Advanced antifouling performance of PSF HNT Al2O3 GO membranes through a synergistic approach using nanocomposite tuning and machine learning

Introduction: This work examines the antifouling characteristics of a new polysulfone (PSF) ultrafiltration membrane augmented with halloysite nanotubes (HNT) and Al₂O₃-GO.

Methods: The membrane was prepared by phase separation with different PSF and HNT/Al₂O₃-GO concentrations. Protein removal, resistance to sedimentation, and pure water flow were used to evaluate the membrane’s performance. After first being modified with Al₂O₃-GO, the HNT nanoparticles were examined by X-ray diffraction (XRD), which was used to assess the membrane’s structure.

Results: Interestingly, we found that at 6 bar pressure, the water flow increased significantly from 190 to 360 L/(m²⋅h), which we ascribed to the functional groups in the Al₂O₃-GO and HNT nanoparticles. A mix of bovine serum albumin (BSA) was used to test how resistant membranes were to fouling. Membranes with 0.75 and 1 wt% HNT were the most antifouling and recovered 100% water flow. We also proposed a double-factorial data relationship method for finding the optimal parameter ranges.

Discussion: We employed machine learning methods, including support vector regression (SVR), random forest (RF), and artificial neural network (ANN), to predict bovine serum albumin (BSA) removal and spread. To optimize outcomes, we modified hyperparameters. This paper discusses how nanomaterials and cutting-edge computer approaches may enhance membrane filter systems.

1 Introduction

Considerable attention has been directed to the several advantages of membrane separation techniques in water purification and desalination (Liang, 2025; Meskher et al., 2025; Gong et al., 2025). According to An et al. (An et al., 2023), this methodology successfully eradicates heavy metals, pollutants, particles, turbidity, and microbes from water sources. The effectiveness of these membranes depends on how well they block biological contaminants and fouling, how well they resist mechanical stress, and how well they fight oxidation and chemical breakdown. Biofouling protection is important for systems that separate things using membranes (Belafi-Bako et al., 2020; Nguyen et al., 2012). Biofouling is the buildup of protein and chemical molecules on barrier surfaces. It can lower output and running costs.

Dadari et al. (2022) investigated how adding boehmite nanoparticles may improve polyethersulfone (PES) membrane antifouling. They observed improvement in the membrane’s efficiency and flux recovery ratio (FRR). Researchers have used many methods to produce antifouling membranes to solve this issue. Conventional polymeric membranes, such as those made from PES, have been extensively utilized in water treatment applications. However, they exhibit several limitations that hinder their performance and longevity (Zhang et al., 2025). A primary concern is membrane fouling, where contaminants like organic matter, microorganisms, and inorganic particles accumulate on the membrane surface or within its pores (Khan et al., 2025). Membrane fouling can be categorized into several types based on the nature of the foulants (Tayeh et al., 2025). Organic fouling results from the deposition of substances such as proteins, fats, oils, and humic compounds (Maeda, 2025). Inorganic fouling, often referred to as scaling, occurs due to the precipitation of dissolved minerals like calcium carbonate or silica (Tong et al., 2023). Biofouling involves the attachment and growth of microorganisms that form biofilms on the membrane surface, and particulate fouling arises from suspended solids such as silt and clay (Gari et al., 2023). This accumulation leads to a decline in permeate flux and necessitates frequent cleaning or membrane replacement, thereby increasing operational costs (Zhang et al., 2025). Additionally, conventional membranes often struggle with the removal of emerging contaminants, such as pharmaceuticals and personal care products, due to their limited selectivity and pore size distribution (HajimohamadzadehTorkambour et al., 2024). Their mechanical and thermal stability may also be inadequate for certain applications, restricting their use in harsh operating conditions (Saleh et al., 2022). Furthermore, the production of these membranes can involve environmentally harmful solvents, raising concerns about sustainability. Phthalate softeners, hydrophilic monomers, and polymer composition all change membranes. Hydrophilic, functionalized compounds incorporating nanoparticles are applied to membranes. The mixture of matrix membranes with inorganic nanoparticles improves their mechanical, thermal, magnetic, and optical properties (Birniwa et al., 2023; Osman et al., 2024). These enhancements are largely attributed to the unique characteristics of nanoparticles, such as their high surface area-to-volume ratio (Dong et al., 2021) and diminutive size (Agarwal et al., 2019), which confer increased reactivity and interaction with surrounding molecules. Zahid et al. (2022) studied the effect of the graphene oxide addition in PES membranes. They observed an improvement in the antifouling properties of the membrane when halloysite nanotubes modified with dextran were added. Wang et al. (2022) saved energy and chemicals by utilizing photocatalysts. Shahkaramipour et al. (2017) examined membrane water purification and the importance of decreasing fouling to save costs.

Polymers like polyvinylidene difluoride (PVDF) and polysulfone (PSF) are often used to make membranes because they offer strong structural and chemical stability. PSF, in particular, is widely used thanks to its durability, resistance to heat and oxidation, ability to form films easily, and a high glass transition temperature of around 194 °C (Remanan et al., 2021). That said, these materials are naturally hydrophobic, which can be a drawback in some applications (Alasfar et al., 2022). To address this, researchers often add nano-sized metal oxide particles. These particles have a large surface area and are highly hydrophilic, which helps make the membranes more water-attracting (Arsuaga et al., 2013; Hendraningrat and Torsæter, 2015).

Polysulfone (PSF) membranes are widely used, but their hydrophobic nature often leads to fouling, especially when filtering protein-rich solutions (Dolatkhah et al., 2022; Eskandari et al., 2024). To overcome this, researchers have explored adding halloysite nanotubes (HNTs), which are naturally hydrophilic and have a high surface area and pore volume. These features make HNTs a great candidate for improving membrane performance (Hong et al., 2021; Kushwaha et al., 2021; Khunová et al., 2021). Their tubular shape and negative surface charge can also help enhance membrane porosity, strength, and even support ion exchange (Pasbakhsh et al., 2013; Hashemifard et al., 2011). To push performance further, combining HNTs with other nanomaterials like aluminum oxide (Al₂O₃) and graphene oxide (GO) has shown promise. Al₂O₃ is known for being highly hydrophilic and chemically stable, which helps improve water flow and resist fouling. GO brings additional oxygen-containing groups that boost hydrophilicity, dispersion, and structural support in the membrane matrix (VS and Xavier, 2025). Despite their individual benefits, there has not been much research exploring a hybrid membrane that combines HNTs with Al₂O₃-GO in a PSF base. This kind of blend could unlock synergistic effects, enhancing both fouling resistance and durability. Some studies even suggest that hydroxyl radicals can help embed Al₂O₃-GO particles into HNTs, improving their water affinity and antibacterial properties (Bao et al., 2021; Vaitsis et al., 2019; Maleki et al., 2019).

The transformative role of machine learning (ML) in optimizing membrane fabrication and filtration processes has been investigated recently (Shahouni et al., 2024; Cao et al., 2024; Ta et al., 2024; Aldrees et al., 2024). Sutariya et al. (Sutariya et al., 2025) developed Random Forest (RF) models to predict nanofiltration membrane performance based on synthesis parameters such as piperazine (PIP), trimesoyl chloride (TMC), sodium lauryl sulfate (SLS) concentrations, and reaction time. Their models achieved high predictive accuracy, with R² values exceeding 0.96 for pure water permeance and salt rejection. Similarly, Lu et al. (2025) employed ML-based Bayesian optimization, utilizing Extreme Gradient Boosting (XGBoost), to design ultrafiltration processes for protein purification. Their approach identified optimal operational parameters, achieving steady flux predictions with errors below 0.5%, thereby reducing experimental workload and enhancing efficiency.

Modified nanoparticles were incorporated into the membrane to evaluate their effectiveness in minimizing sediment buildup. Antifouling performance was assessed by analyzing flux recovery after the cleaning phase, supported by experimental evidence (Shahouni et al., 2024; Cao et al., 2024; Ta et al., 2024). This approach represents a novel contribution that, to the best of current knowledge, has not been previously reported. An optimization method was developed using empirical correlations within a double-factorial design to identify the optimal composition of membrane components. Additionally, machine learning techniques, such as support vector regression (SVR), random forest (RF), and artificial neural networks (ANN), were applied to predict the absorption and removal of bovine serum albumin (BSA). Each model underwent hyperparameter tuning to enhance prediction accuracy. A thorough evaluation identified the most effective settings for each algorithm.

2 Experimental setup

2.1 Preparation of HNT/Al₂O₃-GO

The HNT/Al₂O₃-GO nanocomposite was synthesized following a standard operating procedure. Initially, a solution was generated through the continuous agitation of 25 mg of GO in 100 mL of distilled water at 25 °C. It was agitated for 1 hour after adding 1.5 g of HNT to this solution. A stirring-conditioned solution of 0.625 g of aluminum nitrate (Al(NO₃)₂) in 50 mL of water was added to the HNT and GO solution. Following the addition of a 12 mL dropwise solution of ammonium hydroxide (NH₄OH) after 30 min, the reaction mixture was agitated at 25 °C for 24 h. The obtained precipitate underwent filtration and was meticulously rinsed using acetone and distilled water. The HNT/Al₂O₃-GO composite was desiccated in an oven for 12 h at 105 °C. The identical synthetic methodology was utilized to generate Al₂O₃ without GO and HNT.

2.2 Synthesis of PSF/HNT/Al₂O₃-GO nanocomposite membranes

Membranes were fabricated using PSF and varying concentrations of HNT/Al₂O₃-GO, as outlined in Table 1. To incorporate HNT/Al₂O₃-GO nanoparticles into the PSF membranes, a phase inversion method was employed. In order to distribute varying amounts of HNT/Al₂O₃-GO, ultrasonication was employed in a specific quantity of N-Methyl-2-pyrrolidone (NMP) following the preparation of the casting solution. A fixed quantity of Polyvinylpyrrolidone (PVP) and Silk Fibroin (SF) was quickly blended into the mixture to eliminate trapped air bubbles. The solution was evenly distributed on a glass plate using a glass stick to maintain a width of 100 μm. The plate was promptly placed into a coagulation water bath. The membrane underwent testing on the glass plate surface following a phase transition. Following that, the membrane was transferred from the coagulation bath to a separate water bath and allowed to sit for 24 h. This step was necessary to eliminate any lingering solvents and facilitate the separation process. Following that, deionized water was utilized to ensure the membrane’s safety. Various solutions were prepared using different concentrations of HNT/Al₂O₃-GO, including 0.5%, 0.75%, and 1%.

Table 1

Table 1. HNT/Al₂O₃-GO loading of embedded membranes.

2.3 Mechanical analysis of the constructed membrane

To eliminate moisture from the HNT/Al₂O₃-GO nanoparticles, a vacuum desiccator was employed for 2 days, after which an oven at 60 °C was utilized for 2 h. X-ray diffraction (XRD) spectrum analysis was utilized to determine the crystal state of the nanotubes. The analysis was performed using the D/max-rB 12 kW Rigaku instrument from Japan. We used a Shimadzu X-ray diffractometer to analyze HNT/Al₂O₃-GO and HNT crystal properties and obtained XRD patterns. With the help of an IMC-159D contact angle measurement instrument by IMOTO Machinery, the contact angle was measured at five locations on the same membrane using the sticky drop method. A 2-h soak in deionized water followed by drying with filter paper was used to determine the porosity of the membranes. We measured the weight difference between the membrane before and after water absorption, and we used the following Equation 1 to determine the membrane’s porosity (Aldrees et al., 2024; Sutariya et al., 2025).

$\epsilon =\frac{W_w-W_d}{{\rho }_{H_{2}O}\times A\times L}\times 100(1)$

Where, A is the effective area of the membrane, L is the thickness of the membrane, $\rho$ is the water density, and $W_w$ and $W_d$ are the weight of the wet and dry membranes. Each sample was averaged by taking three measurements.

2.4 Performance study

BSA rejection and pure water flux were measured to evaluate membrane performance. A rotary filtration system with an effective membrane surface area of 14 $c{m}^2$ with the flow of 2 $l/\mathit{min}$ was used to study the performance. Water flow was measured at 1–5 atm pressures with 1 atm increments. The water flux $j_w$ was calculated using the following Equation 2 (Lu et al., 2025).

$j_w=\frac{\mathrm{v}}{A∆t}(2)$

Where, v is the weight of permeated pure water, A is the effective area of the membrane, and $∆t$ is the permeation time. Filtering tests were performed at 20 °C. An evaluation of the performance was conducted by examining the inhibition of BSA.

Nutritional BSA solution at 200 mg/L was prepared for use in aqueous medium. Rejection is defined according to the following Equation 3 (Manouchehr et al., 2017).

$R=\left(1-\frac{c_p}{c_f}\right)\times 100(3)$

Penetrant concentration is $c_p$, and feed concentration is $c_f$. At 280 nm, a UV spectrophotometer measured BSA concentration.

2.5 Membrane fouling tests

Sedimentation experiments were carried out using the transverse flow smoothing unit in 1 bar, which was prepared in a laboratory. After filtering the pure water for 65 min, the feeding was started, and the measurement of the permeate solution began 10 min later. After filtering the BSA for 75 min, 30 min of distilled water washing without pressure was followed. A filtration test was performed, and the overall time was 200 min. The membranes that have nanoparticles show a nodal arrangement on the surface of the membrane. Different orientations of feed flow states are studied with this nodal arrangement. A parallel flow of feed flowed to the nodal arrangement. This filtration experiment used a perpendicular feed flow and a perpendicular membrane rotation at 90 °C. As shown in Figure 1, the cross-flow smoothing unit can operate in several modes.

Figure 1

Figure 1. The flow diagram in the ultrafiltration device.

The FRR is formulated as Equation 4 (An et al., 2023).

$FRR=\left(1-\frac{J_{w,2}}{J_{w,1}}\right)\times 100(4)$

Where, $J_{w,1}$ and $J_{w,2}$ are the pure water flux after 65 and 145 min of filtering.

Filter membranes with a high FRR have better antifouling properties. To calculate fouling ratios ($R_t$), reversible fouling ratios ($R_{rev}$), and irreversible fouling ratios ($R_{ir}$), the following Equations 5–7 are used (Manouchehr et al., 2017; Yang et al., 2019).

$R_t=\left(1-\frac{J_P}{J_{w,1}}\right)(5)$

$R_{rev}=\left(\frac{J_{w,2}-J_p}{J_{w,1}}\right)\times 100(6)$

$R_{ir}=R_t-R_{rev}=\left(\frac{J_{w,1}-J_{w,2}}{J_{w,1}}\right)\times 100(7)$

Where, $J_p$ is the permeate flux at 135 min of filtering when the feed is a BSA solution.

3 Results and discussion

Determination of HNT/Al₂O₃-GO nanoparticles was done using XRD analysis. In order to study changes in appearance, HNT/Al₂O₃-GO was compared to composite membranes. Figure 2 depicts the XRD of HNT/Al₂O₃-GO and HNT. The $2\theta$ peaks at (14), (19), (21), (26), (36), and (63), which are the peaks of the XRD profile of the Al₂O₃-GO-HNT nanocomposite, closely resemble that of HNT. Nearly identical peaks at slightly shifted angles indicate strong interaction among Al₂O₃, GO, and HNT in the composite material (Wang et al., 2021; Ortiz-Negrón and Suleiman, 2015).

Figure 2

Figure 2. Crystal structure of modified HNT and HNT/Al₂O₃-GO.

Table 2 shows how the finger-like channels increase porosity on the membrane surface due to the slight difference in the lateral cavities. A mold polymer layer’s hydrophilic property and its viscosity are opposite effects of phase transformation. In an asymmetric membrane, higher hydrophilicity increases nonsolvent flux and porosity. Table 2 displays that adding HNT/Al₂O₃-GO makes the material more hydrophilic and increases the number of pores. It also makes the material more viscous. Because they are hydrophilic, HNT/Al₂O₃-GO hybrid PSF membranes can make shapes with holes. Nanocomposite membrane permeability can increase by 72%–80% when PVP levels go up and polymer amounts decrease. PVP that dissolves in water can be washed off the membrane during phase change. Hydrophilic nanoparticles can be mixed into the PSF polymer matrix to improve this exchange rate. This makes the membrane more porous overall.

Table 2

Table 2. Comparison of contact angle, porosity, and viscosity of four membranes.

To find out the impact position, sliding drop technology was used. The contact angle gets smaller as the amount of HNT/Al₂O₃-GO in the membranes grows. The membrane’s hydrophilic features get better when hydrophilic HNT/Al₂O₃-GO spacers are added. It has been seen that PSF has the largest contact angle, at 70° ± 20°. On the other hand, the membranes that had 0.5, 0.75, and 1 wt% of HNT/Al₂O₃-GO had contact angles of 65, 63, and 58, respectively. The HNT/Al₂O₃-GO functional groups are to blame for this drop.

3.1 Water flux and BSA removal

Water flux is affected by the hydrophilic property. Figure 3a shows the flux for all membranes. It has been found that the water flux increases according to the hydrophilicity property. The tendency to increase in Pure Water Flux (PWF) is consistent with improving the hydrophilicity property according to the HNT/Al₂O₃-GO concentration. The membrane flux increases with more HNT/Al₂O₃-GO concentration (Li et al., 2012; Vadhva et al., 2021). The results show that it reaches its highest value when the amount of HNT/Al₂O₃-GO is 1 wt%. During the phase transformation process, Al₂O₃-GO increases water flux due to its hydrophilic properties. Improved water permeability results from increased membrane porosity.

Figure 3

Figure 3. (a) Pure water flux, (b) BSA removal, and (c) Permeation flux after 120 min for PSF, 0.25 HNT/Al₂O₃-GO/PSF, 0.5 HNT/Al₂O₃-GO/PSF, and 1 HNT/Al₂O₃-GO/PSF.

Figure 3b shows the change in BSA removal and permeation flux in filtration. The PSF and HNT/Al₂O₃-GO -0.5 composite membrane flux often remains constant after 40 min, and the BSA removal after 40 min is close to 100%. On the other hand, the fluxes of the HNT/Al₂O₃-GO -0.75 and HNT/Al₂O₃-GO -1 composite membranes gradually decrease, and the BSA removal increases over time. Finally, after 140 min from the time of filtration, the BSA removal is close to 100% and 95%, respectively. As a result, BSA molecules gradually close the large pores in the last two layers of the skin. While 140 min have passed, the fluxes of HNT/Al₂O₃-GO -0.75 and HNT/Al₂O₃-GO -1 composite membranes are still much higher than PSF and HNT/Al₂O₃-GO -0.5.

3.2 Antifouling study

Membrane reproducibility in liquid filtration is strongly dependent on membrane sedimentation. An excellent membrane has a low sedimentation and high selectivity and flux over time. Cake layer (mold) formation and concentration polarization hole closure reduce flux. During sedimentation, membrane surface behavior plays a crucial role. Hydrophobic membrane surfaces explain the weak antifouling property. It has been suggested that polymer composition materials and surface modification can be modified to improve membrane permeability and antifouling properties (Li et al., 2012; Vadhva et al., 2021; Mirzaei et al., 2021).

You can combine hydrophilic additives with the above methods to improve the anti-deposition property. The membrane was installed perpendicular to the flow direction, and 200 ppm of BSA solution was applied. Figure 3C depicts the permeation flux. Switching to BSA solution decreases the fluxes of pure PSF and HNT/Al₂O₃-GO -0.5 membranes. After the flux goes back to pure water, it is not completely recovered.

On the other hand, according to HNT/Al₂O₃-GO -0.75 and HNT/Al₂O₃-GO -1 composite membranes, when the feeding of BSA solution starts, the flux decreases drastically. After approximately 12 min from the infiltration of pure water, the recovery begins.

The FRR is shown in Table 3. A higher FRR enhances membrane antifouling properties. Clean PSFs have a lower FRR (58.59%) than membranes containing nanotubes embedded inside. The HNT/Al₂O₃-GO -0.5 composite membrane shows approximately an FRR of 72.5%, while both 0.75% and 1% membranes show an FRR of 90%.

Table 3

Table 3. Water FRR percentage of membranes.

This shows that the fouling resistance increases with the participation of HNT/Al₂O₃-GO. In Table 4, FRR is observed to be hydrophilic. In addition to absorbing water molecules, the hydrophilic surface can delay precipitation and absorb protein molecules. Graphene oxide, multiwalled carbon nanotubes, and silica exhibit lower FRRs than other carbon nanofillers.

Table 4

Table 4. Fouling of nanocomposite membranes with different percentages.

There are two kinds of membrane fouling: fixable and non-fixable. Reverse hydraulic contamination involves the facile removal of materials via water washing. Conversely, fouling comprises substances that adhere very firmly to the membrane surface and are not removable.

In this case, the reverse washing process makes the membrane less valuable and raises the cost of running it. Chemical cleaning can remove irreversible fouling, but the membrane’s lifespan is reduced. Table 4 demonstrates different types of fouling. Modified membranes have lower resistance coefficients but higher flux recovery ratios. It is concluded that the modified membranes are more susceptible to fouling. The membrane’s irreversible resistance decreased dramatically from 22.5% to 3%. Also, Atomic Force Microscopy (AFM) imaging of the surface of the membrane revealed improved fouling of the embedded HNT/Al₂O₃-GO membranes and improved surface characteristics.

3.3 Empirical correlations and optimization

In this section, we propose a high-accuracy empirical correlation to predict the removal percentage of BSA, flux, and permeation flux. Our correlation models are developed based on the key parameters of pressure, time, and HNT/Al₂O₃-GO concentration, which have been identified as crucial factors affecting the mentioned parameters. We want to have a thorough grasp of the process of pollution removal by considering these aspects.

Equation 8 presents a multivariate polynomial correlation used to predict BSA removal percentage, pure water flux, and permeation flux as functions of three key parameters: HNT/Al₂O₃-GO concentration (C, wt%), operating pressure (P, bar), and filtration time (t, min). These variables were selected due to their strong influence on membrane behavior: nanomaterial concentration affects hydrophilicity and pore structure, pressure drives water transport through the membrane, and time reflects the duration of fouling exposure. Each term in the polynomial captures linear, interaction, and higher-order effects among these variables. Despite its complexity, this structure is essential to represent the nonlinear dependencies observed experimentally.

$Y=C_1+C_{2}x+C_{3}y+C_4{x}^2+C_{5}xy+C_6{y}^2+C_7{x}^{2}y+C_{8}x{y}^2+C_9{y}^3(8)$

Furthermore, it is important to note that our correlation models have been validated and demonstrate high accuracy (Chai et al., 2020; Alkhouzaam and Qiblawey, 2021). This guarantees that our suggested strategy is reliable and resilient. Researchers and practitioners may better use operating circumstances and water treatment system efficiency by using these correlations to learn more about the pollutant removal process. Table 5 displays the valued constants that have been optimized.

Table 5

Table 5. The constant values for the parameters in Figures 4a–c and the evaluation of the correlations using RSME and $R^2$.

A time limit of more than 100 min is needed to get the best rate of BSA removal, as shown in Figure 4a. Additionally, keeping the HNT/Al₂O₃-GO mixture between 0.6% and 0.9% seems to be the best choice. On the other hand, things go badly when both time and HNT/Al₂O₃-GO levels are low.

Figure 4

Figure 4. (a) The BSA removal percentage based on HNT/Al₂O₃-GO concentration and time, (b) the flux based on pressure and HNT/Al₂O₃-GO concentration, and (c) the permeation flux based on time and HNT/Al₂O₃-GO concentration.

There is a clear trend in the data showing that the removal of BSA is significantly better when the treatment lasts 120 min. Also, the clearance rate increases noticeably when the amount of HNT/Al₂O₃-GO goes above a certain level of about 0.7%.

As shown in Figure 4b, there is a clear link between the rise in flow and the rise in pressure. The effect of the HNT/Al₂O₃-GO concentration also aligns with this trend. So, the highest flow is reached when the pressure is 6 bar, and the concentration of HNT/Al₂O₃-GO is 1%. While looking at the information in Figure 4b, we can see that the flux goes up in the same way that the pressure on the system goes up. In the same way, a higher quantity of HNT/Al₂O₃-GO leads to a higher flux level. The best flux is at 6 bar and 1% HNT/Al₂O₃-GO. The results suggest that achieving optimal control over the flow in the membrane separation process requires meticulous regulation of the pressure and amount of HNT/Al₂O₃-GO. Specialists and researchers may enhance the efficiency of water purification systems by adjusting the settings of these components based on different flow rates.

Figure 4c shows the permeation flux in a very useful way. Following our findings, it is clear that the concentration of HNT/Al₂O₃-GO is more important than time, as the trend shows. Interestingly, the highest diffusion flux is seen in the 0.75%–1% concentration range for HNT/Al₂O₃-GO. The biggest absorption flow happens at the start and end of the process considering the time factor. On the other hand, when the HNT/Al₂O₃-GO content is 0.2%, the penetration flow is the lowest.

4 Machine learning predictions

4.1 Machine learning algorithms methodology

In this study, three machine learning algorithms ANN, RF, and SVR were employed to predict the BSA removal efficiency and permeation flux of nanocomposite membranes. Contact angle, viscosity, porosity, and HNT/Al₂O₃-GO concentration were selected as input features based on strong correlations with BSA removal and permeation flux. These factors influence membrane hydrophilicity, pore structure, and transport behavior. The HNT/Al₂O₃-GO concentration ranged from 0% to 1.0%, contact angle from 58° to 70°, and porosity from 72% to 80%, with viscosity varying accordingly. These ranges ensured meaningful variation while avoiding issues like nanoparticle agglomeration or high casting viscosity. Limitations included non-linear interactions and fabrication challenges at high concentrations, which justify the use of machine learning for robust modeling. These variables were selected as inputs based on Pearson correlation analysis, which confirmed their strong influence on the target outputs. The machine learning models were developed using a dataset consisting of 40 data points, representing variations in membrane composition and performance characteristics. Prior to training, all input features were normalized using MinMax scaling. The dataset was randomly divided into 70% training (28 samples) and 30% testing (12 samples) sets to evaluate model generalization. To ensure robustness and mitigate overfitting, 5-fold cross-validation was applied during hyperparameter tuning for each algorithm. All machine learning models were implemented using the Python programming language (version 3.10.12). The Random Forest and SVR models were developed using the scikit-learn library (version 1.3.2), while the ANN model was built using TensorFlow (version 2.14.0) with the Keras API (integrated with TensorFlow). The dataset was preprocessed using MinMaxScaler from scikit-learn for normalization, ensuring that all input features were scaled to a uniform numerical range (Kallem et al., 2022; Jia et al., 2019; Hashemi et al., 2022; Karakurt and Kartal, 2023; Alayande et al., 2022).

The ANN model was designed as a multilayer feedforward network consisting of an input layer, two hidden layers, and a single output layer. Each neuron in the network computes a weighted sum of its inputs and applies a non-linear activation function. The mathematical formulation for the output of an ANN can be written as Equation 9:

$\widehat{y}=f\left({\displaystyle \sum _{j=1}^n}{w}_j.g\left({\displaystyle \sum _{i=1}^m}{x}_i.v_{ij}+b_j\right)+b\right)(9)$

where $x_i$ are the input variables, $v_{ij}$​ are the weights connecting the input and hidden layers, $w_j$​ are the weights from the hidden to output layer, $b_j$​ and b are bias terms, and $g\left(·\right)$ and $f\left(·\right)$ represent activation functions. The rectified linear unit (ReLU) function was used in the hidden layers, while a linear activation was applied to the output layer. The network was trained using the Adam optimization algorithm with a learning rate of 0.001, and the loss function minimized during training was the mean squared error (MSE), expressed as Equation 10.

$MSE=\frac{1}{n}{\displaystyle \sum _{i=1}^n}{\left(y_i-\widehat{y_i}\right)}^2(10)$

Model parameters such as the number of neurons per layer, batch size, and number of epochs were optimized using a grid search. The model was trained for 100 epochs with early stopping to prevent overfitting. Among all tested models, the ANN achieved the highest accuracy in terms of both coefficient of determination (R²) and mean absolute error (MAE) (Khosravi et al., 2022).

RF regression was also applied as a robust ensemble method that constructs a collection of decision trees during training and outputs the average prediction from all trees. The prediction function in RF is given by Equation 11:

$y=\frac{1}{T}{\displaystyle \sum _{t=1}^T}{h}_t\left(x\right)(11)$

where T is the total number of trees in the forest, and $h_t\left(x\right)$ denotes the prediction of the t-th tree. Each decision tree is trained on a random subset of the data and features, a process known as bootstrap aggregating or bagging. The algorithm uses the reduction in impurity (typically measured by mean squared error for regression tasks) to decide on feature splits at each node. Important hyperparameters, including the number of trees, the maximum tree depth, and the minimum number of samples required for a split, were tuned through grid search. In addition to its accuracy, the RF model provided insights into feature importance, helping to quantify the relative contribution of each input variable to the predicted outputs (Lu and Elimelech, 2021).

SVR was employed to construct a regression model that finds a function with at most ε deviation from the actual outputs while maintaining model complexity as low as possible. The regression function is expressed as Equation 12:

$f\left(x\right)=〈w,x〉+b(12)$

where w and b are the weight vector and bias term, respectively. The optimization problem seeks to minimize Equation 13:

${\mathit{min}}_{w,b,\xi ,{\xi }^{*}}\frac{1}{2}{‖w‖}^2+C{\displaystyle \sum _{i=1}^n}\left({\xi }_i+{\xi }_i^{*}\right)(13)$

subject to the constraints of Equation 14.

$y_i-〈w,x_i〉-b\le \epsilon +{\mathrm{\xi }}_{\mathrm{i}},〈\mathrm{w},{\mathrm{x}}_{\mathrm{i}}〉+\mathrm{b}-{\mathrm{y}}_{\mathrm{i}}\le \mathrm{\epsilon }+{\mathrm{\xi }}_{\mathrm{i}}^{*},{\mathrm{\xi }}_{\mathrm{i}},{\mathrm{\xi }}_{\mathrm{i}}^{*}\ge 0(14)$

Here, C is a regularization parameter that controls the trade-off between flatness and error tolerance, while ε defines the width of the margin in which no penalty is given for prediction errors (El Jery et al., 2023a; El Jery et al., 2023b; Chandrashekar and Sahin, 2014; Chaurasia and Pal, 2021; Bagherzadeh et al., 2021; Chang and Gupta, 2024). To model non-linear relationships between input and output variables, the SVR implementation used a radial basis function (RBF) kernel (Batool et al., 2024), defined as Equation 15:

$K\left(x_i,x_j\right)=\exp \left(-\gamma {‖x_i-x_j‖}^2\right)(15)$

where $\gamma$ is the kernel coefficient. The SVR model’s hyperparameters, including C, ε, and γ, were optimized using a grid search with cross-validation.

All three models were trained on 80% of the dataset, with the remaining 20% used for testing. Model performance was evaluated using the MAE and R² (Eskandari et al., 2022; Zhao et al., 2020; Alimoradi et al., 2020), where using Equations 16, 17, respectively.

$MAE=\frac{1}{n}{\displaystyle \sum _{i=1}^n}\left|y_i-\widehat{y_i}\right|(16)$

$R^2=1-\frac{\sum {\left(y_i-\widehat{y_i}\right)}^2}{\sum {\left(y_i-\overline{y_i}\right)}^2}(17)$

4.2 Feature selection procedure

Selecting appropriate input parameters is critical for effective data analysis (Alimoradi and Shams, 2017; Chen et al., 2024; Ismail et al., 2024; Abba et al., 2024). Heat maps are a widely used tool for visualizing the strength and direction of correlations between variables. Each cell in a heat map represents the correlation coefficient between two parameters, with color gradients indicating the degree of association. This visual representation helps identify strongly related features, redundant variables, and underlying patterns in the data (Gbadamosi et al., 2024; Tao et al., 2024).

Figure 5 presents the heat map of the Pearson correlation of contributing parameters for both desired features. The results show the parameters’ independence and how each affects the output parameter. Therefore, the selected parameters as the input of the machine learning algorithms are contact angle, viscosity, concentration of HNT/Al₂O₃-GO, and porosity.

Figure 5

Figure 5. The Pearson correlation among the contributing factors to (a) BSA removal percentage and (b) permeation flux.

4.3 Surrogate models

The results of the predictive models for BSA removal percentage are presented in Figure 6. Figure 6a displays the outcomes obtained from the ANN model, demonstrating remarkable accuracy with an MAE of 1.04% and an R² value of 0.99. Furthermore, the figure includes a linear regression plot that aligns closely with the ideal case ($y=x$), indicating the model’s high precision. Moving on to Figure 6b, it showcases the results of the RF algorithm, which exhibits a notably low MAE of 1.98% and an R² value of 0.97. Although the linear regression slightly deviates from the accurate case, it is worth noting that the intercept of this model is higher than that of the ANN model. Finally, Figure 6c presents the SVR model, which demonstrates comparatively lower accuracy than the other two models. This is evident from the relatively lower R² value of 0.96 and a higher MAE of 2.84%. Additionally, the linear regression plot in this model showcases even more deviation from the accurate case.

Figure 6

Figure 6. The predictions for BSA removal percentage using (a) ANN, (b) RF, and (c) SVR methods.

Figure 7 shows a similar study that was conducted on permeation flux. Figure 7a shows that the ANN model has a very high R² value of 1 and an MAE of 1.35. The regression line lines up perfectly with the $y=x$ line, which shows how accurate the model is. The deep structure of the ANN models lets them make such accurate predictions. This is the second most accurate model, with an MAE of 2.12% and a R² value of 0.98. The RF model for permeation flow is shown in Figure 7b. The regression line, on the other hand, seems to diverge a little more than the ANN model. The SVR model in Figure 7c has an R² value of 0.97, which can predict what will happen. It has a relatively low MAE of 2.87%, even though it is the least reliable model compared to the other two. It is worth highlighting that the SVR model exhibits high predictive capabilities for both output parameters despite its lower accuracy when compared to the other models.

Figure 7

Figure 7. The predictions for permeation flux using (a) ANN, (b) RF, and (c) SVR methods.

The ANN emerged as the most accurate model for both parameters. A big reason for this is that deep learning models use the backpropagation method. The ANN changes its weights and biases every epoch, which makes it more accurate. This important trait is why ANN is used so much and is a good choice in many areas.

5 Conclusion

This study developed nanocomposite PSF membranes incorporating HNT/Al₂O₃-GO to enhance antifouling performance, with experimental results showing improved porosity, hydrophilicity, and BSA rejection, especially at 0.75–1.0 wt% loading. Due to the nonlinear relationships between material properties (e.g., porosity, contact angle, and viscosity) and membrane performance, machine learning (ML) models were employed to enable accurate prediction and optimization. Using a dataset of 40 samples split 70/30 for training and testing, and applying 5-fold cross-validation, three ML algorithms, ANN, RF, and SVR, were trained, with ANN achieving the highest accuracy (R² = 0.99, MAE = 1.04%). ML proved essential for modeling complex multivariate interactions, guiding feature selection, and reducing reliance on trial-and-error experimentation. Compared to empirical correlations, ML offered more robust, generalizable, and scalable performance prediction. Thus, integrating ML into this membrane development process was not supplementary but necessary, enabling data-driven optimization of membrane properties for enhanced water treatment efficiency.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

SM: Conceptualization, Writing – original draft, Validation, Software, Visualization, Methodology. HO: Writing – review and editing, Conceptualization, Software, Formal Analysis, Data curation. AV: Conceptualization, Formal Analysis, Validation, Software, Writing – review and editing. AA: Conceptualization, Writing – review and editing. ShS: Project administration, Data curation, Visualization, Writing – review and editing, Conceptualization. SaS: Visualization, Resources, Writing – review and editing. AS: Conceptualization, Investigation, Funding acquisition, Writing – review and editing, Resources, Data curation.

Funding

The author(s) declare that financial support was received for the research and/or publication of this article. This research is partially funded by Zarqa University and Northern Border University (project number “NBU- FFR-2025-289-12”).

Acknowledgments

This research is partially funded by Zarqa University. Also, the authors extend their appreciation to the Deanship of Scientific Research at Northern Border University, Arar, KSA for funding this research work through the project number “NBU- FFR-2025-289-12”.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declare that no Generative AI was used in the creation of this manuscript.

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