Estimation of specific surface area and higher heating value of biochar and activated carbon produced by pyrolysis and physico-chemically assisted pyrolysis of biomass using an artificial neural network (ANN)

In the experimental studies, TW and HS were used as biomass for the production of biochar and activated carbon, as explained in the supplementary file (SF) and Fig. 1.

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In this study, biochar (BC) and activated carbon (AC)) were produced by different methods, including conventional pyrolysis, acid, and base activation, and pyrolysis after microwave (MW) and ultrasound (US) activation following acid and base activation. For conventional pyrolysis, 5 g of the dried TW was filled into a quartz tube with a glass funnel and placed in the area where the isothermal temperature of the oven is located as seen in Fig. 1, and pyrolyzed at 300, 500, 700, and 900 °C for 1 h using a horizontal tube furnace (Protherm furnace) in a 20 mm ID quartz tube under the flowing nitrogen gas (80 mL/min) at a rate of 10 °C per minute. These materials produced by conventional pyrolysis of biomass (in a nitrogen atmosphere) are called biochar (BC). The biochar samples obtained were washed with distilled water until a clear filtrate was obtained and dried at 80 °C for 12 h. These samples were labeled as TWBC-Px, where P and x stand for pyrolysis and pyrolysis temperature, respectively. 5 g of dried HS were pyrolyzed for 1 h at 500 °C with a ramp of 10 °C per minute under a flowing N₂ atmosphere as described for TW. After pyrolysis, the HS biochar was washed and dried at 80 °C for 1 h and denoted as HSBC-P500. For the activation of biomass with phosphoric acid (H₃PO₄) and potassium hydroxide (KOH) solution (3 M), 5 g biomass (TW or HS) for each study was added to a beaker, and mixed with 15 mL of 85% H₃PO₄ or 15 mL of 3 M KOH solution. The mixture was either US-activated for 90 min or left for 24 h. The US activation was performed at 250 Watt (28 kHz) for 90 min. The US activation duration was determined according to previous study [8]. After US activation, the mixture was exposed to MW in a microwave digestion system (Cem Mars 6) for 900 W with a frequency of 2.45 GHz for 30 s. US and MW exposed mixtures were pyrolyzed at 500, 700, and 900 °C for 1 h with a ramp of 10 °C /min under the flowing N₂. The materials produced by pyrolysis of physically and/or chemically activated biomass are called activated carbon (AC). The produced activated carbon samples were labeled as TWAC-y-US90-MW-Pz, where y and z indicate activation chemical (H₃PO₄ (A) or KOH solution) and pyrolysis temperature, respectively. Additionally, the biomass mixed with H₃PO₄ or 3 M KOH solution was pyrolyzed at 300, 500, 700, and 900 °C after waiting for 24 h. The activated carbon samples were labeled as TWBC-y-Pz, where y and z indicate activation chemical (H₃PO₄ (A) or KOH solution) and pyrolysis temperature, respectively. To determine the effect of MW on biomass activation with H₃PO₄ and 3 M KOH, 30 s MW was applied to the biomass activated with H₃PO₄ or 3 M KOH for 24 h, and the sample was pyrolyzed at 500 °C for 1 h with a heating rate of 10 °C/min under the flowing N₂. The samples were denoted as TWAC-y-MW or TWAC-y-MW-P500, where y indicates activation chemical (H₃PO₄ (A) or KOH solution). Similar to TW, HS activated with H₃PO₄ was either pyrolyzed directly or pyrolyzed after exposure to MW for 30 s in N₂ atmosphere for 1 h at 500 °C with a heating rate of 10 °C/min. HS was used instead of TW in naming the produced samples. The preparation scheme and list of biochar and activated carbons are shown in Fig. 1 in Table S1, respectively.

An elemental analyzer (Thermo Scientific& Flash 2000/ MAS 200R) was used to determine the elemental composition (C, H, N, and S) of the biomass, biochar, and activated carbons, and Eq. (1) was used to compute the sample’s oxygen (O) concentration. Analysis was repeated twice for each sample and averaged.

The weight loss of the samples in a heating oven (Nuve FN-400) at 105 °C was used to measure their moisture content. Samples (0.5 g) were heated to 750 °C for 8 h in order to measure the ash concentration, which was then computed from the variations in sample weight. A closed crucible containing 0.5 g of the sample was heated to 900 °C in an oxygen-limited atmosphere for 10 min in order to measure the volatile matter concentration. The following formula is used to determine the fixed carbon content.

The higher heating value (HHV) of carbonaceous materials indicates the upper limit of the thermal energy produced by the complete combustion of the material and is measured as a unit of energy per unit mass or volume of the material. The HHV is measured based on the condensation of water that brings all combustible products to standard conditions (25 °C). For this purpose, the IKA C4000 calorimetric bomb was used to determine the HHV of various samples. Approximately 200–500 mg of the dried sample were placed in the bomb of the calorimeter and loaded with oxygen. Before loading with oxygen, a 13 cm long copper wire was used to establish conductivity between the sample and the calorimeter bomb. The bomb was then placed in the calorimeter, and the sample was completely combusted. During combustion, the first temperature (T1) and the second temperature (T2) were measured. The calorimetric value was calculated using the heat capacity of the calorimeter.where HHV: Calorific value or higher heating value (J/g),

Cp_K: Heat capacity of the calorimeter (8531.59 J/^oC),

Zwo: Length of initial copper wire (cm).

Zw: length of copper wire after burning(cm).

C_W: Calorific value of 1 cm copper (J/cm).

Q: Heat capacity of copper wire (J).

m: Mass of the sample,

∆T: Difference between the final and initial temperatures of the substance.

A relationship between HHV and LHV is given in Eq. (20).

Using a gas sorption analyzer (AUTOSORB 1C, Quantachrome Corp, USA), the SSA, total pore volume, and average pore diameter of the various biochar and activated carbon samples were determined, as previously described [8]. Before analysis, the materials were degassed in a vacuum atmosphere at 300 °C. Degas temperature for biomass was chosen to be 30 °C to prevent structural and chemical degradation of the material. The purpose of degassing is to remove moisture and volatile substances from the surfaces of materials and to open the pores.

For the ANN model as shown in Fig. 2, the TW and HS biomass samples were used. In addition, pyrolysis conditions (temperature, operating time, and heating rate), proximate analysis (volatile matter, fixed carbon, moisture, and ash), and ultimate analysis (C, H, N, O, and S) were taken as input data, whereas HHV and SSA of biochar and activated carbon samples were used as output data for ANN models. The selection of input variables, including pyrolysis parameters and feedstock properties, was based on their well-documented influence on the physicochemical properties of biochar and activated carbon. Pyrolysis temperature, heating rate, and residence time are known to affect pore development, carbon structure, and energy content, making them essential predictors for biochar characteristics [31, 32]. Similarly, biomass composition—particularly its carbon and hydrogen content derived from proximate and ultimate analyses—has been widely recognized for its role in determining the HHV [23, 32, 33]. By incorporating these variables, the ANN model was designed to capture the non-linear relationships between input factors and output responses, providing accurate predictions without the need for extensive experimentation [23].

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The dataset in this study comprises 40 samples. The features used in the ML analysis were derived from 160 proximate analysis values and 200 ultimate analysis values, while the outputs correspond to 40 HHV analysis values and 40 SSA analysis values for carbonized materials. To improve the learning speed of the ANN and ensure that the data falls within a specific range, normalization of the input and output data was carried out. Data normalization was performed in MATLAB 2016 using the mapminmax() [−1, 1] algorithm, as shown in the equation below [23].where x is the original data,\({x}_{max} and {x}_{min}\) are the maximum and minimum values in the original data, y is the normalized data, \({y}_{max} and {y}_{min}\) are the maximum and minimum values of normalized data.

No manual weighting of input variables was applied before model training. The parameters of the ANN, including the initial weights, were randomly initialized before training. Instead, the ANN was designed to automatically optimize the weights during the training process, ensuring that the significance of each variable is learned through its contribution to minimizing prediction error.

An ANN’s architecture abstracts the link between input and output by utilizing hidden layers with varying numbers of neurons. Through a comparison of the created ANN model’s outputs with experimental data, the network’s efficacy is assessed [34, 35]. The MSE and MAE values are used to calculate the optimum number of neurons in the hidden layer. Optimizing the ANN architecture’s parameters, such as the number of hidden layers and neurons in each layer, is essential to reducing network error. Here, theoretical knowledge and the trial-and-error approach are used to determine the number of hidden layers and the number of neurons in each layer. In this study, to find the optimal number of hidden layers, a trial-and-error method was applied between 1 and 20 hidden neurons. In addition, performance evaluation using the R² and R coefficients, as well as MSE and MAE errors, facilitated the search for the optimal number of hidden layers for each learning algorithm.

The tangent sigmoid (Tansig) for the hidden layer and the linear purelin for the output layer were the transfer functions used in an ANN trained using the feed-forward technique.

An ANN is a predictive model that is driven by data and has to be trained to find correlations between inputs and outputs. The ANN iteratively modifies the weights and biases of the connections bridging the network’s neurons during training [36]. Feed-forward neural networks have been trained using backpropagation, which may be utilized in batch or incremental mode. This approach uses gradient descent, where weights are modified based on an algorithm-determined performance gradient. After training using input data to forecast output, the network compares the predicted output against the actual output to determine errors. The network’s weights and biases are then changed in another way, from the output layer to the input layer, based on the errors. Gradient descent, gradient descent with momentum, gradient descent with adaptive learning rate, resilient backpropagation (RProp), scaled conjugate gradient, conjugate gradient with Powell/Beale, Fletcher-Powell, or Polak-Ribiére Conjugate approaches, Levenberg–Marquardt, quasi-Newton, one step secant, and Bayesian regularization fast backpropagation algorithms were the training methods employed to update weights and biases, which are the trainable parameters of the ANNs in this study, The MATLAB functions used for each algorithm are provided in Table S2 (e.g., trainlm() for Levenberg–Marquardt, trainbr() for Bayesian regularization, and trainrp() for RProp) [37‐39]. These functions allowed systematic exploration and comparison of various optimization strategies within the ANN training process. Furthermore, the following choices were used for the ANN model’s training parameters: There is one input layer including twelve inputs, one hidden layer with a variable number of neurons ranging from one to twenty, one output layer with 2 nodes, one hundred training repetitions for each method, and one thousand epochs. Each training algorithm listed in Table S2 was evaluated using these ANN architectures with variable activation functions (tansig, purelin) to comprehensively explore potential configurations. For model training, 70% of the data was used for training and 30% for testing. Testing data was used as validation to overcome the overfitting problem because data is limited. The architecture yielding the best results based on R, R², MSE, and MAE was selected for each training method to ensure optimal performance.

Although the dataset in this study comprises 40 samples, several strategies were implemented to ensure robust training and mitigate potential overfitting in the ANN model. First, a shallow architecture with a single hidden layer and a minimal number of neurons were used to keep the model complexity low and suitable for the limited data. Second, early stopping was applied during training, halting the process when the validation error began to increase, thereby preventing the model from memorizing the training data. Third, the number of trainable parameters was kept low, and a carefully selected optimization technique was employed to ensure stable convergence without overfitting.

These practices are well-established in the literature for training ANN models with small datasets [40‐42]. Studies have shown that even with limited data, ANN can achieve accurate predictions when model simplicity and regularization techniques are appropriately balanced. For example, Pasini [41] demonstrated that ANN models, when properly designed, can outperform traditional methods in small dataset applications by leveraging their ability to learn non-linear relationships. Similarly, Yu et al. [42] highlighted that with appropriate optimization strategies, small datasets can be effectively used for accurate property predictions. The reasonable prediction accuracy observed in our study (as reflected by the R² and MSE values) further supports the validity of this approach.

Performance metrics, including the R, R², MSE, and MAE, were used to evaluate the effectiveness and precision of the regression models that were created. R evaluates the linear relationship between predicted and actual values, as given in Eq. (8). While the ML model can learn non-linear patterns, R shows how well it captures them if there is a linear relationship between predicted and actual values. A value close to 1 indicates a strong positive correlation, while a value close to −1 suggests the model may have learned the relationship incorrectly.where \({y}_{i}\) and \(\widehat{{y}_{i}}\) are the actual and predicted values and \(\overline{y }\) and \(\widehat{\overline{{y }_{i}}}\) are the mean of the actual values and predicted values.

R², which ranges from 0 to 1, is the ratio of variation to total variance as given in Eq. (9).

Here \({SS}_{res}\) and \({SS}_{total}\) are the sum of residuals’ squares and the total sum of squares.

There is no standard rule for the level of predictive acceptance (R² value), but a value approaching 1 corresponds to the best-fitting model. Regression models with an R² value of more than 75, as defined by Hai et al. [43], are considered important predictive models; models with R² values of 0.25 to 0.75 and less than 0.25, on the other hand, are classified as moderate and low analytical models. In parallel with R², the performance of the models developed was also evaluated in terms of MSE (\({SS}_{res}/N\)) and MAE (\((\sum_{i=1}^{N}\left|{(y}_{i}-\widehat{{y}_{i}}\right|)/N\)).

Table 2 shows the results of the proximity analysis of biochar and activated carbon produced under different operating and activation conditions. The results showed that the moisture content of TW biochar during conventional pyrolysis ranged between 2.0 and 7.83 (wt)%, while the fixed carbon content varied between 3.60 and 0.93 (wt)%. In conventional pyrolysis, the moisture content increased with increasing pyrolysis temperature. However, the solid carbon content increased to 44.70% at a pyrolysis temperature of 500 °C and then decreased to 0.42 and 0.93 at temperatures between 700 and 900 °C. The The activation conditions and pyrolysis temperature affected the moisture and ash content of the activated carbon samples. Regardless of the activation conditions, the moisture and ash contents of the materials produced by pyrolysis at 300 °C increased. Moisture and ash contents of biochar and activated carbon obtained by pyrolysis at 300 °C increased independently of activation conditions. The lowest ash content (2 wt%) during pyrolysis at 300 °C was observed for sample TWAC-KOH-P300. The thermogravimetry -differential thermal analysis (TGA–DTA) and differential scanning calorimetry (DSC) results of the mixture of TW and 3 M KOH showed the occurrence of two peaks at about 100 °C and 212 °C at a pyrolysis temperature of less than 300 °C (Figure S1). The peak at about 100 °C is due to the water evaporated in the aqueous KOH solution. The negative peak in the DSC and the positive peak in the DTA at 212 °C is the result of the interaction between KOH and biomass. Combined with the low ash content of TWAC-KOH-P300, this result could be due to the conversion of KOH to silicate by SiO₂ according to Eq. (23):

Silica removal by washing the AC after pyrolysis reduced the ash content of the AC. However, pyrolysis assisted by MW and KOH increased ash content and decreased moisture content.

MW activation increased the interaction between KOH and carbon precursors, depending on the amount of carbon in the AC. This led to a partial elimination of water and an increase in the KOH concentration [8]. Depending on the activation circumstances, pyrolysis at temperatures up to 500 °C displayed varying behaviors. Moisture content decreased in the presence of H₃PO₄ and increased slightly in the presence of KOH. OH groups separated from KOH can settle into the gaps in the structure and cause the formation of oxygen-containing groups (i.e., -OH, C = O, -COOH, C-O, O-C = O) [49]. In addition, it was found that the ash content of the activated carbon produced by activation with KOH at all temperatures of 500 °C and above is high. This is due to the formation of K₂CO₃, K₂O and metallic K together with the ash content that TW forms. For this, a previous study [50] has shown that the reaction of carbon with KOH according to Eq. (24) can lead to carbonate. This reaction takes place thermodynamically between 475 and 530 °C. The resulting metallic K is mobile in the biochar matrix and also contributes to pore expansion by intercalation between the carbon layers [50].

The decomposition of K₂CO₃ into CO₂ and K₂O takes place at temperatures higher than 700 [51].

Potassium reactions are highly favorable, exhibiting large negative free energies at the reaction temperature [52]. Additionally, it is well-established that alkali metal carbonates can decompose at temperatures below their melting point when in the presence of carbon [50]. Furthermore, temperature-programmed desorption experiments showed the evolution of CO and CO₂ from KOH/C mixtures at temperatures above 700 °C [53]. Consequently, the K₂O formed may also be expected to react with carbon via the following reaction:

Increasing the pyrolysis temperature to 700 °C showed different properties depending on the activation conditions. Moisture content decreased in the presence of H₃PO₄ and increased in the presence of KOH. The ash content of all materials produced at 700 °C increased due to the elimination of volatile substances during pyrolysis. According to the proximate analysis results in Table 2, at the pyrolysis temperature of 900 °C, the moisture content was the lowest and the ash content was the highest due to the maximum temperature. This significant increase in ash content may also be attributed to the significant elimination of volatile compounds during pyrolysis [54]. During the carbonization phase, a high volatile matter content often lowers the solids yield, but a low inorganic content is important as it leads to a low ash content and a high fixed carbon content [55]. When examining the results of the proximate analysis, it was found that the moisture content of TW was lower than that of HS.

Table 3 shows the results of the elemental and HHV analyses of biochar and activated carbon samples prepared under different operating and activation conditions. TW contains 45.4% C and its pyrolysis increases to values between 54.4% and 70.3% depending on the activation conditions and temperature. Pyrolysis in the presence of H₃PO₄ and KOH led to an increase in C content of 64.2% and 70.3%, respectively, and to a decrease in H, O, and N content. This is due to the loss of volatile compounds during the carbonization process, decarboxylation, and dehydration reactions [56]. However, the effect of KOH on the carbonization and dehydration of TW was greater than that of H₃PO₄. When biomass is activated with KOH at 300 °C, the oxygen concentration decreases, while the changes are negligible when activated with H₃PO₄. For these activations at 300 °C, the HHV values are between 20.48 and 26.53 MJ/kg. The most interesting parameters in terms of energy are the C and H concentrations, which contribute the most to the stored energy in the samples. Ash, O and N are also important energy indicators [57]. The C content of the biochar produced increased to 68.2% when TW was pyrolyzed at 500 °C. After TW activation with H₃PO₄ and KOH, the C content of the activated carbon increased to 69.2% and 80.1%, respectively, due to pyrolysis at 500° C. The C content was highest during KOH activation. MW activation with H₃PO₄ and KOH reduced the C and H content, but increased the O content compared to conventional pyrolysis at 500 °C. This is due to the interaction between the biomass and the activating chemical [58]. Pyrolysis of the TW at 500 °C increased the HHV of the biochar produced to 24.85 MJ/kg. After activation of the TW with H₃PO₄ and KOH, the pyrolysis at 500 °C increased the HHV of the activated carbon to 25.96 and 28.29 MJ/kg, respectively. It was also found that the HHV of TWBC-KOH-P500 was higher than that of H₃PO₄. Similar results were obtained for the conventional pyrolysis of HS at 500 °C, and the biochar produced has a HHV of 32.4 MJ/kg.

The pyrolysis of TW at 700 °C increased the C content to 69.5%. After activation of TW with H₃PO₄ and KOH, pyrolysis at 700 °C increased the C content of the activated carbon to 54.5% and 70.2%, respectively. Subsequently, pyrolysis of TW activated with H₃PO₄ and KOH at 700 °C increased the activated carbon’s HHV to 19.27 and 24.38 MJ/kg, respectively.

As can be seen from Table 3, the C content of the biochar produced was increased to 72.6% by pyrolysis of TW at 900 °C. After TW activation with H₃PO₄ and KOH, the C content of the activated carbon decreased to 37.2% and 64.3%, respectively, due to pyrolysis at 900 °C. In addition to TW activation with H₃PO₄ and KOH, pyrolysis at 900 °C reduced the HHV of the activated carbon to 11.52 and 15.03 MJ/kg, respectively, which can be attributed to the significantly lower carbonization rate. In the pyrolysis of TW with MW and US, the composition of the activated carbon varied depending on the activating agent. The C content of the activated carbon increased when activated with KOH and decreased when activated with H₃PO4. This decrease could be due to the dilution effect that H₃PO₄ exerts on the biomass during the activation process [20].

The results show that KOH activation leads to the highest increase in HHV, reaching 28.29 MJ/kg at 500 °C, compared to 25.96 MJ/kg for H₃PO₄ activation at the same temperature. Similarly, KOH activation at 700 °C resulted in a HHV of 24.38 MJ/kg, while H₃PO₄ activation reached 19.27 MJ/kg. However, at 900 °C, both activations decreased, with KOH-treated samples reaching 15.03 MJ/kg and H₃PO₄-treated samples reaching 11.52 MJ/kg, indicating a decreasing effect at higher pyrolysis temperatures.

The SSA, total and micro pore volume, and average pore radius of biomass, biochar and activated carbon samples are shown in Table 4. These properties of the produced materials varied depending on the operating parameters and activation conditions. Conventional pyrolysis of TW at 300 °C decreased the SSA value and increased the average pore diameter of the biochar, indicating the formation of macrospores. In addition, pyrolysis at 300 °C in the presence of KOH slightly increased the SSA (17.3 m²/g) of the activated carbon, while the pore radius was reduced from 55.6 Å to 24.7 Å.

The pyrolysis of TW at 500 °C led to a slight increase in the SSA of the biochar from 10.40 m²/g to 13.60 m²/g. However, pyrolysis at 500 °C in the presence of H₃PO₄ significantly increased the SSA (943 m² /g) and total pore volume (1.1 cm³ g⁻¹). In addition, MW-assisted acid-activated pyrolysis significantly increased the SSA (1556 m²/g) and total pore volume (2 cm³/g) of activated carbon, probably due to enhanced acid-biomass interaction and homogeneous heat distribution [8]. Activation of TW with KOH supported by MW (30 s) and US for 90 min at 500 °C increased the SSA and total pore volume to 274.9 m²/g and 0.22 cm³/g, respectively. Increasing the conventional pyrolysis temperature to 700 °C increased the SSA, total pore volume, and pore radius to 13.9 m²/g, 0.039 cm³/g, and 66.2 Å, respectively. Increasing the pyrolysis temperature to 700 °C in the presence of KOH led to a significant increase in the SSA of the activated carbon. This increase is probably due to the formation of additional micropores.

In addition, acid activation supplemented by MW and US prior to pyrolysis increased the surface area and total pore volume to 883.5 m²/g and 0.2 cm³/g, respectively. As shown in Table 4, increasing the temperature of conventional pyrolysis to 900 °C resulted in an increase in SSA, total pore volume and average pore radius by 24.5 m²/g, 0.049 cm³/g and 80.1 Å, respectively. Activation with KOH in combination with MW and US activation prior to pyrolysis led to a significant increase in SSA and total pore volume to 2011 m²/g and 1.106 cm³/g, respectively. After pre-activation of this sample, 24 h were waited before pyrolysis, so it can be said that the conduction time during biomass pre-activation has a significant effect on the SSA of activated carbon. The activation of HS showed different behaviors depending on the activation conditions. Activation of HS with H₃PO₄ at a pyrolysis temperature of 500 °C significantly increased the SSA of activated carbon from 16.95 to 1283 m²/g. MW-assisted activation of HS with H₃PO₄ significantly increased the surface area to 1731 m²/g with a simultaneous increase in pore volume.

The SSA values varied significantly depending on the activation method. H₃PO₄ activation at 500 °C significantly increased SSA to 942.8 m²/g, whereas KOH activation combined with MW treatment reached 274.9 m²/g under the same conditions. Moreover, MW-assisted H₃PO₄ activation at 500 °C further enhanced SSA to 1556 m²/g, demonstrating the effectiveness of combined physicochemical activation strategies. At 900 °C, KOH-MW-assisted activation resulted in the highest SSA value of 2011 m²/g, showing the influence of high-temperature and chemical activation synergy.

In the study, the ANN model was compared with other ML techniques such as RT, GPR, and SVM. The comparative results of these models are shown in Table 6. The GPR model with the matern kernel function indicated a moderate predictive capability for HHV and the SSA of biochar and activated carbon materials, with R values ranging from 0.7325 to 0.6524, and R² values ranging from 0.5366 to 0.4256. RT model gave a predictive potential with an overall R² between 0.6263 and 0.8729, and R between 0.7914 and 0.9343 for testing and training data. The SVM model with a polynomial kernel function demonstrated predictive potential, with overall R² values ranging from 0.6267 to 0.7260, and R values ranging from 0.7916 to 0.8520 for both testing and training data. Furthermore, the performances of ML models in estimating surface area were generally low. This is particularly evident in the case of SSA predictions, where models struggled to achieve reliable test performance. As seen in Table 6 and Fig. 7, the R values of the SVM, RT, and GPR models were greater than 0.75.

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In addition, the performances of MLR, KRR, and GBR were presented in Table 6. Although these models performed well during training, their performance on the test data was considerably lower, as shown by low R² values (e.g., 0.2922 for MLR and 0.5784 for GBR). This indicates overfitting, where the models fail to generalize effectively to unseen data despite achieving high training accuracy. Similarly, SVM, RT, and GPR models exhibit varying degrees of overfitting, with RT and GPR showing significant discrepancies between their training and test results. Although SVM achieved the best overall test results among these models, its performance still highlights moderate overfitting, particularly in surface area predictions. These observations highlight the advantage of using a model like ANN, which demonstrated superior performance by balancing high accuracy with improved generalization to unseen data, effectively addressing the overfitting issues observed in SVM, RT, GPR, and regression-based models through consistently high R and R² values across both training and test datasets. This reflects its ability to learn complex, non-linear relationships while resisting overfitting through mechanisms such as early stopping, optimized architecture, and robust training parameters. As shown in Table 6 and Fig. 7, the ANN model achieved the highest R values (0.9133 for testing and 0.9735 for training) and low MSE and MAE errors, highlighting its capability to deliver accurate and reliable predictions for both HHV and SSA.