Response Surface Methodology–Artificial Neural Network (RSM-ANN) Approach to Optimise Photocatalytic Degradation of Levofloxacin Using Graphene Oxide-Doped Titanium Dioxide (GO-TiO₂)

Abstract

Harnessing the synergistic potential of graphene oxide-doped titanium dioxide (GO-TiO₂), this study pioneers an advanced photocatalytic approach by incorporating graphene oxide-doped titanium dioxide (GO-TiO₂) as a catalyst to enhance the photocatalytic degradation of levofloxacin (LVX), with optimisation of parameters using response surface methodology (RSM) and artificial neural networks (ANNs). By adjusting key operational parameters such as catalyst dosage, LVX concentration, pH, and percentage dopant in TiO₂, the study aimed to maximise degradation efficiency. The RSM statistical model highlighted optimal conditions, i.e., neutral pH, 0.1 g/g dopant, 1.1 g/L catalyst, and 25 ppm LVX concentration, achieving a degradation efficiency close to 80% (R² = 0.88). An ANN model was also developed, offering a three-layer neural network that accurately predicts LVX degradation under varied conditions, with R² reaching 0.97. Current modelling techniques frequently fail to strike a balance between practical insights for optimising photocatalytic degradation and predictive accuracy. By combining the parametric insights of RSM with the nonlinear predictive power of ANN, this study closes that gap and develops a sustainable, data-driven framework for effectively breaking down pharmaceutical pollutants and developing environmentally friendly wastewater treatment methods.

1. Introduction

Antibiotics’ ability to effectively inhibit dangerous bacterial species, viruses, and other microorganisms has led to a sharp increase in their use worldwide. A popular fluoroquinolone antibiotic, levofloxacin (LVX), is preferred due to its strong ability to treat bacterial infections. However, aquatic ecosystems and beneficial microorganisms are at risk due to its persistent nature and release into the environment through industrial wastewater, which poses serious toxicological risks [1].

Conventional wastewater treatment methods (physical, chemical, and biological) often fail to remove persistent pharmaceutical pollutants like levofloxacin due to their complex structures and resistance to degradation [2]. This inefficiency underscores the urgent need for sustainable alternatives, such as advanced oxidation-based photocatalytic processes. Among them, TiO₂ photocatalysis has shown promise in degrading organic contaminants, yet its reliance on UV light, which constitutes only a small portion of solar radiation, limits practical applications [3,4]. Selecting an optimal light source is crucial for enhancing efficiency while ensuring economic and environmental viability [5,6]. Recently, visible LED light has emerged as a superior alternative, offering greater durability, energy efficiency, and operational safety over conventional UV sources [7]. This study addresses these limitations by exploring graphene oxide-doped TiO₂ under visible light, providing a sustainable and effective solution for tackling pharmaceutical pollution in wastewater treatment.

Doping TiO₂ significantly enhances its photocatalytic performance by improving light absorption and charge separation compared to pure TiO₂, which is primarily active under UV light. This limitation restricts its efficiency in utilising visible light, a major component of natural sunlight [8,9]. Introducing dopants such as metals (Fe, Ag, or Cu) or non-metals (like nitrogen, carbon, or sulphur) alters the electronic structure, allowing the material to absorb visible light more effectively. This expands the photocatalytic activity into the visible spectrum, increasing its potential to degrade pollutants under natural sunlight [10,11]. These modifications reduce the recombination of electron–hole pairs and promote the generation of reactive species, such as hydroxyl radicals, which degrade pollutants effectively under sunlight [12,13].

Metal-doped TiO₂ photocatalysts face limitations such as photo corrosion, instability, and poor visible light activity due to the lack of significant bandgap reduction. Metal ions often act as recombination centres, reducing photocatalytic efficiency. Also, thermal instability and the high costs of metal dopants, such as noble metals, hinder their practical applications [14,15].

Non-metal-doped TiO₂ offers distinct advantages over their metal-doped counterparts. Non-metal doping narrows the TiO₂ bandgap by forming hybrid orbitals above the valence band, enabling visible light absorption. Non-metals also enhance electron–hole pair separation and serves as a conductive network, improving charge transport and reducing recombination rates. Moreover, non-metal-doped TiO₂ exhibits more excellent stability and cost-effectiveness, making it ideal for scalable photocatalytic applications [15,16].

Many studies report photocatalytic degradation based on a single parameter, often overlooking the intricate interplay of multiple factors. A systematic approach is essential to understand the combined effects of pH, dopant type, catalyst dosage, and pollutant concentration. Unlike most research limited to 20–25 ppm, we have successfully degraded levofloxacin concentrations up to 100 ppm, addressing real-world industrial challenges where higher pollutant loads demand more effective solutions. Additionally, we emphasise the use of visible light over conventional UV, making the process more cost-effective, environmentally friendly, and safer for long-term application. Our approach also optimises degradation efficiency within just three hours, eliminating the need for prolonged sunlight exposure.

Recently, response surface methodology and artificial neural networks have been shown to provide superior prediction accuracy for nonlinear datasets in diverse domains such as food processing, environmental engineering, and biotechnology [17,18]. To further refine and scale this approach, we employ response surface methodology (RSM) to systematically evaluate and optimise critical operational parameters influencing levofloxacin degradation using GO-TiO₂. Coupled with artificial neural network (ANN)-based predictive modelling, this integration provides deeper insights into parameter interactions, ensuring both accuracy and scalability. The findings highlight the enhanced performance of GO-TiO₂ under visible light, reinforcing its potential as a sustainable and high-performance solution for pharmaceutical wastewater remediation—an increasingly urgent environmental challenge.

2. Materials and Methods

2.1. Materials

TiO₂ material was synthesised through a sol–gel process [19] using titanium tetra isopropoxide (TTIP) (>98%), which was purchased from Spectrochem Pvt. Ltd., Mumbai, India, and isopropanol (IPA) was from Merck Specialities Pvt. Ltd., Mumbai, India. Graphene oxide was obtained from Sigma-Aldrich Chemicals Pvt. Ltd., Bangalore, India, and it was used as a dopant. Ammonia was procured from S D Fine-Chem Limited, Mumbai, India, and was used as a hydrolysis agent. Levofloxacin antibiotic was acquired from Rhombus pharma private limited, Ahmedabad, Gujarat, India. All aqueous solutions were prepared with deionized water.

In our previous study [19], the synthesised graphene oxide (GO)-modified TiO₂ photocatalyst was comprehensively characterised to evaluate its structural and optical enhancements. X-ray diffraction (XRD) confirmed the anatase phase formation, with crystallite sizes decreasing from 69.08 nm for pure TiO₂ to 51.04 nm for GO-TiO₂. Brunauer–Emmett–Teller (BET) surface area analysis revealed a significant increase in surface area for GO-TiO₂ (61.3 m²/g) compared to pure TiO₂ (15 m²/g), indicating enhanced adsorption capacity. UV–vis spectroscopy showed a bandgap reduction from 3.18 eV to 3.09 eV, promoting better visible light absorption. FTIR spectra exhibited Ti–O–C bonding, confirming successful GO integration. Transmission electron microscopy (TEM) images further revealed a mesoporous structure with uniformly distributed spherical grains. The reaction followed pseudo-first-order kinetics, yielding a rate constant of 0.015 min⁻¹, and it conformed well to the Langmuir–Hinshelwood model.

2.2. Experimental Methods

Levofloxacin (LFX) degradation was evaluated at an initial concentration of 50 ppm using 1 g/L of catalyst under neutral pH and magnetic stirring at 500 rpm, with visible irradiation from a 40 W white LED lamp (peak emission ~455 nm within the visible light range) positioned at a fixed distance of 15 cm from the reaction surface [19]. Bare TiO₂ and graphene oxide-modified TiO₂ (GO–TiO₂) were tested at GO loadings of 0.05, 0.10, and 0.15 g g⁻¹, which corresponded to 1.6%, 2.85%, and 3.1% carbon incorporation, respectively, as confirmed by elemental analysis. After 3 h of irradiation, degradation efficiencies rose from 40% for bare TiO₂ to 57%, 86%, and 88% for the 0.05, 0.10, and 0.15 g g⁻¹ GO–TiO₂ samples. Degradation (%) and kinetics were calculated via [%] = [(C₀ − C)/C₀] × 100, where C₀ and C are the LFX concentrations (mg L⁻¹) before and after irradiation, as shown in Figure 1, and LFX concentrations were determined against a calibration curve of absorbance versus concentration. To determine the concentration of LFX during the photodegradation experiments, absorbance intensity at λmax of 288 nm was checked using an Agilent Cary 5000i spectrophotometer, Santa Clara, CA, USA.

3. Results

3.1. Degradation of LFX

An observation that can be drawn from Figure 1 is that the excessively reduced graphene oxide loading can obstruct the TiO₂ component’s ability to capture light, limiting the number of TiO₂ sites that reach the excited state, thereby diminishing the catalyst’s photocatalytic efficiency [20]. Hence, after dopant loading of 0.15 g g⁻¹, there is no major change observe compared to 0.1 g g⁻¹. The kinetics of LFX degradation followed a pseudo–first-order Langmuir–Hinshelwood model, which assumes that surface oxidation is rate-determining at full catalyst coverage.

At neutral pH, 0.1 g g⁻¹ graphene oxide-doped TiO₂ at about 1g/L, as shown in Figure 2, exhibited enhanced photocatalytic degradation efficiency, primarily due to the adsorption of levofloxacin via the nitrogen atom in its piperazinyl ring, which facilitated ligand-to-metal charge transfer (LMCT). Under basic conditions, LFX tended to adsorb through its carboxylate group, resulting in reduced photocatalytic activity. In acidic environments, the lower degradation performance was attributed to a combined effect of decreased adsorption and the involvement of the ketone–carboxyl functional group of LFX in interacting with the TiO₂ surface [1].

GO–TiO₂ also exhibited excellent recyclability, as shown in Figure 3, maintaining its activity over three consecutive cycles. The degradation efficiency was recorded as 90%, 86%, 84%, 72%, and 63% from the first to fifth cycle, respectively. The gradual decline in efficiency indicates partial catalyst deactivation, likely due to surface fouling, the adsorption of intermediates, or photocorrosion. The catalytic activities can be regained by using popularly used either thermal or solvent treatment [21]. The enhanced photocatalytic performance is attributed to carbon doping, which increases TiO₂’s electrical conductivity and promotes charge transfer from the bulk lattice to the surface.

A major challenge is to optimise four critical factors, namely pH, dopant type, pollutant concentration, and catalyst dosage. An integrated RSM-ANN framework unlocks a deeper understanding of the nonlinear interactions that drive photocatalytic performance and provides the predictive power needed for reliable scale-up. By systematically exploring each variable with RSM and then refining the parameter space with ANN’s machine learning algorithms, researchers can rapidly identify robust operating conditions while quantifying synergistic effects that traditional designs often miss.

3.2. Response Surface Methodology

The next stage after the single-parameter method is process optimisation. Methodologies like response surface methodology, genetic algorithms, and Taguchi can be used to optimise processes [22,23]. RSM offers a systematic and efficient approach to investigating and optimising the intricate mechanisms of the degradation of persistent pharmaceutical and pesticide compounds [24,25,26,27,28,29,30]. This study aims to delve into the intricacies of the photocatalytic degradation process, shedding light on how RSM can be harnessed to enhance its efficiency and effectiveness [18,24,25,31,32,33].

The selection of an appropriate design approach greatly influences the construction of a response surface and the precision of the predictive model, especially in physicochemical pollutant removal. Key design strategies include full factorial design (FFD), central composite design (CCD), Box–Behnken design (BBD), and Doehlert design (DD) [34,35].

In this study, using Design Expert software (https://www.statease.com/software/design-expert/ (accessed on 6 August 2025)), RSM was used to optimise the degradation of LFX. The four independent parameters chosen for this study were the pH of the solution, the concentration of the solution, catalyst loading, and dopant loading. Central composite design, the most frequently used form of RSM, was employed to evaluate the influence of these four variables across 30 experiments. CCD was selected for its ability to efficiently combine factorial, axial, and centre points, enabling a robust assessment of linear and quadratic effects with fewer experimental runs. Its flexibility in scaling and precise curvature estimation makes CCD particularly suitable for optimising complex processes like LFX degradation [36,37]. The experimental range and levels are as shown in

Table 1. Experimental range and levels of the independent test variable ranges.

Process Variables	LEVELS
	−α	−1	0	1	α
pH	3	5	7	9	11
Dopant (g/g)	0	0.05	0.1	0.15	0.2
Catalyst (g/L)	0	0.5	1	1.5	2
Pollutant (ppm)	0	25	50	75	100

.

3.3. Experimental Results of RSM

Using a cubic composite design approach, RSM was employed to investigate the photocatalytic degradation of LFX using TiO₂ particles. The study considered pH, dopant source, catalyst, and pollutant concentration as dependent variables. RSM has been developed for the following models: linear, two-factor interaction (2FI), quadratic, and cubic polynomials to find the best-fitting model. According to these sequential models, the best fit for the developed response is the highest-order polynomial with significant additional terms that was not aliased.

Table 2. Experimental CCD for forecasting LFX degradation using GO-TiO₂ particles.

Run No.	pH (A)	Dopant (B)	Catalyst (gm/L) (C)	Pollutant (ppm) (D)	Experimental Degradation (%)	CCD Predicted (%)	Residue
1	9	0.15	0.5	25	25	31.54212	−6.542
2	7	0.1	1	50	68	70.501	−2.501
3	9	0.05	0.5	25	44	37.45879	6.541
4	5	0.15	0.5	75	17	21.87693	−4.877
5	7	0.2	1	50	55	39.501	15.499
6	11	0.1	1	50	10	14.83456	−4.835
7	5	0.05	0.5	75	15	15.2936	−0.294
8	7	0.1	2	50	50	33.16777	16.832
9	9	0.05	1.5	25	54	55.70886	−1.709
10	5	0.05	1.5	25	35	48.29202	−13.292
11	7	0.1	1	100	58	57.67015	0.330
12	5	0.05	1.5	75	23	23.04367	−0.044
13	5	0.15	1.5	25	45	53.37535	−8.375
14	7	0.1	1	50	73	70.501	2.499
15	9	0.05	0.5	75	35	33.21044	1.790
16	7	0.1	1	50	71	70.501	0.499
17	9	0.15	1.5	75	30	33.54384	−3.544
18	7	0	1	50	38	39.83433	−1.834
19	7	0.1	1	0	100	86.66685	13.333
20	5	0.05	0.5	25	26	29.04195	−3.042
21	3	0.1	1	50	20	1.500877	18.499
22	7	0.1	0	50	5	8.167627	−3.168
23	7	0.1	1	50	70	70.501	−0.501
24	5	0.15	1.5	75	28	28.627	−0.627
25	5	0.15	0.5	25	28	35.12528	−7.125
26	7	0.1	1	50	69	70.501	−1.501
27	9	0.15	1.5	25	42	48.79219	−6.792
28	9	0.15	0.5	75	34	27.79377	6.206
29	9	0.05	1.5	75	40	39.96051	0.039
30	7	0.1	1	50	72	70.501	1.499

displays the entire matrix of experimentation results.

Table 3. Model summary statistics.

Source	Std. Dev.	R2	Adjusted R2	Comments
Linear	22.65	0.1613	0.0271
2FI	25.60	0.1854	−0.2433
Quadratic	10.96	0.8820	0.7720	Suggested
Cubic	9.09	0.9622	0.8433	Aliased

shows model summary statistics based on which we can say that quadratic and cubic fit perfectly, but due to the high level of interaction, quadratic is selected for optimisation.

Analysis of variance (ANOVA) was applied to evaluate the adequacy of the model [34,36,38]. From the ANOVA of the empirical second-order polynomial model, as shown in

Table 4. Analysis of variance (ANOVA) of the input parameters on degradation efficiency.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value	Remarks
Model	13,484.12	14	963.15	8.01	0.0001	Significant
A-pH	266.67	1	266.67	2.22	0.1571
B-Dopant	0.1667	1	0.1667	0.0014	0.9708
C-Catalyst	937.50	1	937.50	7.80	0.0137
D-Pollutant	1261.50	1	1261.50	10.49	0.0055
AB	144.00	1	144.00	1.20	0.2910
AC	1.0000	1	1.0000	0.0083	0.9285
AD	90.25	1	90.25	0.7507	0.3999
BC	1.0000	1	1.0000	0.0083	0.9285
BD	0.2500	1	0.2500	0.0021	0.9642
CD	132.25	1	132.25	1.10	0.3109
A2	6660.76	1	6660.76	55.41	<0.0001
B2	1629.76	1	1629.76	13.56	0.0022
C2	4257.19	1	4257.19	35.41	<0.0001
D2	4.76	1	4.76	0.0396	0.8449
Residual	1803.25	15	120.22
Lack of Fit	1785.75	10	178.58	51.02	0.0002	significant
Pure Error	17.50	5	3.50
Cor Total	15,287.37	29

, p-values indicate that the model is highly significant.

In the ANOVA table, the p-value indicates the statistical significance of each factor, interaction, or overall model in influencing the response variable. A p-value less than 0.05 signifies a significant effect, meaning the corresponding term has a meaningful impact on the response. For instance, factors like C-Catalyst (p = 0.0137), D-Pollutant (p = 0.0055), and quadratic terms A², B², and C² (p < 0.05) significantly affect the response. In contrast, others, such as A-pH, B-Dopant, and interactions (e.g., AB, AC), with p-values greater than 0.05, are less influential within the studied range. Additionally, the model’s p-value (<0.0001) confirms that the overall model is statistically significant.

A second-order polynomial (quadratic) equation was used to fit the experimental results of CCD as follows:

$$\begin{gathered} Y\left(\%\right)=b_0+b_1{x}_1+b_2{x}_2+b_3{x}_3+b_4{x}_4+b_{12}{x}_1{x}_2+b_{13}{x}_1{x}_3+b_{14}{x}_1{x}_4+b_{23}{x}_2{x}_3+b_{24}{x}_2{x}_4+b_{34}{x}_3{x}_4 \\ +b_{11}{x}_1^2+b_{22}{x}_2^2+b_{33}{x}_3^2+b_{44}{x}_4^2 \end{gathered}$$

(1)

where Y represents the response variable (degradation% efficiency), b_i, b_ii, and b_ij are the regression coefficients for linear and quadratic effects and the coefficients of the interaction parameters, respectively, and x_i represents the independent variables studied.

Based on the experiments carried out, a second-order polynomial equation in terms of coded actual factors was found that demonstrates the empirical relationships between the independent variables and the response:

$$\begin{gathered} \%Degraation=\left(-227.02083\right)+\left(57.08333\times A\right)+\left(830.00000\times B\right)+\left(126.41667\times C\right)- \\ \left(0.469167\times D\right)-\left(30\times A\times B\right)-\left(0.25\times A\times C\right)+\left(0.0475\times A\times D\right)-\left(10\times B\times C\right)+\left(0.1\times B\times D\right)- \\ \left(0.23\times C\times D\right)-\left(3.89583\times A^2\right)-\left(3083.3333\times B^2\right)-\left(49.8333\times C^2\right)+\left(0.000667\times D^2\right) \end{gathered}$$

(2)

The coded terms A, B, C, and D represent pH, dopant, catalyst dosage, and pollutant concentration. A positive synergic effect indicates a positive impact; a negative antagonistic impact suggests a negative impact [35].

The contour and surface plot, as shown in Figure 4, gives information regarding how the pH varies concerning changes in the dopant source. As we increase the dopant up to 0.1 gm/gm, we can see an increase in degradation under neutral pH conditions. Still, beyond that, we cannot see a significant change in degradation even after varying the pH and dopant. Similarly, a catalyst dosage beyond 1 g/L and neutral pH conditions do not increase degradation significantly. So, from the numerous runs with varying parameters, we can conclude that the optimised dopant and catalyst should be 0.1 g/g and 1 g/L, respectively, to achieve the effective degradation of pollutants.

As shown in Figure 5, the optimised result can be inferred from the desirability plot, which shows an operating pH around 7, dopant around 0.1 g/g, catalyst dosage near 1.1 g/L, pollutant loading 25 ppm, and degradation achieved close to 80%. After the validation run of the desirability plot, the percentage degradation was 83% based on 288 nm as the maximum wavelength with a shift in peak after 120 min.

Applying the central composite design approach within RSM provided valuable insights into photocatalytic degradation, identifying critical factors like pH, dopant concentration, catalyst dosage, and pollutant concentration. The quadratic polynomial model, validated through an ANOVA, demonstrated its adequacy in predicting degradation efficiency with high accuracy, as evidenced by the R² value of 0.8820 and minimal residual errors. The contour and surface plots further clarified the interactions between the key parameters, confirming optimal degradation conditions at pH 7, a dopant concentration of 0.1 g/g, catalyst dosage of 1 g/L, and pollutant concentration of 25 ppm, achieving a predicted degradation near 80%, as per the desirability plot shown in Figure 5.

The RSM results were integrated with an ANN model to enhance the predictive and optimisation capability. This hybrid RSM-ANN approach builds on the robust statistical foundation of RSM while leveraging the flexibility of ANN to capture complex, nonlinear relationships in the system. The following section explores the implementation of the RSM-ANN model, its validation against experimental data, and its scalability for real-world applications in wastewater treatment.

3.4. RSM-ANN Model for Predicting Percentage Degradation

ANNs are powerful for predicting nonlinear and multifaceted models [35,39,40]. Among the various ANN architectures, the multi-layer perceptron (MLP), with its robust feedforward structure, is one of the most widely used for data prediction across numerous fields of science and technology [40,41,42]. The MLP network excels at identifying relationships between dependent and independent variables, even in complex scenarios [43,44,45]. A typical MLP consists of input, hidden, and output layers, as shown in Figure 6. ANN models rely on three key transfer functions, namely exponential sigmoid, tangent sigmoid, and linear functions, which together can form either linear or nonlinear algebraic equations [19,28]. Networks with bias tend to outperform non-biased ones, as bias is applied across all network connections, adding an extra degree of freedom to the system [46].

A hybrid RSM-ANN model has been developed to improve the model’s performance based on the data obtained from RSM for optimal degradation forecasting [29,47,48,49]. Data for the ANN model was obtained from photocatalytic experiments designed using the central cubic design based on RSM. In total, 30 experiments were developed through the CCD approach and used as input for fitting the ANN model. The model datasets were split into three parts, namely training (70%), testing (15%), and validation (15%).

The error objectives were set to 0.0001 and Mu at 0.01, employing the Levenberg–Marquardt algorithm. The optimal number of neurons in the hidden layer was determined empirically by evaluating models with 2, 4, 5, 7, 9, 10, 11, 12, 15, and 20 nodes, as illustrated in Figure 7. Among these configurations, the model with 10 neurons in the hidden layer exhibited the best performance in terms of training accuracy and generalisation capability, as assessed by the mean squared error (MSE) and coefficient of determination (R²) metrics. As shown in Figure 8, the ANN model with a 4–10–1 architecture (comprising four input nodes, ten hidden nodes, and one output node) demonstrated superior fitness characteristics.

To further evaluate the model’s performance, we applied k-fold cross-validation with k = 3. The dataset was divided into three equally sized folds, each containing 10 data points. The validation results for each fold are presented in

Table 5. Validation results for each fold with MSE and R².

Fold	MSE	R2
1	0.00418	0.9711
2	0.00423	0.9713
3	0.00398	0.9686
Average	0.004129	0.97036

. These results clearly confirm that the 4–10–1 architecture delivers superior predictive performance. Consequently, this configuration was selected for all subsequent modelling and analysis.

Regression analysis was conducted to evaluate the performance of the ANN (4–10–1) architecture by comparing the network outputs with the corresponding targets. The total regression graph, as illustrated in Figure 9, shows the relationship between network outputs and targets. The observed correlation coefficients for training, validation, and testing are 0.9983, 0.9907, and 0.8981, respectively, with a combined correlation coefficient of 0.9704 for all datasets. These high correlation values indicate minimal error in the ANN predictions, demonstrating the model’s accuracy. The close agreement between experimental and predicted values highlights the low prediction error, emphasising the reliability of the ANN in modelling the response.

In an ANN, the inputs or features directly influence the behaviour of each neuron through a network of weights and biases. Each input variable, such as pH, catalyst, dopant, and pollutant, is associated with a weight, which reflects the strength and nature of its influence on a given neuron. For instance, as shown in

Table 6. Values of connection weights and biases for the completed neural network model.

W1	N1	N2	N3	N4	N5	N6	N7	N8	N9	N10	Bias 2
pH	−2.34	2.99	2.42	−2.54	−0.95	0.04	3.46	0.63	1.23	−2.42
Catalyst	2.27	−2.44	0.35	5.33	1.87	7.62	1.83	−4.02	−5.21	−6.65
Dopant	3.37	−2.37	4.91	−2.17	1.45	−0.65	−3.31	−5.51	0.92	−0.78
Pollutant	−6.28	−0.11	1.52	0.89	5.87	3.67	−0.10	1.19	−2.97	−0.68
Bias 1	2.89	−4.17	−2.74	3.45	4.07	0.61	4.79	−1.15	4.05	−3.35	5.09

, the weight associated with pH on neuron N1 is −2.34, while for neuron N2, it is 2.99. This difference in weights indicates that pH has a repressive effect on N1 and an excitatory effect on N2. In other words, a positive weight reflects an excitatory impact, increasing the neuron’s output as the input increases. In contrast, a negative weight indicates a repressive effect, decreasing the neuron’s output as the input increases.

Each neuron processes a weighted sum of its inputs. For example, the output of N1 can be calculated as follows:

$$N1=(pH\times -2.34)+(Catalyst\times 2.27)+(Dopant\times 3.37)+(Pollutant\times -6.28)+Bias1$$

(3)

In this equation, the weights (−2.34, 2.27, 3.37, and −6.28) represent the influence of each respective feature, while the bias term (Bias1) provides additional flexibility, allowing the neuron to adjust its activation threshold. This bias allows the neuron to produce meaningful outputs even when the input value is zero, thus enhancing the network’s capacity to model complex, nonlinear relationships. This step enables the network to model intricate patterns within the data [35].

Biases are often applied at multiple stages within an ANN. In the example above, Bias1 is applied to each neuron individually within a given layer (such as N1 through N10), modifying the neuron’s activation threshold for that specific layer. Additional bias terms like Bias2 may be applied at subsequent or output layers. These biases allow the network to adjust its activation function further, facilitating flexibility and enabling the model to fit the data accurately [23,50].

Ultimately, the neural network leverages these weights and biases to process inputs through multiple layers of neurons, transforming the data and producing a final output. The network optimises these weights and biases through iterative training, learning from the data and capturing the underlying relationships to generalise new data effectively.

4. Conclusions

In summary, the GO-modified TiO₂ photocatalyst demonstrated significantly improved photocatalytic activity under visible light, which can be attributed to its enhanced surface area, reduced bandgap, and effective charge separation. These structural and optical improvements, as confirmed in our previous characterisation study [17], contributed to the efficient degradation of levofloxacin and reasonable recyclability across multiple cycles. The findings reinforce the potential of GO–TiO₂ as a cost-effective and scalable photocatalyst for wastewater treatment applications.

This study used a combination of single-parameter analysis and RSM based on CCD to successfully determine the ideal conditions for the photocatalytic degradation of LVX. A neutral pH, a pollutant concentration of 25 ppm, a catalyst dosage of 1 g/L, and a dopant source concentration of 0.1 g/g were among the optimised parameters. With an R² value of 0.88, an adjusted R² of 0.774, and a significant p-value of 0.0001, a regression model derived from single-parameter experiments was validated by an ANOVA and showed a strong model fit, suggesting a good correlation between the experimental and predicted data. Additionally, the study predicted LVX degradation using a three-layer ANN model, and the outcomes closely matched those from the CCD optimisation. These results highlight the potential of combining ANN and CCD approaches for predictive modelling and optimisation in environmental applications, as well as the efficacy of GO-TiO₂ under ideal conditions for pharmaceutical pollutant degradation. This all-encompassing strategy supports the effectiveness of photocatalytic techniques for purifying water and offers a strong foundation for further studies on the degradation of pollutants with cutting edge materials.