection of these pores and altering the fiber morphology. Additionally, varying levels of humidity were found to impact the size distribution of the nanofibers. Under low humidity conditions, larger nanofibers with a more homogeneous size distribution were observed, whereas higher humidity levels resulted in the production of smaller nanofibers with a similarly uniform size distribution. A larger fiber diameter is achieved as a result of airflow above the needle, which accelerates the evaporation rate over convection [113].

As previously stated, it’s essential to observe and monitor the process parameters that affect electrospinning and fiber formation. This ensures the identification of optimal operating conditions capable of producing the desired fiber diameter, tailored to meet the specific requirements of intended applications. Consequently, there is a need for the advancement of robust and efficient ML models to predict the target diameter of electrospun nanofibers accurately. Numerous research endeavors utilizing ANNs ML models to predict the properties of electrospun nanofibers have been undertaken.

Overview of machine learning technologies

In the early stages of AI development, the primary focus was addressing problems characterized by rules that were intellectually straightforward for computers to comprehend yet presented challenges for human understanding. To surmount these intricacies, a systematic approach involving the incorporation of encrypted expressions denoted as “if and else” statements was introduced into the computational framework [114]. Numerous machines endowed with AI have harnessed the power of a knowledge-based paradigm to transcend human capabilities. Despite the notable strides made in AI, it is crucial to acknowledge that AI-based systems, while formidable, are not impervious to imperfections. Indeed, in numerous instances, these systems exhibited suboptimal performance, encountering challenges in executing routine tasks that, to a typical human, might appear ostensibly straightforward.

Consequently, contemporary AI systems have encountered difficulties in identifying alternate methodologies for imparting intuition to computer systems. In response to the challenges mentioned above, the integration of ML emerged as a critical strategy within AI. This infusion of ML into AI frameworks marked a transformative juncture, gaining substantial momentum and prominence as a distinct branch of AI during the 1990s [115]. ML typically revolves around imbuing machines with the ability to learn from observations, past encounters, and training datasets. It encompasses a variety of algorithms aimed at constructing learning models and enhancing their performance with exposure to new datasets. Nonetheless, ML boasts a wide range of application domains. Within these varied application domains, prediction stands out as the most pertinent application domain, leveraging historical datasets to discover future probabilities and provide more accurate estimations of future occurrences [116].

The fundamental concept underlying ML revolves around the notion that a computer program attains proficiency through experiential learning within a specific set of tasks and corresponding performance metrics. The improvement in task performance, gaged by specific performance measures, serves as an indicator of the program’s learning process. Typically, the development of an ML system is imperative when leveraging ML methodologies to address a defined problem effectively. The universal paradigm of such ML systems is that the addition of a goal, sample, and algorithm is the model. The goal describes the specified problem, typically articulated in the shape of an objective function. The sample pertains to a selectively chosen subset of the population designated for analysis through a defined procedure. Broadly, the process of data preprocessing encompasses tasks such as data cleaning and feature manipulation. These preparatory measures are implemented to transform the raw, unprocessed data into the sample. The algorithm confines both the algorithm for ML and the algorithm for optimizing models, which delineates a comprehensive and self-contained sequence of operations designed to be executed systematically. It functions as a step-by-step guide outlining the operations required for a particular task. The model component serves as a conceptual representation of a system expressed through mathematical concepts. In addition, the model describes the algorithm that has been acquired through learning from the designated sample [117].

Moreover, ML can be categorized into three main groups: supervised learning, unsupervised learning, and reinforcement learning, depending on the type of available training data. In this review, we focused more on supervised learning. Supervised learning is known to obtain a hypothesis that approximates the underlying function or delineates the relationship between the provided inputs and their respective outputs. For instance, in material science, a dataset might contain nanofiber structures as well as resultant properties. In this way, the nanofiber structures serve as the independent variables, influencing the data analysis, while the resultant properties denote the dependent variables. The ML algorithm is configured to acquire the function that delineates the intricate relationship between independent and dependent variables. Both regression and classification are undertaken within the horizon of supervised learning, which involves the ML system mapping inputs to predicted outputs and may be displayed as numerical values or labels. In specific instances, such as regression problems, the ML system employs continuous variables like melting temperature, bandgap energy, and elastic modulus to make predictions about the dependent variable [118,119,120]. Several regression ML techniques are available to address the complexities of such issues, including linear regression (LR), multiple linear regression (MLR), random forest (RF) regression, gradient boosting (GB) regression, kernel ridge (KR) regression, support vector regression (SVR), and ANNs.

The use of ML models for predicting properties in materials science and engineering is rapidly increasing. This trend is driven by the fact that ML involves the development and creation of refined algorithms that can identify intricate patterns within experimental data sets. ML models enhance the understanding of materials science and engineering by employing a more adaptive and data-driven approach rather than relying on pre-established equations as models. This flexibility allows ML algorithms to evolve and improve as they process more data, making them highly effective at identifying complex patterns and relationships within experimental data sets. By analyzing this data without the constraints of predetermined models, ML can generate intelligent decisions and predictions that contribute to a deeper understanding of material characteristics [121].

Typically, the objective of ML is to develop computer systems that can learn from experiential data and adapt their behavior in response to changing environmental conditions. This adaptive learning process allows ML systems to continuously improve their performance, making them highly effective for a range of applications. In research studies, ML demonstrates performance levels comparable to those of human researchers, showcasing its versatility and efficacy. Due to its robust data processing capabilities and relatively low barrier to entry for research, ML has the potential to significantly reduce both human and material costs associated with predicting material properties. Consequently, ML can streamline the research and development cycle, enabling faster innovation and development of new specific electrospun nanofibers. Therefore, ML has emerged as a pivotal methodology for significantly enhancing the efficiency and accuracy of material property prediction. This advancement allows for more reliable predictions of material properties, streamlining the research and development process. Hence, ML is replacing conventional research and development approaches, offering a faster, more cost-effective, and highly accurate alternative. The fundamental concept of ML revolves around acquiring common patterns from training data, which are then used to make accurate predictions on new, unfamiliar datasets. This approach enables ML models to generalize from known data to handle various predictive tasks effectively. The development of an ML workflow follows a structured six-stage framework, as depicted in Figure 3.

Figure 3
figure 3

Construction of ML workflow.

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Workflow of machine learning

Data collection

In ML, where models serve as the dynamic engines orchestrating a collection of tasks, the role of data emerges as the fuel propelling these models. The operational functionality of any given ML model is based on the presence of an adequate volume of data, establishing it as a needed prerequisite for optimal performance. It is crucial to highlight that the significance of data transcends sheer quantity, with data quality equally pivotal to running the ML model effectively. Owing to this, substantial data quantities are of vital importance to ML [122]. It is crucial to recognize that both the quantity and reliability of the available data directly influence the ultimate results of ML models. The quantitative and qualitative training datasets utilized for the learning process substantially influence the accuracy of a predictive model.

Consequently, a thorough approach is imperative in the generation of training datasets to ensure optimal outcomes. Usually, the procurement of training data encompasses three primary methodologies. The first approach involves extracting data from published literature. Data acquired through this avenue not only tend to be more pertinent but also serve as a valuable source that offers insights into practical applications. It is essential to recognize that specific data sources or published articles may not include all the variables that were taken into consideration. Subsequently, the second method involves the utilization of high-throughput computations or experiments to gather data. The third avenue involves the acquisition of data from open databases accessible on repository websites. As theoretical and experimental research consistently progresses, datasets stemming from both experimental trials and computational simulations, encompassing failed data, have been merged within these databases. The main principle underpinning these repositories is data sharing, streamlining the accessibility of essential information [123].

Data preparation

Following the collection of appropriate data, preprocessing is conducted, involving tasks such as cleaning and formatting. From the collected data, unprocessed datasets present a challenge for analysis, often rendering them impractical due to inconsistencies, missing values, and noise. To depict those datasets suitable for use, it becomes imperative to uphold a standard of quality. Data cleaning comes into play as an operation applied to existing datasets, serving the purpose of rectifying anomalies and culminating in a refined data collection, which stands as an accurate and distinctive representation of the tiny world under consideration. This process encompasses the eradication of errors, reconciliation of inconsistencies, and standardization of data into a cohesive and uniform format [124]. Formatting gives the data a framework, thereby improving its quality. The task of data cleaning is accomplished through the systematic mitigation of noise, fulfillment of missing values, rectification of inconsistencies, and identification of outliers within the dataset. Various prevalent techniques employed for noise smoothing include clustering, binning, and regression [125].

Integral to the preparatory phase of data in ML is the process of feature engineering. The process of transforming raw data into specific attributes is subsequently utilized as input for the chosen algorithm, which is an essential stage in achieving accurate outcomes, commonly referred to as feature engineering. This pivotal step not only enhances learning accuracy but also contributes to heightened comprehensibility within the model [126]. Rational feature selection emerges as a critical determinant in the construction of ML models, holding the potential to establish the upper boundary of the prevalent model performance. Moreover, various conditional factors may impact any acquired sample, with not all these factors holding significance for features. Certain features are omitted during the cleaning step to maintain the consistency of all extracted values and ensure data quality. For instance, when investigating the prediction of lithium ionic conductivity, multiple internal and external factors may have impacted it. However, only a subset of four factors holds direct relevance to decision attributes, such as ion diffusivity, average volume, transition temperature, and experimental temperature. Hence, the adoption of an appropriate feature selection method becomes imperative in the process of identifying the subset of attributes intended for incorporation into the final assessment. Also, it should be noted that the process of systematically choosing these features rationally can often be both resource-intensive and challenging. In past studies, the task of feature selection has traditionally been executed manually. However, the constraints associated with manual feature engineering have frequently hindered the ability to identify the most expected features. Automated feature engineering has become increasingly popular in recent times. This technique involves creating new potential features automatically by analyzing the data and then selecting the most relevant ones for training the model. This automated approach presents a potential resolution to the challenges encountered in manual feature engineering [127].

Selection of machine learning models

Upon the accumulation and refinement of an adequate dataset, an appropriate ML algorithm is employed to construct an ML model. This ML model building basically operates as a black box, establishing a connection between input data and output data through the engagement of specific nonlinear or linear functions. ML furnishes a mechanism for leveraging instances of a target function to discover the coefficients that allow a designated mapping function to approximate the target function closely. The ML model serves to delineate the correlations between input features and decision outputs predicated on the collected data sample. The knowledge acquired through the application of ML is assimilated into a format that is not only readily accessible but also conducive to subsequent applications, notably for predicting the target properties [128]. This section explores various available ML models. The structure of different ML models is presented in Figure 4. Given that prediction accuracy is fundamentally tied to the selection of a suitable ML algorithm, which emphasizes the key role in the predominant ML workflow. ML algorithms are often made using specialized libraries such as sci-kit-learn, Keras, PyTorch, TensorFlow, or mlpack, each of which is proficient in programming languages like Python, C++, and R. The following section provides a brief description of the most commonly used ML algorithms in the literature.

Figure 4
figure 4

Reproduced with permission from reference [129]. Copyright 2023, John Wiley and Sons.

Structure of different ML models: a KR regression, b RF regression, c SVR, d GB regression, and e ANNs [129].

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Linear/multiple regression

Within ML, regression stands as a venerable and prevalent technique for prediction. The linear regression model defines the linear relationship between a dependent variable and one or more independent variables. This technique elucidates a linear relationship between variables, often depicted as a straight line; accordingly, the LR model endeavors to enhance the alignment of a straight line with a provided dataset. However, the reliability and precision of regression’s accuracy have often been called into question due to structural limitations. In scenarios where a solitary variable is in consideration, the analysis is termed simple linear regression, while when dealing with more than one variable, the approach transforms into multiple linear regression. MLR serves as a valuable tool for predicting the result of a dependent variable by considering various parameters. Through MLR, an equation is derived from the results and information acquired from the prediction model. However, it is essential to note that MLR comes with certain constraints, including the inability to ensure accuracy in achieving desired results [130].

Support vector regression

SVR is a constituent of the SVM category. The core functionality of SVR lies in its ability to discover intricate patterns within datasets, which is accomplished by fitting a hyperplane that effectively incorporates the maximum feasible number of data points while maintaining a specified tolerance margin [131]. In the dataset handled by SVR, some data points lie beyond the defined tolerance margin, known as slack variables. These variables indicate the degree to which particular observations diverge from the perfect hyperplane. A few optimization techniques are utilized to boost the accuracy of the SVR model. These optimization techniques play a crucial role in refining the SVR model by imposing penalties for the mentioned slack variables, thereby mitigating their influence on the model’s performance. The primary aim of this optimization process is to amplify the margin, which essentially equates to minimizing a methodically designed function of weights that decreases monotonically [132].

Kernal ridge regression

KR regression is an advanced iteration of SVR, alternatively termed least squares support vector regression (LSSVR), and it represents a nonparametric approach that directly computes the target based on the input. Unlike traditional regression methods, KRR is adept at handling nonlinearity in data by integrating regularization techniques, thereby preventing the issue of overfitting. Hyperparameters, which refer to the parameters governing the learning procedure, and the size of the training data play critical roles in identifying the efficacy of the KRR learning model. One of the notable benefits of the KRR model stems from its adept handling of the bias-variance trade-off, wherein a slight bias is instituted to enable a significant reduction in variance. This delicate balance ensures the model’s optimal performance and generalization capability across different datasets. While the KRR model may not perfectly fit the training data, its strength lies in its capability to supply more precise predictions for unseen test data over the long term, which aids in mitigating issues such as model complexity and overfitting [133].

Random forest regression

RF regression is notable as a technique in the ensemble learning approach employing multiple DTs to generate the final output instead of depending on a single DT. In the RF ML model, the DT undergoes training on a randomly selected subsample extracted from the dataset. The ultimate prediction is then derived through the process of averaging the outputs generated by the DTs. This technique serves as a safeguard against overfitting and a predicament frequently encountered when employing a DT. In such instances, the model becomes overly fitted to the training data, thereby compromising its accuracy in predicting the results of novel data inputs. Although these models exhibit a low training error rate, it is not uncommon for the test error to be significantly larger. One effective solution to this challenge is the utilization of RF regression, which stands out for its exceptional speed and capability to manage datasets with high dimensionality as well as larger input datasets when assessed with alternative approaches [134].

Gradient boosting regression

GB regression is a collective learning technique employing a combination of weak learners to form a strong learner collectively. The algorithm involves the incremental incorporation of weak learners into the ensemble, with each subsequent learner focused on rectifying the errors of its predecessor. These weak learners are commonly DTs, and the training process of the ensemble is facilitated through a gradient descent algorithm [135]. GB regression typically has higher accuracy than other ML algorithms, such as DT, RF, and SVR, which is attributed to the algorithm’s capacity to assimilate insights from the errors of preceding weak learners, subsequently refining its predictive accuracy incrementally over time. Popular GB algorithms include XGBoost, AdaBoost, LightGBM, and CatBoost. XGBoost is a proficient GB regression that employs a strategy wherein it constructs a DT by computing the disparity between the outcome of the base learner and the actual value, aiming to diminish the variance between the model’s output and the observed value, thereby mitigating the risk of overfitting.[136]. XGBoost possesses the capability of customizing loss functions to satisfy specific requirements, making it an exceedingly adaptable tool. Among its numerous attributes, XGBoost is particularly notable for its exceptional efficiency.

Artificial neural networks

ANNs are models used in ML that draw inspiration from the biological structure and function of neural networks. These models are made up of layers of interconnected nodes that are strategically organized to process input data and produce corresponding output. In the context of ANNs, arranging input data in the forward direction is termed a feed-forward neural network. Within a feed-forward neural network, the output of each node undergoes multiplication by weight coefficients before being fed into the input layer, where it is subjected to a nonlinear activation function. The interconnections within ANNs, denoted as edges, play a pivotal role, with their weights dynamically adjusting throughout the learning process. In the architecture of an ANN, every connection forged between any two nodes symbolizes a weighted value that signifies the strength of the signal traversing across that connection, effectively corresponding to the recall of the ANNs [137]. Various transformations are applied to inputs as they traverse through various layers of the network. The architecture of ANNs comprises three primary components: the input layer, the hidden layer (middle), and the output layer. The input layer serves as the ingress point for input parameters, transmitting them during both model training and testing phases. The hidden layer, positioned between the input and output layers, plays a key role in facilitating connections and interactions between the input and output layers, thus serving as the central component in the overall architecture of the ANNs. Each hidden layer within this structure encompasses a set of neurons, contributing to the complexity and adaptability of the network. Finally, the output layer is entrusted with the responsibility of generating the final result or outcome [138].

The ANNs undergo training through the assessment of samples featuring both known inputs and outputs alongside probability-weighted associations embedded in the network’s data structure. The ANNs’ training process relies on evaluating the disparity between the processed output and the target output, commonly referred to as the error. This error value serves as a critical metric to guide the adjustment of the ANNs’ weighted associations. A learning rule, coupled with the error value, dictates these adjustments. Within ANNs, when the training data are presented to the network, there is an intricate task involving the iterative adjustment of network weights. The primary purpose of this network weight adjustment is to minimize the discrepancy between the current output generated by the network and the predetermined target output. The iterative nature of this training process entails repeated modifications to the network’s parameters until results are closely aligned with the desired outcomes [139].

When modeling neural networks, a crucial step involves the identification of the number of hidden layers and neurons within the network architecture. This decision-making process holds paramount importance, as an insufficient number of hidden layers may impede the model’s capacity to address nonlinear and intricate problems effectively. Conversely, an increase in the number of hidden layers and neurons within the neural network can extend the training time. This increase in the architectural complexity of the model may result in poor performance, as it could lead to the network learning irrelevant behaviors rather than accurately capturing the relationships between parameters. ANNs find widespread application in planning scenarios, mainly in assessing and determining the probability of events. The utility of ANNs begins with its capacity for learning and mapping, primarily driven by the presentation of empirical data. In addressing various problems, these networks can be employed, with a focus on prediction tasks, especially in the domain of complex systems that either defy modeling or pose significant challenges in modeling [140]. While the ANNs ML model stands out as a potent instrument for addressing intricate challenges in engineering and science, it is not without its drawbacks. These drawbacks are the protracted duration required for training, the proliferation of numerous parameters, and the unintended convergence.

Model training

The chosen ML algorithm undergoes rigorous training by utilizing preprocessed input data. This dataset is refined and systematically partitioned into three distinct segments: the data set of the training, the cross-validation, and the testing. Each of these segments serves a distinct purpose in the training and validation pipeline, ensuring robust model performance and generalizability across diverse datasets and scenarios. The ML model undergoes a transformative learning process wherein it acquires the capability to process and interpret data through exposure to a curated training dataset. This iterative process entails the seamless integration of the input dataset with the ML algorithm, facilitating the model’s comprehension and adaptation to the underlying patterns and structures within the data. A dedicated cross-validation dataset is employed to play a pivotal role in fine-tuning the model’s parameters and mitigating overfitting [141]. Overfitting is wherein the model overly memorizes the training data, presenting a formidable challenge as it can lead to an inflated training accuracy approaching 100% [142]. In most ML algorithms, the refinement of hyperparameters is paramount, necessitating adjustments tailored to various training tasks to attain optimal model performance. The integration of cross-validation techniques improves the resilience of model evaluation processes, furnishing a reliable foundation for finding the model’s efficacy. It is widely acknowledged that the ML model’s aptitude lies in its performance on the test dataset, reflecting its aptitude in real-world application scenarios. [143]. While the proportion of data allocation between the training and test datasets is not fixed, the conventional practice often entails a division ratio of 80/20, wherein 80% of the data is allocated to training and 20% to testing.

Machine learning model evaluation

A model embedded with data is expected to exhibit commendable performance, not solely on familiar datasets but also new, unseen data. In the typical evaluation paradigm, the abstraction errors of models are assessed through calculation-centric tests, and the outcomes are instrumental in determining the optimal model. The broad applications and diverse features in various ML models collectively contribute to their competence as formidable predictive tools. In this context, each ML model adheres to a distinct framework tailored to reach its foremost objective. The identification of weaknesses in preceding models consistently acts as a catalyst, forcing researchers to devise novel and more streamlined efficient models [144]. The accuracy and performance of the ML model’s predictions are evaluated by assessing an algorithm, a crucial aspect involving subjecting it to testing to measure its performance. This extends to the assessment of the model’s predictive accuracy, where the experimental data are systematically compared with their corresponding predicted counterparts. The evaluation of ML models is performed by performance metrics, such as the coefficient of determination (R2), mean absolute error (MAE), mean absolute percentage error (MAPE), mean squared error (MSE), root-mean-square-error (RMSE), and mean percentage error (MPE). These performance metrics serve as statistical indicators, offering comprehensive insight into various aspects of the model’s functionality. These metrics furnish critical information regarding the model’s proficiency in predicting mean values, its resilience when encountering outliers, and the degree of uncertainty inherent in its predictions, among other pertinent details. The mathematical formulations delineating each of these performance metrics are detailed in the following equations [145]:

$${R}^{2}= 1-\frac{\sum_{i=1}^{n}{({y}_{i}-f({x}_{i}))}^{2}}{\sum_{i=1}^{n}{({y}_{i}- \overline{y })}^{2}}$$
(1)
$$\text{MAE}= \frac{1}{n}\sum_{i=1}^{n}|{y}_{i}-f\left({x}_{i}\right)|$$
(2)
$$\text{MAPE}= 100 \times \frac{1}{n}\sum_{i=1}^{n}|\frac{({y}_{i}-f\left({x}_{i}\right))}{{y}_{i}}|$$
(3)
$$\text{MSE}= \frac{1}{n}\sum_{i=1}^{n}{({y}_{i}-f({x}_{i}))}^{2}$$
(4)
$$\text{RMSE}= \sqrt{\frac{1}{n}\sum_{i=1}^{n}{({y}_{i}-f({x}_{i}))}^{2}}$$
(5)
$$\text{MPE}= \frac{1}{n}\sum_{i=1}^{n}\frac{({y}_{i}-f\left({x}_{i}\right))}{{y}_{i}}$$
(6)

The R2 value, ranging from 0 to 1, serves as a pivotal gage of model accuracy, with a value of 1 representing the most accurate and 0 denoting a lack of correlation. In essence, R2 denotes the degree of accuracy in predictions made by the model. If the value of R2 is 0, then it signifies a model’s ineffectiveness, suggesting an inability to predict labels with satisfactory accuracy. Conversely, if the value of R2 is 1, then it signifies a robust predictive capacity, implying that the model excels in generating highly accurate results. Within these performance metrics, R2 stands out as a dimensionless quantity, while MAE shares the same dimensions as the output values under consideration. The MAE evaluates the absolute discrepancy between the forecasted and actual values, adopting a linear approach in penalizing errors, thereby treating deviations with uniform significance. This characteristic renders MAE robust, as it penalizes outliers in the dataset with an equal degree of magnitude as data points clustered around the mean [146].

Moreover, the MAE can transform into a percentage-based metric known as the MAPE, achieved by standardizing each error measurement against the corresponding actual value. Additionally, the MSE operates a quadratic approach in penalizing errors, wherein errors are penalized proportionally to the square of their magnitude. Notably, outliers exert a more significant influence on MSE compared to MAE, given the quadratic nature of MSE’s penalty function. One drawback associated with the MSE lies in its reporting of errors, which are expressed in terms of the square of the units predicted via the model [147]. Several users express a preference for an error metric that aligns with the units of the predicted values, which prompts the adoption of the RMSE. The RMSE incorporates a square root transformation to ensure compatibility with the units under consideration. From a statistical standpoint, the RMSE serves as a discerning indicator of large errors, even within a single prediction, as it demonstrates sensitivity to deviations of significant magnitude. In contrast, the MAE offers an overall deviation and exhibits no sensitivity against the influence of isolated large errors.

Model deployment

An additional notable benefit offered by ML is its capacity to seamlessly incorporate the model into a production-based application programming interface (API). Traditionally, in research settings, the development of an optimization model entails reporting the findings alongside the potential impacts of various input process parameters. Conversely, the deployment of ML models in the form of web-based software facilitates a more accessible approach, enabling others to harness the optimization method without necessitating prior expertise in ML model development. This transition toward deploying ML models into a user-friendly API framework not only streamlines accessibility but also fosters collaboration and knowledge exchange within the research community [148]. In addition to the deployment of ML models as web-based services, there has been a notable trend toward embedding ML models directly into operating sensors. This integration into sensor technology presents various considerations when transitioning toward production-based products. One critical aspect to consider is computational performance, where attention must be directed toward assessing the scalability of the ML algorithm. It becomes imperative to ensure that the ML algorithm can efficiently handle increasing volumes of data without compromising performance. This emphasis on scalability highlights the necessity for robust and efficient algorithms that can seamlessly adapt to evolving demands in real-world applications. Furthermore, it is essential to recognize that most ML algorithms lack autonomy, necessitating periodic training as the dataset grows over time. Additionally, it is imperative to acknowledge that ML models are inclined to degradation and need regular inspection and maintenance to uphold their performance standards [149].

Benefits of using machine learning for electrospun nanofibers

The integration of ML into the fabrication of electrospun nanofibers presents numerous advantages. One of the most significant benefits is the optimization of process parameters involved in the electrospinning process. This optimization not only enhances the quality and consistency of the nanofibers produced but also significantly reduces manufacturing costs. Traditional optimization methods for determining the best settings for process parameters rely on extensive trial-and-error experimentation. This approach involves repeatedly adjusting parameters and conducting experiments to find the optimal conditions, which can be both time-consuming and inefficient.

The primary drawback of this method is the significant amount of time required to conduct numerous experiments, each with slight variations in parameters. Additionally, this trial-and-error process is costly due to the high expense of materials needed for each experiment and the labor-intensive nature of performing and analyzing these tests. However, ML algorithms offer a more advanced and efficient approach by analyzing historical and published data from past experiments. These algorithms can process vast amounts of data to identify patterns and relationships between different process parameters and the resulting nanofiber characteristics for a wide range of applications [127]. By identifying the optimal combination of process parameters using historical and published data from previous experiments, ML significantly reduces the consumption of costly materials and minimizes waste. This advanced predictive capability accelerates the optimization process and leads to faster development cycles. This streamlined approach not only enhances the efficiency of the fabrication process but also leads to significant cost savings. By reducing material usage and minimizing experimental waste, ML contributes to more sustainable and economical production of electrospun nanofibers [150].

Another pivotal benefit of integrating ML into the electrospinning process is the precision it offers. ML models can be trained on extensive datasets, enabling them to achieve high accuracy in predicting the outcomes of the electrospinning process, which leads to improved control over the targeted properties of electrospun nanofibers. The ability to accurately predict and control fiber diameter is particularly crucial, as it directly influences critical properties such as mechanical strength, electronic conductivity, and specific surface area. These properties are essential determinants that define the suitability of nanofibers for various applications. For example, precise control over mechanical strength is critical for tissue engineering applications, while specific surface area and electronic conductivity are vital for applications in sensors and energy storage devices. This level of precision ensures that the fabricated electrospun nanofibers consistently meet the standard requirements necessary for any relevant applications [151].

The innovative potential of ML in this context cannot be overstated. ML not only enhances the accuracy and reliability of the electrospinning process but also opens new avenues for research and development. By uncovering hidden patterns and relationships within complex datasets, ML provides deeper insights into the electrospinning process. These insights can lead to the discovery of novel parameter combinations and fabrication techniques that were previously unattainable through traditional methods. ML algorithms enhance the design of experiments by precisely identifying the most informative and relevant data needed to optimize the process parameters. This targeted data collection ensures that scientists and researchers gather critical insights, leading to more accurate predictions and better control over the nanofiber properties [152]. This approach significantly reduces the number of experiments required and accelerates the overall development process. ML can design experiments that systematically vary multiple process parameters simultaneously, enabling them to identify their combined effects on fiber diameter and alignment efficiently.

Furthermore, the application of ML can lead to significant improvements in the microstructure of electrospun nanofibers. The microstructure contains the intricate structural details that define the fibers at a microscopic scale. These details are crucial for determining the overall performance and functionality of the nanofibers in various applications. Critical aspects of the microstructure include fiber diameter, alignment, porosity, and surface roughness. As previously mentioned, ML can significantly enhance precision and control over the electrospinning fabrication process, resulting in electrospun nanofibers with exceptional and consistent microstructural qualities. One of the critical advantages of ML is its ability to adjust fabrication process parameters in real time based on continuous feedback. This dynamic adjustment ensures that the parameters remain optimal throughout the production process, leading to consistent and high-quality nanofibers [153].

Adaptive control systems, driven by reinforcement ML algorithms, offer a refined method for continuously monitoring the electrospinning process in real time using sensors. These advanced systems can dynamically adjust process parameters to achieve and maintain optimal microstructures of the electrospun nanofibers. For example, real-time experimental data on critical process parameters such as the applied voltage or the solution feed rate can be utilized to make immediate modifications to the fiber diameter and morphology. This instantaneous adjustment ensures that the electrospun nanofibers produced consistently adhere to the desired specifications. By continuously monitoring these parameters and dynamically altering them as needed, the fabrication process can maintain optimal conditions. This real-time responsiveness is crucial for producing nanofibers with precise and consistent characteristics, such as uniform diameter and specific morphological features, tailored to meet the requirements of various advanced applications. In addition, this real-time control is crucial for maintaining consistency in the electrospinning process, significantly when external conditions such as temperature and humidity fluctuate. ML plays a pivotal role in enhancing the overall quality and reliability of the fabricated electrospun nanofibers by continuously monitoring and adjusting process parameters to counteract these environmental variations. By minimizing deviations in the microstructure, ML ensures that the produced nanofibers consistently meet the stringent quality standards required in various industrial applications [154].

Moreover, characterizing electrospun nanofibers involves a comprehensive analysis of their microstructural and functional properties, including porosity, tensile strength, fiber diameter, and conductivity. This detailed characterization is essential to ensure that the nanofibers meet distinctive application requirements. ML plays a crucial role in this element by enabling accurate property prediction and advanced data analysis. ML algorithms possess the remarkable capability to automate the extraction of critical features from diverse characterization data sources, such as microscopic images, spectroscopic data, and mechanical testing results. By leveraging ML, scientists and researchers can gain detailed insights into critical attributes of electrospun nanofibers, including fiber diameter, porosity, and alignment. This automated feature extraction process not only enhances the efficiency and accuracy of data analysis but also provides a more comprehensive understanding of the nanofibers’ properties. ML algorithms can analyze microscopic images to accurately predict key characteristics of electrospun nanofibers, such as fiber diameter, pore size, and fiber alignment. Supervised ML algorithms can be trained to identify and quantify these features with high precision. Once trained, ML algorithms can automatically measure fiber diameter, assess alignment, evaluate porosity, and determine surface roughness. This capability ensures that the analysis is both efficient and accurate. After consistent training, ML models can be used to predict the properties of new electrospun nanofibers based on their observed microstructural features [155, 156].

Automated image processing significantly accelerates the characterization process of electrospun nanofibers while also enhancing the consistency and reliability of the results. This automated approach can swiftly and accurately analyze microscopic images by employing ML algorithms with advanced pattern recognition capabilities. It ensures that the characterization of features such as fiber diameter, pore size, and alignment is not only faster but also more precise. Moreover, ML’s refined pattern recognition can detect anomalies in nanofiber structures. These anomalies could include irregularities in fiber diameter, unexpected pore formations, or misalignment of fibers. Identifying such defects is crucial for maintaining high-quality control in the production process. By catching these subtle variations and irregularities, ML enhances the overall quality assurance of electrospun nanofibers, ensuring that they meet quality standards for their intended applications. Numerous studies have demonstrated that the microstructural performance of electrospun nanofibers in applications such as tissue engineering and drug delivery can be accurately predicted using ML models. These models are trained on extensive datasets of experimental results, enabling them to identify patterns and correlations that might not be evident through traditional methods [157]. This predictive capability is precious as it allows scientists and researchers to fabricate electrospun nanofibers with specific microstructures tailored to achieve targeted properties for particular applications [158].

Furthermore, comprehending the intricate relationship between the microstructure of nanofibers and their functional properties is essential for the successful fabrication of electrospun nanofibers tailored for specific applications. ML algorithms excel in this area by detecting subtle patterns and anomalies that traditional image analysis methods might overlook. These advanced capabilities of ML offer a more comprehensive and detailed interpretation of the microstructure of electrospun nanofibers. This enhanced level of analysis allows scientists and researchers to adjust the fabrication process, ensuring that the electrospun nanofibers exhibit the desired properties for their intended applications. Whether it’s enhancing mechanical strength for tissue engineering scaffolds or optimizing surface properties for drug delivery systems, ML provides the tools to achieve precise control over nanofiber microstructures. Predictive ML models provide scientists and researchers with the ability to anticipate how variations in the fabrication process will influence the microstructure of electrospun nanofibers. This foresight is invaluable for selecting the appropriate materials and optimizing process parameters to meet the specific requirements of various applications. Furthermore, one of the significant advantages of ML models is their ability to control noisy experimental data, which is often encountered in nanofiber characterization. Traditional methods may struggle with inconsistencies and inaccuracies in the data. However, ML algorithms are designed to process and interpret complex datasets, filtering out noise and extracting meaningful patterns. By learning from extensive datasets, ML models can effectively filter out noise and concentrate on the most relevant features. This capability ensures that the ML models remain robust and reliable, even when the experimental data is imperfect [159, 160].

ML holds immense potential to enhance the microstructure of electrospun nanofibers, thereby improving their overall performance, consistency, and scalability. By optimizing the electrospinning parameters, ML enables precise adjustments to parameters, which are critical for achieving the desired fiber diameter, alignment, and porosity. Additionally, ML algorithms can effectively control environmental conditions, such as temperature and humidity, ensuring that the electrospinning process remains stable and consistent. This level of control helps in producing nanofibers with uniform microstructural features, which is crucial for maintaining high-quality standards across large-scale production [161]. As ML continues to advance, its integration into the fabrication and characterization of electrospun nanofibers is poised to move powerfully in the field of materials science and nanotechnology. This ongoing advancement will unlock new opportunities for both research and industrial applications.

Industrial production of electrospun nanofibers using machine learning

The industrial production of electrospun nanofibers has been a long-standing goal due to their extensive applications in fields such as biomedical engineering, filtration, and energy storage. While electrospinning is a well-established technique for producing nanofibers, scaling up the process to meet industrial needs has been challenging. One of the primary challenges in the industrial production of electrospun nanofibers is scalability. Traditional electrospinning techniques usually face difficulties in consistently producing nanofibers on a large scale. Ensuring uniformity in fiber diameter and morphology across extensive batches is challenging due to the need for precise control over a group of process parameters. Additionally, sustaining consistent high quality is necessary for applications where performance is vital [162].

Variations in fiber characteristics, such as diameter, alignment, and morphology, can significantly impact the effectiveness and reliability of the final product, which is predominantly factual for biomedical applications, where precise fiber properties are essential for tissue engineering and drug delivery, as well as in filtration systems and energy storage solutions, where uniformity and performance directly influence efficiency and functionality. Another significant challenge lies in the cost and efficiency of the production process. Scaling up the electrospinning process to an industrial level while keeping production costs low and maintaining high efficiency is difficult. The high costs associated with raw materials, energy consumption, and labor, connected with the time-consuming nature of traditional optimization methods, make large-scale production of electrospun nanofibers expensive. Traditional approaches to optimizing the electrospinning process involve extensive trial-and-error experimentation, which is not only labor-intensive but also costly in terms of both materials and time. The electrospinning process itself is complex, involving numerous interdependent parameters. Each of these parameters must be precisely controlled and adjusted to achieve the desired fiber characteristics. This complexity further complicates optimization efforts, as changes in one parameter can affect others, necessitating a holistic approach to process control [163, 164].

The integration of ML into the electrospinning process offers a promising solution to overcome these obstacles, making the industrial production of electrospun nanofibers not only feasible but also efficient and cost-effective. Electrospinning involves a multitude of process parameters, such as applied voltage, polymer concentration, flow rate, and needle-to-collector distance, all of which significantly influence the properties of the resulting electrospun nanofibers. By learning from historical and published data from past experiments, as well as small sets of experimental designs, ML models can quickly determine the optimal patterns and conditions to attain the targeted nanofiber characteristics, such as uniform fiber diameter distribution, appropriate porosity, and specific mechanical properties. This capability significantly enhances the efficiency and scalability of nanofiber production, making it more feasible to scale up to an industrial level [165]. Moreover, ML can be further enhanced through virtual experimentation. ML models can simulate various process parameters and predict the desired outcomes with high accuracy. These simulation capabilities enable companies and research institutions to explore various parameter combinations and production conditions without the necessity of conducting extensive physical trials. By using virtual experimentation, scientists and researchers can efficiently identify the most promising conditions for fabricating nanofibers with specific characteristics. As a result, possible problems can be determined and addressed early in the development process, significantly reducing the risk of costly errors during the actual production phase [166].

Maintaining high-quality and defect-free electrospun nanofiber production is crucial for industrial manufacturing. Defects in the nanofibers can result in significant material waste and elevated costs for both companies and research institutions. ML can play a pivotal role in enhancing real-time quality control during the electrospinning process. By integrating sensors that continuously monitor various parameters, ML algorithms can analyze the data in real time to detect any anomalies or deviations from the desired production standards. This continuous monitoring allows for immediate adjustments to be made, ensuring that the electrospun nanofibers remain consistent and defect-free throughout the production process. Convolutional neural networks (CNNs) and other neural network (NN) algorithms can effectively analyze captured data to detect defects in electrospun nanofibers, such as irregular fiber diameter, bead formation, and alignment issues. These advanced ML algorithms can identify these defects rapidly and accurately. Once an issue is detected, the algorithms can suggest real-time adjustments to the process parameters to correct the problem, which ensures that the produced electrospun nanofibers are free from defects and meet the desired specifications [167].

This proactive quality control approach significantly reduces the amount of defective material produced and minimizes the need for rework, thereby lowering overall production costs. By detecting and addressing issues early in the production process, ML ensures that only high-quality nanofibers are produced. In the biomedical field, ML-optimized electrospinning has been successfully utilized to produce nanofibers for advanced wound dressings. These wound dressings greatly benefit from the consistent quality, defect-free nature, and tailored properties of ML-optimized nanofibers. As a result, they provide improved healing outcomes, offering better support for tissue regeneration and faster recovery for patients. Also, in tissue engineering, the precise control over nanofiber diameter and morphology afforded by ML is crucial to producing scaffolds that effectively support cell growth and tissue regeneration. This precision ensures that the scaffolds have the ideal structural properties needed to facilitate cellular attachment, proliferation, and differentiation. By optimizing the electrospinning process through ML, scientists and researchers can produce nanofibers with consistent and uniform characteristics, which are essential for creating a conducive environment for tissue engineering. The ability to tailor the nanofiber properties to meet specific biological requirements highlights the critical role of ML in the fabrication of high-quality biomedical materials [168].

The cost of materials used in the electrospinning process is a significant factor, especially when dealing with expensive polymers, solvents, and other consumables. Conducting numerous experimental trials to determine the optimal process parameters can become prohibitively expensive under traditional methods. However, ML offers a more efficient solution by drastically reducing the number of trials needed. By analyzing smaller datasets and providing accurate predictions, ML can optimize the process parameters with much less material waste and lower costs. For example, ML algorithms can predict the precise concentration of polymer solution required for a specific production run, thereby minimizing wastage. ML facilitates cost-effective production by significantly minimizing the amount of polymer and solvent required during the experimentation phase. By optimizing the process parameters through ML techniques, companies, and research institutions can achieve the targeted outcomes with fewer resources. Additionally, this optimization contributes to more sustainable manufacturing practices by minimizing waste and reducing the environmental impact associated with the use of high-cost polymers and solvents [121].

The electrospinning process can be highly energy-intensive, and optimizing it for energy efficiency can result in significant cost savings. ML models can analyze the energy consumption patterns of the equipment involved in the electrospinning process. By examining these patterns, ML can identify strategies to reduce energy usage without compromising the quality of the produced nanofibers. For instance, optimizing process parameters to achieve the targeted fiber properties in the quickest possible time can significantly reduce the energy required for each production run. These energy savings directly contribute to lower operational costs, as less power is consumed during production. In addition, the reduction in energy usage aligns with goals for more sustainable manufacturing practices, minimizing the environmental impact of the production process. This dual benefit of cost reduction and sustainability highlights the value of integrating ML into the optimization of electrospinning parameters, ultimately enhancing the overall efficiency and ecological footprint of nanofiber manufacturing. Several companies and research institutions have already successfully integrated ML into their electrospun nanofiber production processes, highlighting the practical advantages of this technology [169].

The successful implementation of ML in nanofiber production, as evidenced by numerous case studies, highlights its transformative potential in the fields of materials science and nanotechnology. ML-driven optimization and control can drive significant innovation, enabling the production of high-performance electrospun nanofibers on an industrial scale [170, 171]. As technology continues to evolve, ML undoubtedly plays an increasingly critical role in advancing nanofiber manufacturing. ML’s ability to analyze large datasets, optimize process parameters, and provide real-time adjustments enhance the precision and efficiency of nanofiber production, which not only improves the quality and consistency of the nanofibers but also reduces costs and energy consumption. Consequently, ML will pave the way for new applications and breakthroughs in materials science and nanotechnology.

Approaches of machine learning for predicting nanofiber diameter

The conception of ML has opened up new opportunities for refining and optimizing electrospinning processes. While the fundamental principles of electrospinning remain unchanged, ML introduces succeeded tools that enhance control over nanofiber properties and the process parameters involved in electrospinning. Over the past few years, various ML models have been extensively applied in materials science to predict the fiber diameter of electrospun nanofibers. Scientists and researchers have dedicated significant effort to refining the fiber diameter of these nanofibers, with the aim of enhancing a variety of critical properties, including surface area, permeability, wettability, porosity, and mechanical flexibility, all of which are essential for the performance and functionality of electrospun nanofibers in various applications [172,173,174]. A subset of scientists and researchers have turned to ML models and empirical equations to predict the fiber diameter of electrospun nanofibers and conserve resources, cost, and time. Furthermore, a broad assessment of the utilization of ML models for predicting the fiber diameter of electrospun nanofibers has been delineated in Table 2. Among the many ML models, ANNs stand out as a significant and powerful modeling tool. ANNs play a critical role in developing new procedures, enhancing efficiency, and transforming strategies and organizational approaches in the production of electrospun nanofibers. ANNs utilize a nonlinear mapping structure inspired by the human neural network and are particularly beneficial for modeling methods where multiple input processing parameters influence the response of interest. The primary objective of using ANNs in this context is to optimize the desired response by accurately predicting the effects of various input variables. This capability makes ANNs exceptionally well-suited for applications in electrospinning, where numerous parameters must be finely adjusted to achieve optimal nanofiber characteristics.

Table 2 A detailed review of using ML models for predicting the fiber diameter of electrospun nanofibers
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From many studies explored, Faridi-Majidi et al. [33] investigated to evaluate the primary factors swaying the fiber diameter of nylon-6, 6 electrospun nanofibers. In their research, they utilized ANNs as the ML model. The study incorporated four key process parameters—polymer concentration, needle-to-collector distance, solution feed rate, and applied voltage—as input process parameters, with the resulting fiber diameter serving as the output. The ML model generated in this study facilitated an in-depth exploration of the intricate interactions among the input variables and their impact on fiber diameter. Findings from this assessment revealed that the solution feed rate and polymer concentration emerged as significant factors influencing fiber diameter, exhibiting inverse and direct relationships, respectively. Conversely, the needle-to-collector distance and applied voltage were found to exert minor but direct effects on fiber diameter. Upon employing the ANNs model, the dataset yielded an optimal predictive model with R2 values of 0.92 and 0.91 for the training and test datasets, respectively. The R2 metric serves as an indicator of the predictive accuracy of the ML model. Given the intricate and highly complex relationships between process parameters and the fiber diameter of electrospun nanofibers, these R2 values signify the successful training of the model, thereby demonstrating its efficacy in capturing the underlying patterns within the data.

In another study, Khatti et al. [175] introduced the ANNs model with the aim of predicting the fiber diameter of PCL derived from the electrospinning technique. This study focused on evaluating key process parameters such as polymer concentration, applied voltage, and needle-to-collector distance. Utilizing the backpropagation algorithm, the ANNs model was designed and trained through sets of input–output patterns to capture the intricate relationships within the data effectively. The R correlation coefficient values for these sets were found to be 0.987, 0.989, and 0.998, respectively, indicating a solid fit between the predicted and observed values. It is evident from the plot that the MSE of the network exhibits a decreasing trend, suggesting that the network is effectively learning and improving over time. The ANNs model exhibited a remarkable performance with an R2 value of 0.97 and RMSE of 3.81, affirming its effectiveness in accurately predicting the PCL fiber diameter. Additionally, the model yielded an MAE of 14.58, further demonstrating its predictive capability. As shown previously, Table 2 presents a comparative overview of RMSE values reported across various studies, providing context for the model’s performance. RMSE, a critical assessment metric quantifying the disparity between model or statistical estimator predictions and actual values, always emerges as a comparative parameter in the majority of studies [176]. It is noted that the diversity in MAE, MSE, and RMSE values stems from various influential factors, including the size and composition of the dataset, the specific type of data employed, and the intricacies of the ML algorithmic methodologies utilized in the analytical process. Hence, the observed variations in MAE, MSE, and RMSE values emphasize the interplay of these factors in shaping the outcomes of the analyses.

Moreover, various configurations of ANNs models were examined to predict the fiber diameter resulting from various solutions, including polyvinyl alcohol, PVA/chitosan (CS), and PVA/aloe vera (AV). The experimental diameters of the electrospun nanofibers spanned a range from 93.52 to 352.1 nm. The input process parameters involved the solution feed rate, applied voltage, solution viscosity, and conductivity. Among the various configurations of ANNs models, the best prediction outcome emerged from the ANNs model featuring three hidden layers. The calculation of R2 yielded values of 0.96, 0.98, and 0.98 for ANNs models equipped with one, two, and three hidden layers, respectively. The analysis revealed that employing ANNs configuration featuring more than three hidden layers did not enhance the accuracy of predicting the fiber diameter of electrospun nanofibers. Regarding MSE, the optimal configuration for predicting fiber diameter using the test dataset was identified as 4-8-16-5-1, comprising three hidden layers, with an MSE value of 0.03. The ANNs predicted a fiber diameter that deviated by 3.79% from the experimental data obtained through scanning electron microscopy for the 4-8-16-5-1 configuration. This substantiates the dependability of the ANNs model with three hidden layers, facilitating the refinement of polymer, solvent, and solution concentration combinations in preliminary phases to streamline the experimentation process prior to electrospinning [35].

Additionally, Premasudha et al. [34] introduced a more intricate ANNs model explicitly designed to predict the fiber diameter of electrospun nanofibers based on polysaccharides (Hylon VII starch). The input layers of the model comprised four neurons involving polymer concentration, solution feed rate, applied voltage, and needle-to-collector distance. Meanwhile, the output layers comprised two neurons, representing fiber diameter and quality classification, which included categories such as good, regular, and bad. Understanding the intricate and nonlinear relationship between fiber diameter and quality in relationship to process parameters is essential for accurate prediction. The ANNs model underwent training utilizing a backpropagation algorithm within its hidden layers, utilizing a learning rate set at 0.4. The ideal configuration involved two hidden layers, with eight neurons present in each layer, resulting in a configuration represented as 4-8-8-2. The outcomes of this configuration revealed an impressive classification accuracy of 93.9% and a prediction accuracy of 95.2%. Lowering the solution feed rate, reducing the polymer concentration, and increasing the applied voltage were found to enhance the production of smaller-diameter nanofibers with superior quality.

Salehi et al. [177] utilized the ANNs model to optimize the properties of electrospun polyacrylonitrile/poly (vinylidene fluoride) (PAN/PVdF) nanofibers. This ANNs model was constructed to predict both the fiber diameter and its standard deviation in electrospun nanofibers. The electrospinning technique was employed to produce PAN/PVdF nanofibers, enabling the establishment of a quantitative correlation between specific process parameters (such as applied voltage, solution concentration, and PVdF concentration) and the resulting fiber diameter. The fiber diameter of the produced nanofibers ranged from 116 to 379 nm. Observations suggest that the fiber diameter tends to decrease with higher PVdF concentration and increase with greater solution concentration. Interestingly, the applied voltage appeared to have a negligible impact on the fiber diameter. The most optimal configuration of the ANNs model is comprised of two hidden layers, each containing five neurons (structured as 3-5-5-3). Khanlou et al. [178] conducted a study focusing on electrospun nanofiber mats, recognizing that fiber diameter plays a crucial role in determining the mechanical, electrical, and optical properties of these mats. Specifically, this study investigated the impact of various process parameters on the fiber diameter of electrospun polymethyl methacrylate (PMMA) nanofibers. Consequently, a three-layered ANNs model was formulated and employed to predict the diameter of PMMA fibers. The R2 value between the outputs and targets for the fiber diameter response was 0.99661 for the ANNs model, which indicates a good fit.

In another investigation by Kalantary et al. [26], efforts were made to create both the ANNs model and MLR methods for forecasting the diameter of poly (3-caprolactone)/gelatin (PCL/Gt) nanofibers. Independent variables included different processing parameters such as weight ratio, applied voltage, solution feed rate, and needle-to-collector distance, while the fiber diameter was considered the dependent variable in the ANNs model. The entirety of the samples (761 in total) was randomly segregated into three distinct subsets to conduct an assessment. The training dataset comprised 457 samples, the validation dataset encompassed 152 samples, and the test dataset comprised the remaining 152 samples. The outcomes obtained from the ANNs model’s predictions, particularly its high accuracy (R2 = 0.959) when contrasted with the MLR results (R2 = 0.564), clearly indicate that this ANNs model outperformed in predicting the fiber diameter of PCL/Gt electrospun nanofibers. Figure 5 illustrates the scatter plot showing a comparison between the output generated by the ANNs model and the observed values for predicting the diameter of nanofibers, including data from the training, validation, test, and overall datasets. Notably, the R2 value between the ANNs output and the target values for predicting the nanofiber diameter demonstrates a high degree of correlation. Through the sensitivity analysis conducted on the ANNs model, it was found that the weight ratio, applied voltage, solution feed rate, and needle-to-collector distance exhibited the most substantial influence on predicting fiber diameter.

Figure 5
figure 5

Reproduced from reference [26]. Copyright 2020, Springer Nature.

Scatter plots illustrating the comparison between output values predicted by the ANNs model and observed values for predicting the diameter of PCL/Gt nanofibers across different datasets: a Training, b Validation, c Test, and d all [26].

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Ma et al. [179] conducted a separate investigation centered on the electrospinning process of PAN nanofibers, exploring various processing scenarios. The ANNs model was used to analyze the relationship between the electrospinning process parameters and the resulting fiber diameter of PAN nanofibers. The process parameters, including polymer concentration, applied voltage, needle-to-collector distance, and solution feed rate, were fed into the model along with the fiber diameter data. This analysis aimed to provide insight into the interplay between these parameters and the resulting fiber diameter of the nanofibers. The findings suggest that among the electrospinning parameters studied, polymer concentration exerts the most substantial impact on the fiber diameter of PAN nanofibers. Notably, the ANNs model exhibited an exceptional level of accuracy, as evidenced by its R2 value nearing 1 for the training set, alongside R2 values of 0.908 and 0.979 for the validation set and the comprehensive dataset, respectively.

Furthermore, the fitting curve between the predicted and target values displayed a remarkable alignment, highlighting the model’s outstanding predictive ability. The R correlation coefficient value serves as an indicator of the degree of fit of the ANNs model concerning the association between the different parameters and the dependent variable, which in this case is the nanofiber diameter. By iteratively adjusting the weights and training the model, as depicted in Figure 6, the ANNs model demonstrated a strong level of alignment with the training dataset, as evidenced by a fit coefficient close to 1. Additionally, the model exhibited a fit coefficient of 0.95287 for the validation set and 0.98952 for the complete dataset, indicating its robust performance across different sets of data.

Figure 6
figure 6

Reproduced from reference [179]. Copyright 2023, MDPI.

Scatter plots of comparison between ANNs model predicted and observed diameters of PAN nanofibers for different sets of data: a Training, b all, and c validation [179].

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Additionally, Roldán et al. [180] fabricated electrospun nanofibrous scaffolds designed for biomimetic vascular implants, enhancing the manufacturing process through the utilization of two ML techniques in combination with statistical methodologies. The scaffolds, which were produced using polyvinyl alcohol, underwent optimization by modifying multiple process parameters, such as polymer concentration, solution feeding rate, applied voltage, collector type, needle size, distance between needle and collector, and rotations of the mandrel. The ANNs model displayed comparable prediction outcomes (R2 = 0.91); nevertheless, when it came to nonparametric circumstances, the ANNs model proved to be the most effective tool, having an MSE value of 0.0001943. Conversely, the MLR model showcased the least accuracy in its predictions (R2 = 0.6).

Based on the studies mentioned above, the ANNs is the most applied ML model for predicting the fiber diameter of electrospun nanofiber. It has been proven to be a powerful tool for modeling electrospinning processes for the prediction of fiber diameter. The distinctive enticement of this model lies in its specific structural characteristics and capacity to adapt and learn from the available data. The ANNs are known for their adeptness in addressing challenges considering nonlinear multivariate regression-based models. The principal benefit of the ANNs is the absence of a prerequisite for a predetermined specification of a suitable fitting function—a feature inherent to the ANNs. In addition, this model demonstrates extensive estimation credentials, requiring a greater number of experiments to construct an adequate model. Nonetheless, the efficiency of the ANNs remains notable even when confronted with limited data and patterns, provided that the data is statistically distributed during the training process and input phases.

Consequently, it becomes apparent that the trial data harnessed by various models should be sufficient for the formulation of a robust and effective ANNs model. Following this observation, conceived ANNs models can be preserved and employed as an estimation tool for optimizing independent variables, thereby mitigating errors and rectifying responses. ANNs serve as powerful tools for discerning patterns and identifying complex trends that may elude human observation or other conventional computer procedures. Presently, numerous ANNs models have gained recognition for their efficacy in addressing a vast range of prediction patterns. However, despite the numerous advantages of ANNs, encompassing their capacity for adaptive learning and adept problem-solving in complex scenarios, several recognized limitations accompany their application. These include their “black box” nature and susceptibility to overfitting [196].

Other machine learning models for predicting the fiber diameter of electrospun nanofibers

ML will remain an essential component in advancing scientific knowledge and understanding in the foreseeable future. As the volume of data generated and captured continues to increase, ML stands poised to revolutionize engineering design and serve as a more accurate predictor of experimental outcomes. Various other branches of engineering have recognized the immense potential of ML and are already embracing its adoption. The utilization of ML in biomedical research holds promise for scientists and researchers, offering them a potent tool to discern intricate patterns within vast datasets. This capability empowers the expeditious advancement and customization of outputs, facilitating the creation of tailored solutions geared toward individualized or personalized applications [197]. Within the domain of ML, data is of paramount significance and carries a substantial influence on the algorithm selection process because the sheer volume of data can slow down the accurate and logical evaluation of specific algorithms. In addition, time emerges as a critical consideration for ML users, mainly when dealing with extensive datasets. The difficulties in data analysis accumulate as the dataset increases. Under some ML algorithms, the data size can pose challenges in terms of both accurate evaluation and computational efficiency. Hence, the selection of an algorithm commensurate with the dataset’s size is of paramount importance.

Given its unique attributes, the ANNs are frequently endorsed by numerous researchers as a pertinent model for predicting target resistance. However, the computational demands of the ANNs are substantial, requiring a considerable amount of time for the iterative tuning process to reach its foremost objective [198]. Another potential drawback associated with the ANNs pertains to the backpropagation process. This error-propagation algorithm employs a gradient descent approach to modify synaptic weights. The gradient descent algorithm navigates along the negative slope of the error, taking incremental steps (determined by the learning rate) to converge toward the optimal value. The optimal value corresponds to the point where the slope of the error becomes zero. Achieving minimal error is based on ascertaining a suitable learning rate. In many real-world applications, the task of identifying the optimal learning rate proves challenging. Opting for a low learning rate introduces the risk of the algorithm becoming ensnared in local minima during the optimization process. Given that local minima share characteristics ideal to the original minimum, within these regions, the slope of the error becomes zero, and the algorithm erroneously perceives it has attained the optimal value. Consequently, the network may not undergo proper training. Conversely, opting for a substantial learning rate may induce erratic behavior in the network, rendering it unstable and thereby impeding convergence and effective training [199].

In addition to ANNs, linear regression algorithms stand out as a frequently employed ML model. LR algorithms offer a few advantages, characterized by their straightforward model structure and efficient training process, mainly when applied to linearly separable datasets. However, these algorithms encounter challenges when confronted with nonlinear datasets and datasets containing complex features similar to those in the electrospinning process dataset. These limitations underscore the need for more versatile ML approaches capable of accommodating the intricacies inherent in such datasets.[200]. When compared with LR, SVR algorithms offer distinct advantages, particularly in handling nonlinearly separable datasets. This efficacy stems from the capability of SVR to project data from the original feature space into a higher-dimensional space through the utilization of kernel functions. Moreover, SVR typically necessitates a smaller training dataset size to attain a commendable level of accuracy, making it an appealing choice for scenarios where data availability is limited. One limitation of SVR lies in its sensitivity to the selection of kernel functions: an unacceptable kernel function can result in training failure. [201]. Moreover, SVR exhibits reduced training efficiency when confronted with massive datasets, posing a challenge in handling large-scale data. In contrast, GB regression emerges as an alternative, with the ability to effectively handle nonlinearly separable datasets and surpass the capabilities of SVR and LR in this regard. In the process of training ML models, GB regression involving methods like XGBoost and AdaBoost can be effectively utilized to enhance both the training efficiency and robustness of the model. This augmentation is particularly beneficial when predicting the target properties of electrospun nanofibers. Numerous studies within materials science have explored the prediction of target properties in manufactured materials, consistently demonstrating that GB regression models yield superior outcomes compared to ANNs models [202, 203]. The challenge associated with GB regression models primarily arises from their complexity, which consequently leads to a surge in computational time required for training and inference tasks. Considering these concerns, adaptive neuro-fuzzy inference system (ANFIS) models emerge as a viable alternative, harnessing the synergistic potential of fuzzy logic (FL) reasoning and ANNs learning capabilities [204].

Challenges and future directions

Gathering accurate and comprehensive data on electrospinning-related process parameters and fiber diameter is crucial. However, it is essential to note that existing datasets pertaining to electrospinning process parameters and fiber diameter remain relatively small in scale, often lacking standardization in characterization methods, and they are not readily accessible to the public. Variability in data collection processes, equipment, and measurement techniques can introduce noise into the datasets and can lead to suboptimal results. Hence, the expansion of ML models to predict the target fiber diameter of electrospun nanofibers needs a change in the approach to data curation. A determined effort toward more deliberate data curation by academic journals or increased sharing of data by scientists and researchers holds the potential to broaden the horizons of ML. This proactive approach to data accessibility can bypass the need to resort to ethically uncertain methods such as web scraping to extract data. Standardization pertaining to the characterization, analysis, and presentation of electrospinning-related process parameters has the potential to facilitate the aggregation of larger datasets. This standardized approach would streamline data collection efforts, rendering the accumulation of comprehensive datasets more achievable. It is crucial to recognize that the selection of features, particularly the process parameters inherent to electrospinning, plays a pivotal role in determining the accuracy and efficacy of ML models. Presently, manual feature engineering, which involves filtering features, is commonly reliant on the researcher’s expertise and intuition. However, this method is susceptible to potential drawbacks, such as overlooking crucial features and potentially inducing overfitting, thereby compromising the model’s ability to generalize unseen data well. Conversely, automated feature engineering offers a promising solution to this predicament. By autonomously generating new candidate features from the data and subsequently selecting the most relevant ones for model training, automated feature engineering has the potential to address the current challenges associated with manual feature engineering effectively. Despite notable advancements, there remain several limitations in the utilization of ML for predicting the target fiber diameter of electrospun nanofibers. Considering these limitations, the following suggestions are offered as potential avenues for future research endeavors:

  • There is an opportunity for further refinement and enhancement of ML models to serve better the specific demands of predicting the target fiber diameter of electrospun nanofibers, which includes enhancing their ability to maintain high levels of accuracy and efficiency in learning and training, especially when dealing with datasets containing intricate features. Additionally, exploring combinations of diverse ML algorithms for data preprocessing could prove advantageous. Such approaches can contribute to improving the accuracy of ML models and optimizing decision-making processes in this domain.

  • ML models hold potential for broader application across various domains beyond their current scope. While existing research has predominantly concentrated on developing ML models for predicting the fiber diameter of electrospun nanofibers, numerous other areas remain ready for exploration and investigation. These include the development of mathematical and physical-based models, analysis of degradation mechanisms, detection of failures, and elucidation of the relationships between micro or nanoscale material attributes and macro-scale performance. Exploring these avenues could yield valuable insights and advancements in diverse fields beyond nanofiber prediction. Numerous challenges in areas such as mathematical modeling, experimental analysis, and numerical simulations often pose formidable obstacles to traditional approaches.

  • ML models can be integrated with other methodologies, such as experimental techniques and numerical simulations; a synergistic approach can be adopted in the development of predictive models for determining the target fiber diameter of electrospun nanofibers. As an illustration, ML can serve as an intermediary tool for processing both experimental and numerical data. This intermediary role aids in informing the design of subsequent experiments or simulation strategies, thereby mitigating the need for redundant experimentation or simulations and expediting the overall development process.

Conclusion

This review explores the use of ML in materials science, specifically in predicting the target fiber diameter of electrospun nanofibers. Electrospinning, due to advancements in nanotechnology, has gained traction across various sectors, notably biomedicine. Electrospinning offers unique characteristics, allowing scientists and researchers to manipulate nanofiber diameter and morphology by adjusting process parameters. However, the impact of these parameters remains debated, posing limitations. ML has emerged as a potent tool to address these challenges, predicting crucial properties for a wide range of applications. This review outlines electrospinning fundamentals, emphasizing process parameter significance. Additionally, it discusses the overview and workflow of ML, along with an introduction to commonly employed algorithms and their application in predicting fiber diameter. Most research favors ANNs due to their popularity in ML and frequent use in materials science. This review suggests that ML models with superior updating capabilities and adeptness in analyzing extensive datasets tend to perform better when assessing experimental data. When selecting a model for predicting the fiber diameter of electrospun nanofibers, various criteria should be evaluated, with a focus on the correlation between electrospinning-related parameters and nanofiber properties. For nonlinear relationships, models like ANNs are preferred due to their commendable performance. Additionally, leveraging GB regression techniques such as XGBoost, AdaBoost, LightGBM, and CatBoost can enhance prediction accuracy and computational efficiency. Hybrid ML models, though requiring longer computation times, offer precise outcomes with large datasets, making them optimal for accurately predicting the fiber diameter of electrospun nanofibers. Expanding ML applications to predict various properties of electrospun nanofibers across different fields holds promise for future scientific research. The integration of ML in materials science and engineering is still in its early stages, indicating vast potential for future innovations.