Optimization of Electrospun PCL–PLGA Substrates for Lung Basement Membrane Applications Using Response Surface Methodology and Machine Learning Approaches

Abstract

Electrospun membranes are widely used in tissue modeling because their tunable fibrous architecture can capture key structural features of the extracellular matrix of native tissues. For functional in vitro lung barrier models, membrane substrates should ideally combine stability and reproducibility with basement-membrane-relevant features, including fine fibers, reduced stiffness, and sufficient strength and extensibility to tolerate breathing-mimetic deformation. Here, poly­(ε-caprolactone) (PCL)–poly­(lactic-co-glycolic acid) (PLGA) blends were optimized to develop fully synthetic electrospun membranes that balance these competing structural and mechanical requirements. Response surface methodology (RSM) was first applied to a Box–Behnken electrospinning design, in which fiber diameter, Young’s modulus, ultimate tensile strength (UTS), and strain at break were treated as coequal responses. The model predicted membranes with a fiber diameter of 0.386 ± 0.004 μm, Young’s modulus of 152.156 ± 1.751 MPa, UTS of 41.850 ± 0.149 MPa, and strain at break of 2.948 ± 0.020, with confirmatory experiments deviating by less than 10% from predicted values. Machine learning (ML) extended this experimentally anchored framework by adding validated augmentation, inverse property-to-parameter prediction, and multiresponse desirability optimization. A six-generator fidelity screen selected Gaussian-Copula augmentation over WGAN-GP for downstream modeling, while leakage-free leave-one-real-observation-out evaluation showed that CatBoost most robustly recovered the polymer-composition targets, with (leave-one-out) LOO R ² values of 0.675 for PCL concentration and 0.747 for PLGA concentration. XGBoost forward-surrogate optimization achieved the highest model-derived desirability at 0.895 ± 0.065, compared with 0.782 for the experimentally confirmed design of experiments reference. Overall, the workflow demonstrates that ML can complement RSM by prioritizing candidate electrospinning windows, quantifying uncertainty, and clarifying property-to-parameter coupling in multiresponse fibrous membrane design.

1. Introduction

Electrospun materials have been widely used in tissue engineering due to their ability to replicate the fibrillar architecture and topography of the extracellular matrix (ECM). , These nanofibrous membranes offer a highly porous nature and interconnected pore structure, facilitating the efficient transport of oxygen, nutrients, and waste. Additionally, the nanofibers significantly enhance cell adhesion, proliferation, and differentiation by providing meso-, micro-, and nanoscale patterns to which cells are sensitive. Optimizing the topographical, physical, and mechanical features of electrospun membranes is essential to effectively mimic the natural tissue microenvironment. The mechanical properties of the ECM, including substrate stiffness, play a crucial role in regulating cell behavior. Relevant mechanical properties promote optimal cell attachment, proliferation, differentiation, and tissue-specific functionality. Moreover, in the context of bioengineered implants, mimicking the mechanical properties facilitates the seamless integration of the engineered construct with the native tissue, ensuring harmonious interaction and functionality with adjacent tissues. The ECM in the alveoli of the lung, referred to as the basement membrane (BM), is a dense, thin nanofibrous layer situated between the alveolar epithelium and capillary endothelium. It provides structural support and functional integrity, acts as a selective barrier, and plays a key role in cell signaling and filtration. The BM’s filtration properties, primarily due to its net-like structure, regulate the movement of molecules, ensuring that only appropriate substances pass between the alveolar space and the bloodstream. In addition to its structural and filtration roles, the BM significantly influences cell behavior through its interaction with cell surface receptors, affecting crucial cellular processes. − The BM layer is composed of superfine fibers with diameters up to 100 nm. The pore size has not been extensively characterized; however, it has been reported that the BM layer contains a large fraction of small pores with diameters of less than 2.5 nm and a smaller fraction of bigger pores with diameters around 0.4 μm. − Nonetheless, in the design of commercial membranes for lung models, pore sizes of 3 to 8 μm are usually considered, particularly for the transmigration of immune cells, which is crucial for immunological studies. Moreover, the alveolar BM shows an elastic modulus of 3 MPa and strength against cyclic stretching tensile forces induced by breathing with elastic elongation up to 12% linear strain.

Recapitulating the diverse cues of the native BM in vitro is challenging, involving tailoring the biochemical, biophysical, topographical, and mechanical properties of electrospun membranes by tuning the fabrication process parameters. In electrospinning, these parameters include solution concentration, polymer molecular weight, solvent system, applied voltage, flow rate, nozzle-to-collector distance, collector unit, and ambient conditions.

A number of studies have modeled the dependence of the fiber diameter on the electrospinning process parameters using design of experiments (DoE) approaches, i.e., response surface methodology (RSM). − While DoE-RSM provides a structured and statistically efficient approach for identifying parameter–response relationships, many electrospinning studies using this approach remain centered on forward prediction and optimization within the experimentally defined design space. DoE is a systematic approach to optimizing experimental frameworks using statistical methods. However, its applicability can be limited since the R ² value, which measures how well the model fits the data, is derived from the same data set used for model development. − This means that while DoE may fit the experimental data well, it does not ensure that the model will generalize effectively to new or diverse experimental conditions.

Machine learning (ML) approaches, on the other hand, often include techniques such as data augmentation and the use of separate test data sets to evaluate model performance on unseen data, thereby enhancing the model’s generalizability. By capturing complex, nonlinear relationships between variables, ML models can complement DoE by providing predictive power that extends beyond the initial experimental data. , Recent work has highlighted the increasing role of ML in electrospinning, particularly for analyzing process–property relationships, reducing trial-and-error experimentation, and guiding the fabrication of electrospun nanofibers with targeted properties. ML-based optimization has also been applied to identify electrospinning conditions for user-defined target fiber diameters, demonstrating the value of data-driven approaches for parameter selection. When integrated with DoE, ML can optimize the experimental design process, reduce the risk of overfitting, and improve the model’s ability to predict outcomes in diverse experimental settings, making the combined approach more robust and adaptable.

Prior studies have demonstrated the potential of combining ML with DoE for predicting specific outcomes in electrospinning processes. − Research in this area has focused mainly on the prediction of the diameter of electrospun fibers. For example, Pervez et al. introduced a new regression method named Locally Weighted Kernel Partial Least Squares that effectively predicted the diameters of electrospun chitosan-based nanofibers using limited, nonlinear data sets. Similarly, Kalantary et al. used artificial neural networks to precisely estimate the diameters of poly­(ε-caprolactone) (PCL) and gelatin nanofibers, demonstrating the effectiveness of ML in analyzing diverse data sets. More recently, Badaraev et al. compared Box–Behnken design (BBD), traditional ML, and deep learning for predicting fiber diameter and tensile strength in electrospun scaffolds. Recent web-based ML tools have also been developed for electrospun nanofiber diameter prediction and fiber-diameter-distribution prediction.

However, within combined DoE–ML electrospinning studies, the focus has remained largely on single-output prediction, particularly fiber diameter. Comparatively fewer studies have applied this combined strategy to predict and optimize multiple membrane properties, including both morphological and mechanical responses, or to perform inverse prediction from desired membrane properties back to processing parameters.

Recent studies have begun to broaden this scope. Roldán et al. applied ML to simultaneously predict the morphology, topography, and mechanical properties of gelatin-based electrospun scaffolds, providing one of the closest published analogues to the multiresponse framework adopted in the present study. In related work, the same group used ML to mechanically assess two- and three-dimensional biomimetic electrospun scaffolds while explicitly considering the balance between predictive accuracy and interpretability, a concern directly relevant to the feature-attribution analysis implemented here. They further extended ML-based optimization to the manufacture of electrospun nanofibrous structures, focusing on the control of fiber diameter and interfiber separation. More recently, FibreCastML was introduced as a distribution-aware platform for predicting full electrospun fiber-diameter distributions rather than mean values alone. Multiobjective strategies have likewise been applied directly to mechanical performance; for example, Yang et al. used multiobjective Bayesian optimization to tune electrospun piezoelectric yarns toward simultaneously higher tensile strength and failure strain. These studies establish multiproperty prediction and ML-guided optimization as viable directions, yet they remain largely forward in orientation, predicting properties from fixed processing conditions rather than inferring conditions from desired targets.

Inverse design, in which predefined material or scaffold targets are mapped back to feasible processing conditions, has only recently begun to emerge in electrospinning. Roldán and Sabir introduced SpinCastML, an open-source, distribution-aware and chemistry-informed ML platform that couples structured sampling with an inverse Monte Carlo engine to identify polymer–solvent and processing parameter combinations capable of achieving user-defined fiber outcomes. This represents the closest available electrospinning analogue to the property-to-parameter inversion pursued in the present study; however, its inverse-design objective is centered primarily on fiber-diameter distributions, whereas the present work extends inverse prediction to combined morphological and mechanical membrane targets.

These limitations motivate the present study, in which a structured DoE data set was combined with ML-based inverse modeling to guide PCL–poly­(lactic-co-glycolic acid) (PLGA) membrane design across multiple structural and mechanical responses relevant to lung-on-chip BM applications. Rather than treating fiber diameter as the sole optimization target, the workflow considers fiber diameter, Young’s modulus, ultimate tensile strength (UTS), and strain at break simultaneously, enabling property-to-parameter prediction within the experimentally defined PCL–PLGA design space. The aim of this study was, therefore, to establish an application-specific DoE–ML workflow for guiding the design of electrospun PCL–PLGA membranes for lung-on-chip BM applications, with simultaneous consideration of membrane properties.

The PCL–PLGA blend was selected to provide a stable, reproducible, and fully synthetic electrospun membrane for lung-on-chip BM modeling. PCL contributes electrospinnability, flexibility, and mechanical resilience under breathing-mimetic deformation, , while PLGA improves the cell–material interface by modulating surface chemistry and supporting adsorption-mediated cell attachment, without requiring additional ECM protein coatings, resulting in a tunable, coating-free fibrous platform for an alveolar model. ,

The present study provides three specific contributions: multiresponse optimization of fiber diameter, Young’s modulus, UTS, and strain at break within a PCL–PLGA membrane system; property-to-parameter inverse modeling to identify candidate processing conditions from desired membrane characteristics; and exploratory data augmentation to support model benchmarking in a small experimental data set.

To implement this framework, we first utilized the RSM to systematically investigate the effects of key electrospinning parameters, PCL and PLGA solution concentrations, flow rate, and working distance, on the target membrane properties. This DoE approach enabled significant parameter–property relationships within the experimental space to be identified and initial optimization models to be derived. The membrane properties were optimized toward basement-membrane-relevant design criteria by minimizing fiber diameter and Young’s modulus while maximizing UTS and strain at break within the experimentally accessible PCL–PLGA electrospinning design space.

However, recognizing the inherent limitations of traditional DoE, particularly its constraint to predefined experimental ranges and difficulty capturing complex nonlinear relationships outside the tested parameter space, we developed a two-stage ML enhancement strategy. First, we employed a Wasserstein generative adversarial network with gradient penalty (WGAN-GP) to generate synthetic data for exploratory model benchmarking within the experimentally defined design space. WGAN-GP was selected because the gradient penalty improves training stability compared with standard Wasserstein GAN training. The generated data were not treated as independent experimental evidence, as synthetic samples preserve statistical patterns from the original data set but do not introduce new physical information. Subsequently, we benchmarked multiple ML approaches, including Random Forest Regression, Support Vector Regression, and Multi-Layer Perceptron Neural Network (MLP-NN), to identify optimal algorithms for different aspects of the parameter–property relationships. This comprehensive approach leverages the complementary strengths of both methodologies: DoE’s systematic experimental design principles combined with ML’s capacity for nonlinear pattern recognition and extrapolation. Figure presents a schematic representation of this integrated workflow, illustrating how the combined approach achieves more robust and comprehensive optimization than either method alone.

1.

Schematic representation of the structured workflow used in this study, outlining the key steps, including input parameters (flow rate, working distance, PCL and PLGA concentrations), measured responses (Young’s modulus, fiber diameter, strain at break, and UTS), and ML steps, including (1) data processing, (2) features and target definition, (3) test and train split into 80% and 20%, (4) model benchmarking and selection, (5) parameter tuning using cross-validation grid search, and (6) prediction of the factors and the evaluation of the model used for each factor.

2. Experimental Section

2.1. Materials

PCL (Mw of 80,000 g/mol) and 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP) were obtained from Sigma-Aldrich (Arklow, Ireland). PLGA 50–50 was purchased from Ashland Specialties Ireland Ltd. (Dublin, Ireland). All reagents were of analytical grade and were used as received.

2.2. Electrospinning

Solutions of PCL and PLGA in HFIP were prepared using the concentration specified by the DoE study design. The selection of HFIP as the solvent for all formulations was based on preliminary solvent-screening experiments and prior studies published by our group, , in which dichloromethane/N,N-dimethylformamide, tetrahydrofuran/N,N-dimethylformamide, and HFIP were evaluated. The solutions were mixed on a stirring plate for 24 h at room temperature (21 ± 2 °C). PCL/PLGA mixture solutions were prepared by mixing PCL and PLGA solutions at a ratio of 1:1 v/v. The solutions were then mixed for a further 2 h to achieve a homogeneous mixture. The basic electrospinning setup with a flat collector was used in this study. The prepared solutions were added to a 20 mL glass syringe with a 20 G attached stainless steel blunted needle. Aluminum plates, 100 mm square with a thickness of 0.25 mm (Goodfellow, UK), were used as the collector targets. A positive bias was applied to the solution via a voltage source, and an electrical ground connection was attached to the rear surface of the plate. A high voltage probe (Radionics, Ireland) was used to ensure a correct voltage bias was achieved. A syringe pump (KDS, US) was used to dispense the polymer solution at a controlled flow rate from the capillary. All electrospinning experiments were conducted within a fume hood cabinet to extract evaporating chemicals. The electrospinning process was conducted at a fixed voltage of 15 kV, fixed PCL MW of 80,000 g/mol, and under controlled environmental conditions (21 ± 2 °C and 60–65% relative humidity).

2.3. Measurement and Characterization

2.3.1. Morphology and Fiber Diameter

The surface morphology of the electrospun fibers was examined by scanning electron microscopy (SEM) (EVO LS15 SEM). Samples were sputter-coated with gold prior to imaging and typically viewed with an acceleration voltage ranging from 10 to 15 kV. ImageJ (National Institutes of Health, USA) was utilized to measure the fiber diameters within the electrospun membrane (n = 100) from the recorded images (50 and 10 μm).

2.3.2. Mechanical Properties

Uniaxial tensile testing was conducted using a Zwick Z005 tensile test machine (Zwick-Roell, Germany) fitted with a 500 N load cell attached. Testing was carried out on “dogbone” specimens prepared using a custom-designed and manufactured stainless steel cutting die. The die consisted of a sample gauge length of 16 mm and a test width of 3.9 mm. Samples were punched from the electrospun membranes using the cutting die and a custom-built sample holder. The testing cycle consisted of an initial preload of 0.05 N to remove any slack from the sample, with the grip separation at this point used as the gauge length. Following this, the sample was elongated at a strain rate of 2 mm/min, with failure determined to occur when the force dropped to 80% of the max force value recorded.

2.4. Response Surface Methodology

2.4.1. Experimental Design

An RSM design consisting of a four-factor three-level BBD was designed using the statistical software package Design-Expert (version 12, Stat-Ease, Inc., Minneapolis, USA). Four independent variables were included in the study, namely, A: flow rate (ml/h), B: working distance (cm), C: PCL concentration (wt %), and D: PLGA concentration (wt %). These variables were studied at three different levels coded as −1, 0, and 1 (Table ). These factors and ranges were selected from preliminary electrospinning trials because they strongly influenced fiber morphology, fiber diameter, and membrane mechanical properties, while defining a stable processing window that produced consistent bead-free fibers and maintained solution processability. The average diameter of as-spun fibers (R1) (μm), Young’s modulus (R2) (MPa), UTS (MPa) (R3), and strain at break (R4) were selected as the responses of the system. Selected ranges were based on our preliminary results, aiming to develop membranes with high-quality fibers free of beads and defects.

1. Factors and Their Levels Used in the Experimental Design.

	parameters	unit	Level 1	Level 2	Level 3
A	flow rate	ml/h	0.1	0.3	0.5
B	distance	cm	10	12.5	15
C	PCL concentration	Wt %	4	6	8
D	PLGA concentration	Wt %	6	8	10

BBD design was selected for utilizing a quadratic response surface model, which included 29 experimental trials with 5 replicates at the center point. These 29 trials and the corresponding responses for each trial are represented in Table . The statistical computations were conducted in Design-Expert. Regression analysis was performed to fit the response as a function of the electrospinning parameters. In a system involving four independent variables, the relationship between the response and the 4 parameters is approximated by the quadratic polynomial model in eq .

$$Y={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2{+\beta }_3{X}_3+{\beta }_4{X}_4+{\beta }_{12}{X}_1{X}_2+{\beta }_{13}{X}_1{X}_3+{\beta }_{14}{X}_1{X}_4$$

$$+{\beta }_{23}{X}_2{X}_3+{\beta }_{24}{X}_2{X}_4+{\beta }_{34}{X}_3{X}_4+{\beta }_{11}{X}_1^2+{\beta }_{22}{X}_2^2+{\beta }_{33}{X}_3^2+{\beta }_{44}{X}_4^2$$ 1

where Y, Xi, β0, βi, βii, and βij are the predicted response value, the ith independent factor, the constant term, the linear effect term, the squared effect term, and the interaction effect term, respectively.

2. Experimental Design and Results of the BBD Design.

	factors				responses
run	A	B	C	D	R1	R2	R3	R4
	flow rate (ml/h)	working distance (cm)	PCL Conc (wt %)	PLGA Conc (wt %)	fiber diameter (μm)	Young’s Modulus (MPa)	UTS (MPa)	strain at break (−)
1	0.3	12.5	6	8	1.200	270.00	23.40	1.51
2	0.1	12.5	4	8	0.798	283.71	22.52	1.07
3	0.3	15.0	6	6	0.455	198.84	20.86	2.08
4	0.3	12.5	4	10	1.175	428.91	35.00	1.01
5	0.3	10.0	8	8	1.489	438.18	21.24	1.90
6	0.1	12.5	6	10	1.358	522.50	81.00	1.40
7	0.3	15.0	8	8	1.530	435.93	17.08	1.83
8	0.5	12.5	6	6	0.602	289.34	26.32	2.80
9	0.3	12.5	6	8	1.300	271.00	18.53	1.99
10	0.3	12.5	8	10	2.070	810.00	44.17	1.49
11	0.3	10.0	6	10	1.250	711.91	49.06	1.27
12	0.5	12.5	4	8	0.420	310.12	14.23	1.90
13	0.3	12.5	6	8	1.250	397.50	19.65	1.66
14	0.5	12.5	6	10	1.640	617.50	29.27	1.34
15	0.1	12.5	6	6	0.581	117.90	21.00	1.84
16	0.3	12.5	8	6	1.260	366.15	21.32	3.00
17	0.3	15.0	4	8	0.493	248.01	15.49	1.01
18	0.3	10.0	6	6	1.200	377.51	21.27	2.06
19	0.5	15.0	6	8	1.460	420.60	15.95	1.94
20	0.3	12.5	6	8	1.310	267.87	23.42	1.80
21	0.5	12.5	8	8	1.780	490.76	23.25	2.60
22	0.3	12.5	4	6	0.369	216.52	15.28	1.20
23	0.5	10.0	6	8	1.560	619.80	45.22	2.42
24	0.1	15.0	6	8	0.560	158.25	49.56	2.10
25	0.1	12.5	8	8	0.915	290.76	44.02	2.40
26	0.1	10.0	6	8	0.641	309.25	15.96	2.15
27	0.3	10.0	4	8	0.350	312.43	14.23	1.10
28	0.3	12.5	6	8	1.470	230.83	19.31	1.40
29	0.3	15.0	6	10	1.372	643.57	29.61	1.26

To validate and verify the models, diagnostic plots were analyzed. These included assessments of the normal probability of residuals, predicted versus actual values, residual versus predicted values, and standardized residuals versus run plots for all response models. These analyses ensured the reliability and robustness of the models, providing valuable insights into their adequacy for representing the data and identifying potential outliers.

ANOVA was performed to evaluate the significance of the model terms. Model terms with p-values below 0.05 were considered statistically significant at the 95% confidence level, while R ², adjusted R ², predicted R ²/PRESS, lack-of-fit testing, and effect size measures were used together to assess model adequacy and small-sample robustness.

2.4.2. Optimization

Following the development of functional relationships between the independent factors and the responses, optimization was carried out with the objective of identifying the parameters required to produce membranes with the lowest fiber diameter and Young’s modulus, and highest UTS and strain at break, according to BM-relevant membrane design criteria within the investigated PCL–PLGA design space. Table displays the lower and upper limits for the process parameters and corresponding response values for fibers fabricated using the optimal process parameters. Multiple response optimization employs a desirability approach, consolidating responses into an overall desirability function. Each response is scaled to a unit between 0 and 1, with values closer to 1 indicating higher desirability, and 1 signifying 100% desirability.

3. Criterion for Numerical Optimization with Respect to BM Properties.

name	goal	lower limit	upper limit
A: flow rate	in range	0.1	0.5
B: distance	in range	10	15
C: PCL concentration	in range	4	8
D: PLGA concentration	in range	6	10
average fiber diameter (μm)	minimize	0.35	2.07
Young’s Modulus (MPa)	minimize	117.9	810
UTS (MPa)	maximize	14.23	81
strain at break	maximize	1.01	3

3. ML Methods

3.1. Synthetic-Data Generation and Validation

The experimental design matrix and measured membrane responses were standardized before synthetic data modeling so that all variables were expressed on a common coded scale. Each variable (X) was transformed to the interval [-1, +1] using eq

$$X_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}=2[(X-X_{\min })/(X_{\max }-X_{\min })]-1$$ 2

where X is the original value and X__min and X__max are the minimum and maximum values observed for that variable within the experimental data set. Synthetic samples generated on the normalized scale were returned to the original experimental units using eq

$$X_{\mathrm{g}\mathrm{e}\mathrm{n}}=[(X_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}+1)/2](X_{\max }-X_{\min })+X_{\min }$$ 3

The original augmentation strategy used a WGAN-GP implemented in TensorFlow version 2.13. Fully connected generator and discriminator networks were trained using the Wasserstein objective with gradient penalty to stabilize training and enforce the Lipschitz constraint. The generator mapped noise vectors sampled from z ∼N (0, I) to synthetic electrospinning factor-response vectors, while the discriminator was trained to distinguish generated from experimental observations. The WGAN-GP was trained using the settings provided in Supplementary Table (Table S1), including the Adam optimizer, a learning rate of 1 × 10^–4, a batch size of 32, and 3000 training epochs. After training, 1000 synthetic samples were generated and rescaled to the original experimental units using eq .

In this workflow, WGAN-GP was retained as the original neural generator comparator rather than used automatically as the final augmentation source. This distinction is important because visual kernel-density overlays, summary statistics, and pairwise correlation matrices can demonstrate marginal similarity, but they do not establish preservation of the full joint distribution, exclude memorization, or demonstrate downstream predictive value on unseen experimental observations.

Generator selection was, therefore, treated as a separate validation step. Six candidate synthesizers were benchmarked under a common fidelity-and-utility battery: WGAN-GP, CTGAN, TVAE, multivariate kernel-density estimation (KDE), physics-informed RSM resampling, and a Gaussian copula with empirical marginals. The validation battery comprised (i) per-column two-sample Kolmogorov–Smirnov tests across the four electrospinning parameters and four measured responses; (ii) joint maximum mean discrepancy (MMD²) with permutation testing; (iii) a classifier two-sample test (C2ST), scored using held-out AUC; (iv) a nearest-neighbor memorization test comparing synthetic-to-real and real-to-real distances; and (v) train-on-synthetic/test-on-real (TSTR) R ² for each inverse target. Full generator-validation outputs are reported in Table S10 and Supporting Information (Figures S8,S9).

The Gaussian Copula with empirical marginals was selected as the canonical augmentation generator for downstream modeling because it provided the strongest joint-distribution fidelity and downstream utility while using a low-parameter representation appropriate for the small Box–Behnken data set.

3.2. Inverse ML Models and Leakage-Free Evaluation Framework

The inverse machine-learning task was formulated with the measured membrane properties as inputs and the electrospinning parameters as outputs. Specifically, fiber diameter, Young’s modulus, UTS, and strain at break were used as input features, while flow rate, working distance, PCL concentration, and PLGA concentration were treated as prediction targets. This property-to-parameter formulation was used to identify candidate processing regions corresponding to desired membrane-property profiles. It was not interpreted as a unique deterministic inverse solution, because multiple processing combinations can generate similar membrane properties within experimental uncertainty.

Two evaluation layers were used. First, the original 80/20 split on the combined real and synthetic pools was retained only as an exploratory augmented-pool benchmark. Second, and more importantly, all canonical performance claims were based on a leakage-free LOO protocol. In each LOO split, the held-out experimental observation was removed before fitting the Gaussian copula, generating synthetic data, selecting hyperparameters, or fitting the final predictive model (search ranges in Table S2). The held-out row, therefore, never entered the synthesizer, inner optimization loop, or model-training stage.

RandomForest, SVR-RBF, XGBoost, LightGBM, CatBoost, and MLP-NN regressors were evaluated. Hyperparameters were selected using an 80-trial Optuna search with 5-fold inner cross-validation inside each training fold. Model performance was assessed using R ² (eq ), mean absolute error (MAE) (eq ), and root-mean-square error (RMSE) (eq )­

$$R^2=1-\frac{\sum _{i=1}^n{(y_i-{ŷ}_i)}^2}{\sum _{i=1}^n{(y_i-{\mathrm{y̅}}_i)}^2}$$ 4

$$\mathrm{M}\mathrm{A}\mathrm{E}=\frac{1}{N}\sum _{i=1}^N|y_i-{ŷ}_i|$$ 5

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\sum _{i=1}^N\frac{{(y_i-{ŷ}_i)}^2}{N}}$$ 6

where y _i is ground truth, ŷ _i is the predicted value, y̅ _i is the mean of actual values, and N is the total sample. These metrics were interpreted together: R ² summarized explained variance, while MAE and RMSE retained the original units of each electrospinning parameter.

The MLP-NN was implemented as a complementary multioutput neural architecture with four membrane-property inputs, dense hidden layers using ReLU activation functions, and output nodes corresponding to the four electrospinning parameters. The MLP-NN model was included to test whether a dense nonlinear architecture recovered the same property-to-parameter relationships as the tree- and kernel-based models, rather than to claim MLP-NN superiority.

3.3. Uncertainty-Calibrated Inverse Prediction and ML Desirability Optimization

For inverse design, the best-performing inverse models were queried by using target membrane-property vectors. Because the inverse mapping is intrinsically nonunique, predictions were reported as uncertainty-calibrated candidate regions rather than single-point optima. A Gaussian-Copula-augmented conformalized quantile regression (Copula-CQR) ensemble was used to generate mean predictions, bootstrap standard deviations (std), and 90% split-conformal prediction intervals for each electrospinning parameter. The conformal calibration was performed on held-out real observations; therefore, the reported intervals quantify finite-sample uncertainty in the inverse predictions within the experimental design space.

To provide an ML analogue of the Design-Expert numerical optimization workflow, forward ML surrogates were also trained to predict the four membrane responses from electrospinning parameters. The same Derringer-Suich desirability criteria used in the DoE workflow were then applied: fiber diameter and Young’s modulus were minimized, while UTS and strain at break were maximized. For each ML family, the overall desirability was maximized over the bounded four-factor design space using differential evolution, and uncertainty was estimated by bootstrap refitting of the augmented training corpus. This analysis was used to compare the DoE boundary optimum with the interior regions favored by ML families under the same multiresponse objectives.

4. Results and Discussion

4.1. Response Surface Methodology

4.1.1. Data Analysis

The analysis of variance for the responses is summarized in Table . The Fisher F-test with a very low probability value (p > F = 0.0001) shows a high significance for the models generated for all the responses (eqs ,,,). Furthermore, the lack of fit p-values of >0.05 for all responses suggested that the obtained experimental data had a good agreement with the models and that the estimated models were able to fit the data. In addition to R ², adjusted R ², predicted R ²/PRESS diagnostics, effect-size interpretation, model-stability checks, and experimental confirmation were used to support the robustness and physical interpretation of the RSM analysis (Table S4 and Figure S7).

4. Analysis of Variance for the Response Surface Quadratic Model for Fiber Diameter, Young’s Modulus, UTS, and Strain at Break.

source	sum of squares	df	mean square	F-value	p-value	comment	R 2	A-R2	P-R2
R1
model	5.26	6	0.8760	18.04	<0.0001	significant	0.831	0.785	0.691
A-flow rate	0.5707	1	0.5707	11.75	0.0024
B-distance	0.0321	1	0.0321	0.6617	0.4247
C-PCL Conc	2.47	1	2.47	50.91	<0.0001
D-PLGA Conc	1.61	1	1.61	33.17	<0.0001
AC	0.3813	1	0.3813	7.85	0.0104
BD	0.1884	1	0.1884	3.88	0.0616
lack of fit	1.03	18	0.0570	5.48	0.0555	not signific
R2
model	7.446 × 105	14	53185.65	10.49	<0.0001	significant	0.913	0.825	0.582
A-flow rate	94652.45	1	94652.45	18.67	0.0007
B-distance	36728.28	1	36728.28	7.24	0.0175
C-PCL Conc	88765.76	1	88765.76	17.51	0.0009
D-PLGA Conc	3.917 × 105	1	3.917 × 105	77.26	<0.0001
AB	580.81	1	580.81	0.1145	0.7400
AC	7533.37	1	7533.37	1.49	0.2430
AD	1460.88	1	1460.88	0.2881	0.5999
BC	966.28	1	966.28	0.1906	0.6691
BD	3043.07	1	3043.07	0.6002	0.4514
CD	13393.43	1	13393.43	2.64	0.1264
A2	563.68	1	563.68	0.1112	0.7438
B2	27234.02	1	27234.02	5.37	0.0361
C2	7696.48	1	7696.48	1.52	0.2382
D2	90459.21	1	90459.21	17.84	0.0009
lack of fit	54710.70	10	5471.07	1.34	0.4163	not signific
R3
model	6071.05	15	404.74	28.97	<0.0001	significant	0.97	0.83	0.67
A-flow rate	711.97	1	711.97	50.96	<0.0001
B-distance	28.31	1	28.31	2.03	0.1782
C-PCL Conc	70.86	1	70.86	5.07	0.0422
D-PLGA Conc	782.30	1	782.30	56.00	<0.0001
AB	988.16	1	988.16	70.73	<0.0001
AC	38.94	1	38.94	2.79	0.1189
AD	813.68	1	813.68	58.24	<0.0001
BD	90.63	1	90.63	6.49	0.0243
A2	553.23	1	553.23	39.60	<0.0001
B2	0.1253	1	0.1253	0.0090	0.9260
C2	71.65	1	71.65	5.13	0.0413
D2	644.47	1	644.47	46.13	<0.0001
A2C	57.75	1	57.75	4.13	0.0630
A2D	91.22	1	91.22	6.53	0.0240
AB2	185.76	1	185.76	13.30	0.0030
lack of fit	159.31	9	17.70	3.18	0.1390	not signific
R4
model	7.45	14	0.5321	10.19	<0.0001	significant	0.91	0.82	0.59
A-flow rate	0.3468	1	0.3468	6.64	0.0219
B-distance	0.0385	1	0.0385	0.7378	0.4048
C-PCL Conc	2.93	1	2.93	56.11	<0.0001
D-PLGA Conc	2.26	1	2.26	43.31	<0.0001
AB	0.0462	1	0.0462	0.8850	0.3628
AC	0.0992	1	0.0992	1.90	0.1897
AD	0.2601	1	0.2601	4.98	0.0425
BC	0.0001	1	0.0001	0.0019	0.9657
BD	0.0002	1	0.0002	0.0043	0.9486
CD	0.4356	1	0.4356	8.34	0.0119
A2	0.8418	1	0.8418	16.12	0.0013
B2	0.0002	1	0.0002	0.0034	0.9542
C2	0.0327	1	0.0327	0.6261	0.4420
D2	0.0109	1	0.0109	0.2088	0.6547
lack of fit	0.5133	10	0.0513	0.9424	0.5754	not signific

Fiber Diameter (μm)

$$\mathrm{R}1=1.1+0.2181\mathrm{A}-0.0518\mathrm{B}+0.4539\mathrm{C}+0.3664\mathrm{D}+0.3088\mathrm{A}\mathrm{C}+0.217\mathrm{B}\mathrm{D}$$ 7

Young’s Modulus (MPa)

$$\mathrm{R}2=287.44+88.81\mathrm{A}-55.32\mathrm{B}+86.01\mathrm{C}+180.68\mathrm{D}+12.05\mathrm{A}\mathrm{B}+43.4\mathrm{A}\mathrm{C}-19.11\mathrm{A}\mathrm{D}+15.54\mathrm{B}\mathrm{C}+27.58\mathrm{B}\mathrm{D}+57.87\mathrm{C}\mathrm{D}+9.32{\mathrm{A}}^2+64.8{\mathrm{B}}^2+34.45{\mathrm{C}}^2+118.09{\mathrm{D}}^2$$ 8

UTS (MPa)

$$\mathrm{R}3=20.86-9.43\mathrm{A}-1.54\mathrm{B}-2.98\mathrm{C}+9.89\mathrm{D}-15.72\mathrm{A}\mathrm{B}-3.12\mathrm{A}\mathrm{C}-14.26\mathrm{A}\mathrm{D}-4.76\mathrm{B}\mathrm{D}+9.24{\mathrm{A}}^2+0.139{\mathrm{B}}^2-3.32{\mathrm{C}}^2+9.97{\mathrm{D}}^2+4.65{\mathrm{A}}^2\mathrm{C}+5.85{\mathrm{A}}^2\mathrm{D}+8.35{\mathrm{A}\mathrm{B}}^2$$ 9

Strain at break

$$\mathrm{R}4=1.67+0.17\mathrm{A}-0.0567\mathrm{B}+0.4942\mathrm{C}-0.4342\mathrm{D}-0.1075\mathrm{A}\mathrm{B}+(-0.1575)\mathrm{A}\mathrm{C}-0.255\mathrm{A}\mathrm{D}+0.005\mathrm{B}\mathrm{C}-0.0075\mathrm{B}\mathrm{D}-0.33\mathrm{C}\mathrm{D}+0.3603{\mathrm{A}}^2+(+0.0053){\mathrm{B}}^2+(-0.071){\mathrm{C}}^2-0.041{\mathrm{D}}^2$$ 10

where A is the flow rate (ml/h), B is distance (cm), C is the concentration of PCL (Wt %), and D is the concentration of PLGA (Wt %).

The coded coefficients in eqs , , , and provide an effect-size ranking in the RSM framework because each coefficient reports the response change when a coded factor moves from 0 to +1, with the remaining factors held at the design center. Standardized effects (twice the coded coefficient), Cohen’s f², partial η², and percentage of total sum of squares are tabulated for every term of every response in Table S5a–d. Maximum variance-inflation factor across the four response models was 1.10, confirming the orthogonality of the BBD and ruling out coefficient inflation from collinearity. For fiber diameter, the terms accounting for ≥5% of the total sum of squares were PCL concentration (C; 39.95% SS, standardized effect 0.89, partial η² = 0.779, p = 2.7 × 10^–6), PLGA concentration (D; 27.88% SS, standardized effect 0.75, partial η² = 0.711, p = 2.1 × 10^–5), flow rate (A; 8.97% SS, partial η² = 0.442, p = 3.6 × 10^–3), and the A·C interaction (6.11% SS, p = 0.012); together, these four terms account for 82.9% of the explained variance, consistent with the perturbation plot (Figure a) and with the physical mechanism in which polymer-solution viscosity and chain entanglement dominate over flow rate-driven Taylor-cone effects. This interpretation is complemented by the F-ratios in Table , the perturbation plots in Figures a, a, a, and a, and the Pareto effect-size plots provided in Figure S6.

4.

Contour plots for the mutual effects of (a) PCL concentration and flow rate and (b) PLGA concentration and distance on fiber diameter.

6.

Contour plots for the mutual effects of PCL concentration and flow rate: (a) PLGA concentration and flow rate (b) on the Young’s modulus of electrospun PCL–PLGA membranes.

8.

(a) Perturbation plot showing the effect of each factor on strain at break, interaction plots between (b) PCL concentration and flow rate, (c) PLGA concentration and flow rate, and (d) PLGA concentration and PCL concentration.

10.

RSM confirmation experiment: (a) SEM image; Scale bar: 10 μm, (b) corresponding fiber diameter distribution, and (c) the stress–strain curve.

Across the four responses, polymer concentration provides the clearest physical axis of control. For Young’s modulus, PLGA concentration is the single largest contributor (partial η² > 0.6), with the PLGA quadratic term and the A·D and C·D interactions reporting medium partial η². For UTS, the A·B and A·D interactions report the largest effect sizes, capturing the coupling between flow rate and the two material-solution variables. For strain at break, PCL concentration again dominates (partial η² > 0.5), consistent with PCL crystallinity governing post-yield extensibility. These effect-size results extend the F-ratio reporting in Table by providing standardized, dimensionless magnitudes that are directly comparable across responses and that match the physical interpretation of the PCL–PLGA blend system.

4.1.2. Validation and Verification of the Models

Figure shows the normal probability assessment, indicating that residuals for all responses adhere to a normal distribution, as made evident by a straight line in the normal probability plot. This confirms residual independence and normality, supporting the validity of the developed quadratic-regression model. This was confirmed by the predicted versus actual plot, where points align closely along the diagonal line, indicating strong agreement between experimental and predicted values with minimal deviation across all responses (Figure S1, Supporting Information). Diagnostic plots confirm the high adequacy and validity of the considered models for approximating the developed quadratic regression.

2.

Normal probability plots for (a) fiber diameter, (b) Young’s modulus, (c) UTS, and (d) strain at break for electrospun PCL/PLGA membranes.

4.1.3. Average Fiber Diameter

The perturbation plot for the average fiber diameter response (Figure a) reveals that the concentration of PCL has the greatest influence on fiber diameter, whereas the distance between the needle and collector is the least influential factor. This is further illustrated by the contour plots (Figure a,b; corresponding 3D response surfaces in Figure S2), which show that when both PCL concentration and flow rate are at their minimum levels, the thinnest fibers are produced. Specifically, fibers generated with a 4 wt % PCL solution are, on average, three times thinner than those produced with an 8 wt % PCL solution when other factors are set to their middle values. Similarly, the perturbation plot indicates that the concentration of PLGA also significantly affects fiber diameter, similar to the PCL concentration. Figure b further details this relationship, demonstrating that at low distances, changing PLGA concentration has a minor effect on fiber diameter. However, at higher PLGA concentrations, increasing the distance leads to thicker fibers, whereas at lower PLGA concentrations, increasing the distance results in thinner fibers. The interaction plots (Figure b,c) provide additional insights into these relationships. Figure b shows that higher PCL concentrations combined with increasing flow rates result in thicker fibers, confirming the findings from the contour plots where high flow rates significantly increase fiber diameter with higher PCL concentrations. Figure c illustrates that for lower PLGA concentrations, increasing the distance between the needle and collector produces thinner fibers, while higher PLGA concentrations with increased distance result in thicker fibers, aligning with the contour plot observations.

3.

(a) Perturbation plot showing the effect of each factor on average fiber diameter, (b) interaction plot between PCL concentration and flow rate, and (c) interaction plot between PLGA concentration and distance.

4.1.4. Young’s Modulus

The perturbation plot for Young’s modulus (Figure a) highlights that the concentration of PLGA has the most significant effect on the elastic modulus, while the working distance (Factor B) has the least effect among the factors examined. Similarly, Figure shows a comprehensive illustration of these relationships. Specifically, lower flow rates and PCL concentrations yield membranes with reduced stiffness (Figure a). For instance, membranes with a Young’s modulus of around 200 MPa are achieved using 4–5.5 wt % PCL solutions and flow rates of 0.1 to 0.15 mL/h. Conversely, a significant increase in Young’s modulus is observed with higher PCL concentrations exceeding 7.5 wt % and a flow rate of 0.5 mL/h, as indicated by the contour plots (Figure ; D response surfaces in Figure S3). Furthermore, increasing the PLGA concentration from 6 to 10 wt % more than doubles the material’s stiffness, aligning with the contour results showing steeper contour lines reflecting higher stiffness values in Figure b. These findings suggest a strong correlation between polymer concentrations, flow rates, and Young’s modulus, emphasizing the pivotal role of these factors in determining membrane stiffness. The significant interaction between flow rate and both PCL and PLGA concentration is observed (Figure b,c). Increasing the flow rate at each utilized PCL or PLGA concentration leads to a corresponding increase in the elastic modulus of the membrane. However, the impact of flow rate on Young’s modulus varies depending on PCL and PLGA concentration parameters and whether higher or lower concentrations are employed. Notably, the flow rate exerts a more pronounced effect on elastic modulus with higher PCL concentrations. For instance, with a 4 wt % PCL solution, an increase in the flow rate from 0.1 to 0.5 mL/h results in a Young’s modulus increase from almost 200 to 250 MPa. Conversely, for an 8 wt % PCL solution, this increase is almost 2-fold over the same range. This difference is less pronounced when altering PLGA concentration, as the increase in modulus upon increasing flow rate remains significant for any used concentration of PLGA solution.

5.

(a) Perturbation plot showing the effect of each factor on Young’s modulus, interaction plots between (b) PCL concentration and flow rate, and (c) PLGA concentration and flow rate.

4.1.5. Ultimate Tensile Strength

The perturbation plot for UTS (Figure a) highlights the significant influence of PLGA concentration (factor D) on material strength, followed by the flow rate (factor A) and PCL concentration (factor C). While working distance (factor B) has a smaller individual effect, it remains statistically significant. PLGA’s inherent strength, coupled with increased concentration in the solution, predictably enhances membrane strength. Increasing flow rate and PCL concentration also contribute to material strength by producing thicker fibers that resist applied forces more effectively. These relationships are illustrated in the contour plot (Figure d; 3D response surface in Figure S4), indicating that higher flow rates combined with lower distances yield stronger structures, while weaker membranes are formed with specific flow rate and distance combinations. The interaction plots in Figure b,c provide insights into the relationship between different factors and UTS. For UTS, lower distance values combined with increased flow rates enhance material strength (Figure b). However, increasing the flow rate with a greater distance between the collector unit and the nozzle can reduce mechanical strength. Additionally, the interactive effect of flow rate and PLGA concentration on UTS (Figure c) shows that stronger membranes result from increasing flow rates with lower concentrated PLGA, while a downward trend in strength is observed with higher concentrated PLGA solutions.

7.

(a) Perturbation plot showing the effect of each factor on UTS, interaction plots between (b) flow rate and distance, (c) flow rate and PLGA concentration, and (d) contour plot for the mutual effects of distance and flow rate on UTS.

4.1.6. Strain at Break

The perturbation plot for strain at break, demonstrated in Figure a, illustrates the significant impact of all selected parameters. Strain at break is notably influenced primarily by the C factor (PCL concentration) and subsequently by the D factor (PLGA concentration). Increasing the PCL quantity in the electrospinning solution leads to a substantial increase in material extendibility, attributable to PCL’s intrinsic elastic properties due to its lower glass transition temperature compared to room temperature. Notably, the effect of flow rate on membrane elasticity outweighs that of distance, which emerges as the least significant individual parameter. The contour graphs for strain at break, generated based on significant interaction terms (Figure ; 3D response surfaces in Figure S5), provide further insights. For instance, adjusting both PCL concentration and flow rate while keeping other variables constant reveals that the least stretchable material is produced using the lowest values of these parameters (Figure b). Furthermore, extreme flow rate values coupled with increased PCL concentration yield significantly extendable material, exemplified by a strain at break of 2.4 at a flow rate of approximately 0.475–0.5 mL/h and PCL concentration of 7.5–8 wt %. Turning to the interaction plots, significant interactions are observed between PCL and PLGA concentrations, as well as flow rate with both PCL and PLGA concentrations. As depicted in Figure b, increasing the flow rate of more concentrated solutions has a lesser effect on membrane extensibility compared to scenarios with lower PCL concentrations. Conversely, for the interaction of flow rate and PLGA concentration (Figure c), a steeper upward trend is observed with more concentrated PLGA solutions. However, membrane elasticity decreases after increasing the flow rate to its middle level before rising again. The interaction between PCL and PLGA concentrations proved to be the most significant (Figure d). While strain at the breaking point increased slightly with higher PCL concentrations in a highly concentrated PLGA solution, the increase was notably steeper with a more diluted PLGA solution. These relationships are further illustrated in Figure a–c. These findings underscore the nuanced interplay between polymer concentrations, flow rates, and membrane extensibility, crucial for optimizing electrospinning processes.

9.

Contour plots for the mutual effects of (a) distance and flow rate, (b) PCL concentration and flow rate, and (c) PLGA concentration and flow rate on strain at break.

4.1.7. Optimization

The optimization results indicate that to achieve the most robust membranes with the lowest Young’s modulus and the smallest average fiber diameter, the following electrospinning parameters should be set: PCL solution concentration at 8 wt %, PLGA concentration at 6 wt %, a flow rate of 0.1 mL/h, and a distance of 15 cm (Table ). The average of the first five solutions was selected for confirmation and further study. The predicted values for the responses, including fiber diameter, Young’s modulus, UTS, and strain at break, are as follows: 0.386 ± 0.004 μm, 152.156 ± 1.751 MPa, 41.850 ± 0.149 MPa, and 2.948 ± 0.020, respectively.

5. Optimal Solutions as Obtained by Design-Expert.

no	A	B	C	D	R1	R2	R3	R4	Des
1	0.100	15.000	7.999	6.002	0.391	154.920	41.885	2.979	0.864
2	0.100	14.999	7.935	6.000	0.386	152.689	41.908	2.952	0.864
3	0.100	15.000	7.914	6.000	0.384	152.027	41.926	2.943	0.864
4	0.100	15.000	7.867	6.000	0.381	150.479	41.944	2.923	0.863
5	0.100	14.953	7.915	6.000	0.389	150.665	41.586	2.942	0.862

4.1.8. Confirmation

Figure presents the SEM image of the electrospun membrane, fiber diameter distribution, and the typical stress–strain curve for the membrane fabricated using the optimized parameters. In the confirmation run, the measured average fiber diameter, Young’s modulus, UTS, and strain at break were 0.409 ± 0.189 μm, 167.42 ± 10.21 MPa, 38.47 ± 6.2 MPa, and 3.18 ± 0.21, respectively. The confirmation experiment validated the model, with the experimental results deviating less than 10% from the predicted values for all responses, demonstrating the model’s precision and reliability.

4.2. Machine Learning

4.2.1. WGAN-GP Results

WGAN-GP was first used to generate an augmented electrospinning data set from the 29 experimental runs. Fidelity was assessed by comparing real and generated data using KDE overlays, summary statistics, and correlation matrices, allowing both marginal distributions and joint parameter–property relationships to be examined.

The initial WGAN-GP diagnostics provided a useful first assessment of distributional agreement, particularly through marginal density profiles and selected pairwise relationships. In the revised workflow, these exploratory comparisons were complemented by a broader validation framework that also considered multivariate consistency, sample-level proximity, and predictive utility on held-out real observations. Accordingly, the WGAN-GP output is retained as the original augmentation benchmark and interpreted alongside the formal five-test generator fidelity assessment reported in the next section (Section ).

The KDE and summary-statistic comparisons showed close marginal alignment for several variables (Figure ), including flow rate (0.295 ± 0.109 mL/h generated vs 0.300 ± 0.129 mL/h experimental), Young’s modulus (376.280 ± 155.488 MPa vs 382.819 ± 167.927 MPa), and fiber diameter (1.092 ± 0.422 μm vs 1.101 ± 0.467 μm). Marginal-density and correlation-matrix evidence of this kind is necessary but not sufficient for generator validation: it does not test joint-distribution fidelity, classifier separability, memorization, or downstream predictive utility. These comparisons, therefore, supported use of the generated data as an initial augmentation strategy, while motivating the expanded five-test fidelity battery and six-way generator comparison reported in the next Section .

11.

KDE plots illustrating the distribution of both experimental and generated data for key factors and response variables in the study. The KDE plots enable a visual comparison of the similarity between real and synthetically generated data, (a) KDE of fiber diameter distribution, (b) KDE of strain at break distribution, (c) KDE of UTS distribution, (d) KDE of Young’s modulus distribution, (e) KDE of flow rate distribution, (f) KDE of PLGA concentration distribution, (g) KDE of PCL concentration distribution, and (h) KDE of working distance distribution.

Correlation analysis further showed preservation of selected pairwise relationships (Figure ), including fiber diameter with Young’s modulus (real: 0.72; generated: 0.73) and working distance with fiber diameter (real: −0.63; generated: −0.64). As reported in n the next Section , the formal joint-distribution and classifier two-sample tests subsequently revealed that the WGAN-GP joint distribution remained statistically distinguishable from the real one (MMD² = 0.595, permutation p ≈ 0; C2ST AUC = 0.98), and that train-on-synthetic/test-on-real R ² was negative on three of the four target parameters. The marginal/correlation evidence alone, therefore, overstated the generator’s downstream usefulness, which is why the augmentation generator was subsequently replaced by the Gaussian Copula identified by the evaluation.

12.

Correlation matrix of experimental and generated data.

4.2.1.1. Synthetic-Data Fidelity Assessment

The six-candidate synthetic-data generators were first evaluated on the same 29-row Box–Behnken data set using the fidelity, local geometry, and downstream utility battery described in Section . The complete numerical results are provided in Table S10, while Figures S8 and S9 summarize the generator comparison and fidelity diagnostics. Across this assessment, the Gaussian copula with empirical marginals achieved the best overall joint score (0.159), reflecting a favorable balance between marginal fidelity, joint-distribution agreement, classifier indistinguishability, and downstream predictive utility.

The Gaussian Copula showed a low mean per-column KS statistic (0.030), a very small joint MMD² (2.06 × 10^–4, permutation p = 1.000), and a near-/below-chance C2ST AUC (0.30), indicating that real and synthetic samples were not readily separated by the two-sample classifier. Its 1-nearest-neighbor ratio was 0.596 and was not significant under the local-geometry test (p = 0.168). In downstream TSTR evaluation, the Copula produced strong positive R ² values for PCL concentration (0.644), PLGA concentration (0.730), and flow rate (0.340), with a near-zero value for working distance (−0.021). This pattern indicates that the generator preserves the strongest polymer-composition structure in the data set while working distance remains the least recoverable target.

By comparison, the WGAN-GP comparator showed weaker joint fidelity in the same assessment (mean KS = 0.563; MMD² = 0.615, permutation p = 0.00498; C2ST AUC = 0.987). Its TSTR R ² values were negative for PCL concentration (−0.530), flow rate (−0.086), and working distance (−0.152) and only weakly positive for PLGA concentration (0.133). The detailed WGAN-GP architecture and training settings are provided in Supporting Information (S)­1 and Table S1, while its leakage-free LOO baseline is retained in S.6. These results justified using the Gaussian Copula as the primary augmentation strategy for the downstream ML analyses.

4.2.2. ML Model Benchmarking under Leakage-Free LOO

The inverse ML task used membrane properties as inputs and electrospinning parameters as the outputs. To avoid circularity associated with augmented-data validation, all primary predictive metrics were calculated under a leakage-free LOO protocol in which the held-out real observation was removed before scaling, synthetic-data generation, hyperparameter tuning, and model training. The per-target winning models and their LOO performances are reported in Table .

6. Leakage-Free Leave-One-Real-Observation-Out Performance for the Per-Target Winning Model Prediction (Real + Gaussian-Copula Synthetic Augmentation; 95% Bootstrap CIs Over 1000 Resamples).

model	target	LOO R 2	95% CI low	95% CI high	MAE	RMSE
CatBoost	flow rate	0.402	–0.016	+0.631	0.0774	0.0978
regressor
CatBoost	working distance	0.470	–0.386	+0.559	1.1850	1.5439
regressor
CatBoost	PCL	0.675	+0.500	+0.770	0.6111	0.7495
regressor	concentration
CatBoost	PLGA	0.747	+0.530	+0.867	0.5323	0.6612
regressor	concentration

Under this stricter evaluation, CatBoost gave the strongest per-target point performance across the four inverse targets. The polymer-concentration targets were recovered with the most robust predictive signal: PCL concentration achieved LOO R ² = 0.675 with a 95% bootstrap confidence interval of +0.500 to +0.770, while PLGA concentration achieved LOO R ² = 0.747 with a 95% bootstrap confidence interval of +0.530 to +0.867. The flow rate showed a positive but less certain signal, whereas the working distance interval crossed zero, indicating weaker predictive resolution for this processing parameter.

The improvement relative to the WGAN-GP baseline further supports the generator selection step. Under the same leakage-free protocol, the WGAN-GP-augmented baseline produced negative LOO R ² values for flow rate (−0.128) and working distance (−0.353) and lower positive values for PCL (0.518) and PLGA concentration (0.479), as shown in S.6. The Gaussian copula pipeline, therefore, improved all four inverse targets, with the clearest gains observed for the two polymer-concentration variables. Figure S11 summarizes the LOO comparison between real-only and augmented training configurations.

The previous 80/20 augmented-pool results are retained only as transparency checks in Tables S7 and S8. They are not used as the basis for the main interpretation, because they do not enforce independence between real held-out rows and the synthetic samples generated from the same experimental corpus. Predicted versus actual plots for the leakage-free per-target winning models are provided in Figure S10.

4.2.3. MLP-NN Prediction as a Cross-Method Consistency Check

The MLP-NN was evaluated under the same leakage-free LOO protocol to test whether a dense neural network architecture recovered the same broad target hierarchy as the tree- and kernel-based models. The MLP-NN achieved LOO R ² values of 0.263 for flow rate, 0.180 for working distance, 0.598 for PCL concentration, and 0.672 for PLGA concentration (Table ). These values were lower than the corresponding CatBoost results for flow rate and both polymer concentrations and only marginally higher for working distance, where neither model produced a statistically strong predictive signal.

7. MLP-NN Hyperparameters and Leakage-Free Leave-One-Real-Observation-Out (LOO) Performance per Target (Real + Gaussian-Copula Synthetic Augmentation).

trget	neurons	learning rate	batch size	epochs	LOO R 2	LOO RMSE
flow rate	32	0.10	128	200	+0.263	0.1086 mL/h
working distance	32	0.10	128	100	+0.180	1.5665 cm
PCL concentration	32	0.01	64	200	+0.598	0.8341 wt %
PLGA concentration	128	0.10	32	100	+0.672	0.7533 wt %

The MLP-NN benchmark, therefore, supports the same main interpretation as the broader model comparison: polymer composition variables are more reliably recovered from membrane properties than geometric/process variables. The MLP-NN is retained as a cross-method check rather than being presented as a superior model. The earlier 80/20 MLP-NN training/test results are provided in Table S8 for traceability but are not used for the primary conclusions.

4.2.4. Property-to-Parameter Coupling Revealed by ML Interpretation

The main value of the ML benchmark lies in the property-to-parameter relationships recovered across model families rather than in identifying a universally superior algorithm. Permutation importance was, therefore, used to determine which measured membrane properties most strongly constrained each predicted electrospinning parameter. The numerical importance values are summarized in Table and visualized in Figure S12.

8. Permutation-Importance Analysis for the Per-Target Winning Inverse ML Models ^,

target	winning model	feature	importance ± std
flow rate	XGBoost	fiber diameter	0.758 ± 0.026
flow rate	XGBoost	Young’s modulus	0.162 ± 0.011
flow rate	XGBoost	UTS	0.149 ± 0.013
flow rate	XGBoost	strain at break	0.038 ± 0.006
working distance	XGBoost	fiber diameter	0.383 ± 0.019
working distance	XGBoost	Young’s modulus	0.285 ± 0.014
working distance	XGBoost	UTS	0.328 ± 0.017
working distance	XGBoost	strain at break	0.306 ± 0.014
PCL concentration	MLP-NN	fiber diameter	0.330 ± 0.040
PCL concentration	MLP-NN	Young’s modulus	0.217 ± 0.013
PCL concentration	MLP-NN	UTS	0.104 ± 0.014
PCL concentration	MLP-NN	strain at break	0.769 ± 0.044
PLGA concentration	CatBoost	fiber diameter	0.823 ± 0.027
PLGA concentration	CatBoost	Young’s modulus	0.358 ± 0.015
PLGA concentration	CatBoost	UTS	0.422 ± 0.013
PLGA concentration	CatBoost	strain at break	0.413 ± 0.023

^aPCL concentration was most strongly associated with strain at break (0.769 ± 0.044), consistent with the contribution of PCL-rich phases to fiber extensibility. PLGA concentration was strongly informed by fiber diameter (0.823 ± 0.027), UTS (0.422 ± 0.013), strain at break (0.413 ± 0.023), and Young’s modulus (0.358 ± 0.015), indicating that PLGA content modulates both fiber formation and bulk mechanical response in the PCL–PLGA membrane. These ML-derived relationships are consistent with the RSM effect-size interpretation supported by Table S5a–d.

^bImportance values represent the decrease in predictive performance following permutation of each membrane-property input and are reported as mean ± std.

Flow rate prediction was dominated by fiber diameter (importance = 0.758 ± 0.026), with smaller contributions from Young’s modulus and UTS. This is physically consistent with the influence of solution delivery rate on jet mass flux and fiber formation. Working distance showed a more distributed importance profile, with fiber diameter, UTS, strain at break, and Young’s modulus all contributing.

Model-family comparisons using paired nonparametric testing and Cliff’s delta further indicate target-specific behavior rather than a single universal winner. The supporting effect-size comparison is shown in Figure S13. This reinforces the interpretation that ML is being used here as a mechanistic and inverse-design aid, not as a generic model-ranking exercise.

4.3. DoE- and ML-Derived Candidate Parameter Regions

The DoE and ML optimization outputs were compared to determine whether the two routes identified compatible regions of the electrospinning design space. The RSM-derived optimum remained the primary experimentally confirmed anchor: 8 wt % PCL, 6 wt % PLGA, 0.1 mL/h flow rate, and 15 cm working distance. At this condition, the RSM models predicted a fiber diameter of 0.386 ± 0.004 μm, Young’s modulus of 152.156 ± 1.751 MPa, UTS of 41.850 ± 0.149 MPa, and strain at break of 2.948 ± 0.020. Experimental confirmation at the same parameter set yielded 409 ± 0.189 μm, 167.42 ± 10.21 MPa, 38.47 ± 6.2 MPa, and 3.18 ± 0.21.

The Gaussian-Copula inverse pipeline identified a candidate region rather than a single deterministic optimum. At the RSM target-property vector, the Copula-CQR ensemble estimated 0.210 ± 0.035 mL/h flow rate, 11.50 ± 0.59 cm working distance, 5.79 ± 0.28 wt % PCL, and 6.22 ± 0.19 wt % PLGA (Table ). The corresponding 90% split-conformal intervals were [-0.013, 0.441] ml/h, [8.11, 14.57] cm, [4.30, 7.55] wt %, and [3.92, 7.08] wt %, respectively. When interpreted within the experimental design space, the flow rate interval is practically bounded by the tested range. The DoE optimum lies within the ML interval for flow rate and PLGA concentration and only slightly outside the upper bounds for working distance and PCL concentration, consistent with the RSM objective pushing toward the boundary of the design space.

9. Comparison of Optimized Electrospinning Parameters Derived from DoE Numerical Optimization and the Gaussian-Copula-Augmented ML Inverse Pipeline.

parameter	DoE optimum	copula-CQR ensemble point ± std	90% conformal interval	width/design range	DoE vs 90% CI
flow rate (ml/h)	0.10	0.210 ± 0.035	[−0.013, +0.441]	114%	DoE within 90% CI
working distance (cm)	15.00	11.50 ± 0.59	[8.11, 14.57]	129%	DoE outside CI, Δ = +0.43 cm
PCL concentration (wt %)	8.00	5.79 ± 0.28	[4.30, 7.55]	81%	DoE outside CI, Δ = +0.45 wt %
PLGA concentration (wt %)	6.00	6.22 ± 0.19	[3.92, 7.08]	79%	DoE within 90% CI

The inverse prediction should, therefore, be interpreted as a statistically supported candidate region and not as a replacement for the experimentally confirmed RSM optimum. This framing is appropriate because the property-to-parameter map is intrinsically nonunique: multiple electrospinning parameter combinations can generate similar membrane-property vectors within experimental uncertainty. Single-point inverse predictions from the earlier WGAN-GP workflow are included in Table S9 for traceability, while the conformal-interval visualization is provided in Figure S14.

The resulting CatBoost and MLP-NN estimates are given in Table . Both models converged closely on the polymer concentrations, whereas flow rate estimates showed greater uncertainty, consistent with the weaker LOO support for flow rate prediction in Section . The full six-family multiobjective desirability optimization is reported in Table S11 and summarized in Table . Among the ML forward-surrogate families, XGBoost achieved the highest desirability (D = 0.895 ± 0.065), while the experimentally confirmed DoE optimum achieved D = 0.782. Because the XGBoost optimum remains a model-derived candidate, the DoE optimum is retained as the physical validation anchor, and the ML-derived optima are presented as prioritized candidates for subsequent fabrication.

10. ML Inverse Predictions of the Optimal Electrospinning Parameters.

parameter	CatBoost (mean ± std)	MLP-NN (mean ± std)	90% conformal interval	within design range?
flow rate (ml/h)	0.134 ± 0.038	0.059 ± 0.063	[-0.070, 0.339]	yes
working distance (cm)	13.002 ± 0.692	12.706 ± 0.996	[9.751, 15.755]	yes
PCL concentration (wt %)	5.756 ± 0.286	5.202 ± 0.681	[4.466, 7.237]	yes
PLGA concentration (wt %)	6.140 ± 0.247	5.968 ± 0.609	[4.667, 7.385]	yes

11. ML Multi-Objective Electrospinning Parameter Optimization.

	flow rate	working distance	PCL concentration	PLGA concentration	fiber diameter	Young’s modulus	UTS	strain at break	desirability
XGBoost	0.23 ± 0.059	13.55 ± 0.89	5.94 ± 0.81	6.73 ± 0.65	0.364 ± 0.191	217.3 ± 66.1	75.65 ± 10.78	2.854 ± 0.306	0.895 ± 0.064

4.4. Integration of DoE and ML for Multiresponse Membrane Design

This study establishes an integrated DoE–ML framework for linking electrospinning conditions with multiple PCL–PLGA membrane properties relevant to lung-on-chip membrane design. The workflow comprises three connected stages. First, RSM was used to define experimentally grounded process–property relationships between electrospinning parameters and four membrane outputs: fiber diameter, Young’s modulus, UTS, and strain at break. Second, synthetic-data augmentation was incorporated only after formal generator-fidelity assessment. The originally implemented WGAN-GP model was retained as a comparator, while Gaussian-copula augmentation was selected for downstream modeling because it provided stronger agreement with the experimental data distribution, local structure, and downstream predictive utility. Third, inverse ML modeling was used to translate target membrane-property profiles into candidate electrospinning regions, with all predictions interpreted relative to the experimentally confirmed RSM optimum and the bounded BBD space.

The principal contribution of this work is, therefore, the bidirectional integration of forward RSM interpretation with inverse ML prediction for a four-response electrospun membrane design problem. In this framework, RSM provides the experimental anchor and interpretable response-surface structure, while ML extends the analysis by supporting inverse mapping, uncertainty estimation, and physically interpretable property-to-parameter relationships. This combined approach is particularly appropriate for small, structured biomaterials data sets, where experimentally validated response surfaces remain essential, but where ML can provide additional insight into nonlinear coupling and candidate processing regions.

The strongest ML-supported findings were the robust recovery of polymer concentration targets and the consistent property-to-parameter coupling structure. Polymer concentrations were more reliably inferred from the measured membrane properties, whereas the flow rate and working distance were retained as candidate-generating outputs and interpreted with broader uncertainty intervals. This distinction is important because the inverse property-to-process mapping is not expected to define a single deterministic optimum; rather, multiple electrospinning parameter combinations may produce similar membrane property profiles within experimental uncertainty. Accordingly, the ML outputs are best interpreted as calibrated candidate regions that complement rather than replace the experimentally confirmed RSM optimum.

Set against the broader ML-for-electrospinning literature, the distinguishing feature of the present work is that it performs inverse design across multiple coequal membrane targets simultaneously, while remaining anchored to experimentally confirmed data. As outlined in the introduction, prior studies have tended to address these aspects separately: forward multiproperty prediction or multiobjective optimization without inversion, or inverse design centered on fiber diameter alone, typically drawing on literature-derived, open, or single-polymer data sets. ,,− ,− In contrast, the present study maps a combined morphological and mechanical property profile, fiber diameter, Young’s modulus, UTS, and strain at break, treated as coequal targets, back to candidate PCL–PLGA processing conditions, frames the optimization around a lung basement-membrane application, and keeps the workflow anchored to an experimentally confirmed RSM optimum rather than relying solely on in silico parameter prediction.

From a translational perspective, this combined DoE–ML strategy offers a practical route for resource-efficient membrane optimization. It reduces reliance on iterative trial-and-error experimentation, allows multiple and potentially competing membrane properties to be considered simultaneously, and provides a structured pathway from desired property windows to candidate electrospinning parameters. Although developed here for PCL–PLGA membranes intended for lung-barrier modeling, the same framework could be adapted to other biomaterial systems where small but information-rich data sets are generated through formal design-of-experiments protocols.

However, two aspects of the present study should be noted. The analysis is based on a relatively small 29-run Box–Behnken data set; this constraint directly motivated the use of a low-parameter Gaussian-Copula generator, the leakage-free leave-one-real-observation-out evaluation with bootstrap confidence intervals, and the reporting of inverse predictions as uncertainty-calibrated candidate regions rather than a single deterministic optimum. The study is also confined to physicomechanical optimization and the DoE–ML framework; biological validation of the optimized membranes, including epithelial and endothelial cell response and barrier-related outcomes, will be reported separately.

5. Conclusions

Developing electrospun substrates that combine fine fibrous morphology, reduced bulk stiffness, and sufficient mechanical integrity remains a key challenge for in vitro lung-barrier membrane design. In this study, a combined DoE–ML framework was developed to optimize electrospun PCL–PLGA membranes toward BM-relevant structural and mechanical design criteria.

RSM provided the experimental foundation of the workflow by defining the process–property relationships within the BBD space. The RSM analysis identified polymer concentration as a dominant contributor to membrane morphology and mechanical response, and the RSM-derived optimum predicted membranes with a fiber diameter of 0.386 ± 0.004 μm, Young’s modulus of 152.156 ± 1.751 MPa, UTS of 41.850 ± 0.149 MPa, and strain at break of 2.948 ± 0.020. This experimentally validated optimum then served as the benchmark against which the ML-derived inverse predictions and desirability-based candidate regions were interpreted.

The ML component extended the RSM workflow. Gaussian-Copula augmentation was selected after generator-fidelity testing; CatBoost most reliably recovered the PCL and PLGA concentration targets under leakage-free LOO evaluation, and XGBoost identified the highest model-derived desirability. These findings indicate that polymer composition is the most reliable inverse target, whereas flow rate and working distance should be treated as lower-confidence candidate generating outputs.

Overall, this work demonstrates a practical RSM–ML strategy that combines interpretable, experimentally validated response-surface optimization with ML-based inverse design, uncertainty-aware candidate-region prediction, and property-to-parameter interpretation, providing a resource-efficient approach for balancing morphology, mechanics, and processing constraints in BM-relevant PCL–PLGA membrane design.

The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.6c03020.

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Department of Chemical Engineering and Applied Chemistry, University of Toronto, 160 College Street, M5S 3E1, Toronto, Ontario, Canada

The authors declare no competing financial interest.