1. Introduction
The characteristics of a nanomaterial and its functional properties for biomedical applications are governed by various parameters pertaining to its synthesis comprising starting precursor materials besides temperature, pressure, and design of the lab scale reactors. It is mostly a trial-and-error approach that is followed to synthesize nanomaterials with the desired properties. This is an expensive, time-consuming, and low-efficiency procedure. With the growing demand for nanomaterials for various applications, it is critical to quickly and precisely predict the characteristics based on synthesis factors [
1].
Computer algorithms are used in machine learning (ML), a branch of artificial intelligence, to create mathematical models that can carry out particular tasks like clustering, dimensionality reduction, and prediction directly from collected data, such as graphs, images, or numerical data, as opposed to from established physical laws. These ML models are especially helpful in situations where interrelationships between input experimental variables and output results are complex, lacking detailed mechanistic understanding governed by fundamental physical laws. Applications of ML include chemical recognition, materials design and discovery, synthesis reaction prediction, and nanoparticle size prediction. Depending on how they learn, machine learning algorithms can be divided into three categories: semi-supervised learning techniques (generative models), unsupervised learning (clustering, association rules, etc.), and supervised learning (decision tree, boosting, support vector machine (SVM), etc.) [
2,
3].
Nonlinear machine learning models, which involve interactions between input circumstances and outputs properties that are not linear, can be categorized into two types of algorithms: instance-based and model-based. By using a model that is defined by a collection of variables that are inferred through training, model-based techniques create predictions. Deep learning and tree-based algorithms are two examples of model-based techniques that have been extensively used for the prediction of results in nanoparticle synthesis. Supervised learning is essentially an attempt to investigate an unknown function in which there is a relationship amongst the variables that are input and an unknown target for the output. Labelled data are used in supervised learning techniques to build a machine learning model that predicts the association between desired attributes and characteristics. We must identify both dependent and independent variables before selecting an algorithm. Next, the correlation between both the independent and dependent variables ought to be ascertained. Unlike supervised algorithms used for predictions, unsupervised methods are utilized for statistical analysis and visualization and do not require training with previous experiments. A type of unsupervised algorithms known as generative machine learning models seeks to produce new data points that resemble those in a selected dataset [
4].
Reaction conditions, such as reaction temperature, reaction time, chemical reagent concentration ratio, reaction precursors, reaction ligands, solution reagents, microreactor channel structure, external stimuli, and so forth, are typically chosen as independent variables in nanoparticle preparation techniques, while the dimension, shape, and electronic and optical characteristics of the nanoparticles are typically chosen as dependent variables. The gathering and preparation of the dataset is a crucial step before developing a machine learning model [
3]. The trial-and-error approach used to collect experimental data for optimizing the synthetic procedure for nanoparticle synthesis is time-consuming and not economical [
1]. Therefore, with the physics-informed ML models, it is possible to optimize and predict the feasible synthetic procedures for producing nanoparticles. Alternatively, for the training of machine learning models, reputable datasets from published articles, on nanoparticle synthesis, are another source. In addition, online search engines could be used to find pertinent datasets from open-source shared information and repositories. Typically, a dataset is separated into two parts: the test set and the training set. The majority of the dataset is used for training the suitable machine learning model, which is subsequently assessed using the test dataset. Typically, two datasets with an 8:2 or 7:3 ratio are created from the data for training and testing the ML models. The superior performance of the machine learning approach cannot be simply assessed using the training set alone [
1,
2,
3,
4]. Any computational technique that helps narrow down the design space by forecasting desired process variables prior to synthesis would be beneficial to reduce the number of steps involved to produce nanoparticles by chemical routes. One crucial physio-chemical characteristic of nanoparticles that can influence their use in nanomedicine is size. For example, it has been discovered that a nanoparticle’s size has a significant role in in vivo experiments performed for various therapeutic applications. Since the size of the nanoparticle influences its permeability and retention, size optimization is also crucial for the design and development of nanoparticles used to treat a range of tumors [
5]. Particle size and particle density index (PDI), two crucial metrics for evaluating a drug-loaded nanoparticle formulation, depend on a number of factors such as composition, the duration of sonication, and extrusion temperature. For achieving an ideal particle size with a narrow size distribution, empirical methods are often employed to adjust these independent parameters through iterative trial-and-error methodology [
6].
Various studies have considered the best model to use for predicting size of the nanoparticles. Silver is one of the most commonly studied nanoparticles, synthesized either through a chemical or green synthesis route. Several studies have been carried out using silver nanoparticles for various fields like biomedical applications [
7], cosmetics [
8], electronic field [
9], etc. Determining the size of the particle is important, for example in the antibacterial activity of the particle [
10,
11], central metabolism of wheat seedlings [
12], etc. In order to predict the size of silver nanoparticles (AgNPs) made using a green approach, Shabanzadeh et al. [
13] proposed an artificial neural network (ANN) model. A number of variables that affect the size of the nanoparticles are taken into consideration by the ANN model, including temperature, starch concentration, and NaOH volumes. The Levenberg–Marquardt (LM) back-propagation algorithm was used to train the network. The coefficient of determination value for the test data was 0.9787, for the best predictive model.
The size of AgNPs in montmorillonite/starch bionanocomposites, prepared through chemical routes, was predicted using an ANN model by Shabanzadeh et al. [
14]. With a log-sigmoid transfer function for hidden layers and a linear transfer function for output layers, the ideal ANN architecture was found to be 4:10:1. To ascertain AgNP’s size, TEM was employed. The concentration of silver nitrate (AgNO
3), the reaction temperature, the starch weight percentage, and the concentration of NaBH
4 served as independent variables. As AgNO
3 concentration, starch percentage, and NaBH
4 concentration increase, the size of the nanoparticles decreases, according to the modelling results.
An ANN was used as computational tool by Shabanzadeh et al. [
15] to model the size of AgNP in montmorillonite/chitosan bionanocomposites (BNCs). The montmorillonite (MMT) interlayer space has been utilized as an adsorbent for cationic ions, as a substrate for anchoring transition metal complexes, and for the production of material and biomaterial nanoparticles. In this study, a one-hidden-layer neural network with a single output was utilized as an ANN. AgNP size was modelled as a function of several parameters, such as d-spacing of clay layers, reaction temperature, percentage of chitosan, and concentration of silver nitrate. The ANN is trained using the back-propagation Levenberg–Marquardt (LM) algorithm. Furthermore, the AgNP particle size and distribution prepared at various experimental values showed that larger AgNP particle sizes were obtained at higher reaction temperatures and Ag
+ ion concentrations; however, AgNP diameters decreased as chitosan percentages increased.
To design an environmental friendly and efficient process for the preparation of AgNP in BNCs matrix through a green synthesis technique, Shabanzadeh et al. [
16] used the relationships between multi-input variables, such as AgNO
3 molar concentration, reaction temperature, percentage of starch, and amount of MMT. MATLAB is used to put the suggested method into practice. To forecast the size of AgNPs, an ANN network consisting of a 4-10-1 feed-forward multilayer perceptron (MLP) with a linear function at the output layer and a tangent sigmoid transfer function at the hidden layers was employed in this study.
The prediction model for determining the size of AgNPs made via green synthesis was developed by Sattari and Khayati [
17] using the gene expression programming (GEP) technique. The data required to build the GEP models were gathered by the researchers through 30 distinct experiments. Plant extract, reaction temperature, AgNO
3 concentration, and stirring duration are among the input factors taken into account by the model.
Nathanael et al. [
18] proposed a technique that combines machine learning with a T-junction microfluidic system to optimize the synthesis of the AgNPs and to forecast the particle size of AgNPs synthesized in microfluidic systemsusing trisodium citrate (TC), tannic acid (TA), and silver nitrate as reducing and stabilizing agents. They have employed a decision-tree-guided design of experiments for determining the size of AgNPs. The synthesized silver nanoparticle’s stability is affected by storage temperature, pH, and concentrations of trisodium citrate, which have influenced nucleation and growth rate—the nucleation constant (k
1) and growth constant (k
2). The Finke–Watzky (F–W) two step mechanism was used in an independent set of beaker experiments to derive the nucleation and growth constants.
Table 1 summarizes the training features (inputs) with the range of those features that have been studied.
Shafaei et al. [
19] predicted the size of AgNPs made using a green synthesis technique using a hybrid artificial neural network particle swarm optimization approach. In order to attain the smallest possible size of AgNPs, the study also focused on optimizing the practical procedure. Silver nitrate, the precursor of silver, and opium syrup, a reducing and stabilizing substance, were used to create silver nanoparticles. An experiment using a factorial D-optimal array design was used to gather the experimental data. The ratio of AgNO
3 to opium syrup, the feed rate at which the reducing agent is added, pH, reaction temperature, and agitation speed all affect the size of the samples. The size of the silver nanoparticle was chosen as the output and the process parameters as the inputs for the optimization process.
Using Vitex negundo L extract as a reducing agent and stabilizer, Shabanzadeh et al. [
20] demonstrated the biosynthesis of silver nanoparticles. The additional reagents that were utilized were Muller Hinton agar, AgNO
3, methanol, and nutrient agar. An ANN model was used in order to predict the nanoparticle size. Thirty produced samples from experimental datasets were used in their work. The molar concentration of AgNO
3, weight% of Vitex negundo extract, reaction temperature, and stirring time are significant variables that can affect the size of silver nanoparticles. Using experimental data for training, the ANN model demonstrated excellent accuracy in forecasting the size of nanoparticles under various conditions. This ANN model served as a valuable tool for developing a sustainable and efficient process for producing silver nanoparticles. It was found that the concentration of AgNO
3, temperature of reaction, stirring time, and the quantity of Vitex negundo L extract had an impact on the size of the nanoparticles; an increase in AgNO
3 concentration, temperature of reaction, stirring time, produced larger nanoparticles, and an increase in Vitex negundo L extract produced smaller nanoparticles.
The use of an ANN model to predict the size of AgNPs synthesized in the interlayer space of montmorillonite was reported in the work of Shabanzadeh et al. [
21]. The ANN model assisted in optimizing the design parameters and in minimizing costly experimental research. For the purpose of modelling AgNP size prediction in their study, a multilayer perception (MLP)-based feed-forward ANN that makes use of an LM-based back-propagation learning method was used. Three sets of the experimental data were randomly selected to serve as training, validation, and testing, respectively. Absolute average deviation, coefficient of determination, and root mean square error are calculated to assess the predictive performance of the ANN model. Their work focused on how various parameters, including montmorillonite d-spacing, UV–visible wavelength, reaction temperature, and AgNO
3 concentration, affect AgNP size. The results of the analysis indicate that the two main variables influencing the size of the nanoparticles are temperature and AgNO
3 concentration.
In the present study, the data were collected from four distinct experimental sets and employed conventional machine learning models. The datasets used for modelling include those from Nathanael et al. [
18], Shafaei et al. [
19], Shabanzadeh et al. [
20], and Shabanzadeh et al. [
21]. The experimental datasets used were synthesized either by chemical or green synthesis routes. The complete dataset for each experiment was split to test and train. Tree-based models such as decision tree regressor, random forest regressor, and extreme gradient boost regressor were used to assess the prediction of the size of the silver nanoparticles. The efficiency of the model was evaluated by determining the coefficient of determination (
R2), mean absolute error (
MAE), and mean square error (
MSE) for all the three models.
When the data availability is less, traditional models can, at times, provide better accuracy compared to other complicated models used. In this paper, the
Section 2 details the processes involved and the various models utilized in our current study. The
Section 3 provides an overview of the different performance measures considered to determine the efficiency of the models. The
Section 4 assesses the effectiveness of several models and presents different plots to corroborate the findings. Moreover, it provides insight into the significance of the features in the model. The summary of the findings is included in the
Section 5.
4. Results and Discussion
The first experimental dataset used for modelling is from the study reported by Nathanael et al. [
18]. Using titanium citrate and tannic acid as reducing agents and silver nitrate as the precursor, they synthesized AgNPs by a chemical route, as shown in
Figure 2. In order to direct the experiments, Nathanael et al. created a DT algorithm that was based on 20 samples that were repeated three times each. To improve the efficacy of the prediction models, they employed ten additional trials, including three replications that were conducted randomly or in accordance with the DT-guided design of experiments. The machine learning model considers the size of the particle, characterized by transmission electron microscopy and dynamic light scattering measurements, as the dependent variable. The independent variables are the nucleation constant, growth rate constant, storage temperature, Reynolds number, and ratio of dean number to Reynolds number.
Table 2 presents performance measure of the original dataset and the decision-tree-guided design of experiments approach for AgNP size prediction using all the three models adopted in their work [
18].
In the present investigation, we used the original dataset collected from the literature [
18], which consisted of 20 samples that were replicated three times for a total of 60 datasets. All three models employed the same dataset, and the more accurate predictive model is obtained with appropriate hyperparameter optimization. The best performance is showcased by XGBoost model with learning_rate = 0.15, max_depth = 4, and gamma = 0.2, which results in the highest coefficient of determination of 0.973 and the lowest
MSE and
MAE of 1.09 and 0.73, respectively.
Figure 3a compares the actual and the predicted values using the scatter plot. In the scatter plot, the points lie close to the best fit line with less deviation, indicating that it is a good model, and by plotting the probability density function for actual and predicted values, as in
Figure 3b, it is observed that the peak of the actual and predicted values matches, which emphasizes the better predictability of the model. The results of the evaluation matrix for all three models are shown in
Table 3.
A summary plot is useful to obtain a thorough insight of each feature value’s contribution to the final forecast for each data point. The impact of each synthesis parameter is displayed in
Figure 4 based on the feature value. For the model output, the synthesis parameters are organized in decreasing order of significance. This indicates that growth constant has the most influence on the outcome of the prediction, whereas the Reynolds number has the least for this model. The
R2 score of the model considering the most significant features such as the growth constant and nucleation constant is 0.973. If these two independent parameters are not considered, the accuracy of the model drops, giving an
R2 score of 0.561, showing how important these features are for predicting a size of the particle.
Figure 5 shows the scatter plot with the error graph of actual values versus predicted values, avoiding the significant features in which the points lie away from the best fit line.
Tree-based models were used to assess the second batch of the 103 dataset, which was derived from Shafaei et al. [
19] where they have synthesized AgNPs through the green approach. Shafaei et al. used a factorial D-optimal array design of experiments to gather experimental data in order to investigate the size of AgNPs. The AgNPs’ size was examined by X-ray diffraction. For training and optimization, their study adopted particle swarm optimization (PSO) and ANN techniques. The AgNO
3/opium ratio, feed rate, pH, temperature, and agitation speed were among the independent characteristics that were used in the investigation. Throughout the synthesis process, these factors were altered to study its influence on the AgNPs’ estimated grain size, which was determined using Scherer’s equation. Since the findings from the various ANN PSO networks were inconsistent, the model was assessed using a combined function as in Equation (7), where the network with a combined function closer to zero has been proposed to perform better. Because ANN-PSO 9’s combined function value is less than 0.101, and the
R2 score is equal to 0.9972, it is regarded as the best network.
To simplify the modelling process, we have employed tree-based models in this instance. The models’ efficiency was assessed using the
R2 score,
MAE, and
MSE.
Table 4’s results demonstrate that XGBoost with learning_rate = 0.05 and max_depth = 3 outperforms the other two tree models in terms of performance.
Figure 6a,b display scatter plot with error graph and kernel density plot for actual values and the predicted values, showing the performance the model. It is observed that in the scatter plot, the points are more scattered and in the plot for probability density function, it is noted that there is a deviation between the peaks of the actual value and the predicted value, which shows the predicted value has a deviation from the actual value. In this case, the size of the particles was examined using XRD, indicating that it is the grain size rather than the AgNP particle size. This could be the reason for the models’ lower score when compared to the datasets from the other three experiments.
Figure 7 illustrates the relative importance of each feature and their role in AgNP size prediction. The relevance of the most important feature for this dataset is shown in
Figure 8 by plotting the scatter plot. It is observed that the points are more scattered than
Figure 6a where all the features are taken into consideration for modelling. The accuracy of the model reduced, giving an
R2 score of 0.65 from 0.79 on avoiding the most significant feature contributing to the model prediction.
The experimental dataset 3 used for our modelling is the synthesized AgNPs by Shabanzadeh et al. [
20] using Vitex negundo L. extract as a reducing agent and stabilizer; thirty prepared samples were made by this route. Using the weight percentage of Vitex negundo L. extract, reaction temperature, stirring time, and AgNO
3 molar concentration as input parameters, an ANN model was created to forecast the size of the nanoparticles in order to construct an efficient green nanoparticle synthesis process. The synthesized AgNPs’ TEM analysis confirms the nanoparticles’ size. The dataset was split into train, test, and validation sets in this study. The correlation coefficient of the ANN model is around 0.998, with a mean square error of 0.4576.
Table 5 shows the results of the
MSE,
MAE, and
R2 score on employing the tree-based models. The dataset is split to train and test sets, with a best train score of 99.9 and test score of 99.4 exhibited by XGBoost with hyperparameter values of learning_rate = 0.15, max_depth = 3. This model has led to an
R2 score of 0.994,
MSE of 0.145, and
MAE of 0. 292. The result shows that the traditional models could also produce high precision in prediction while comparing with the complex neural networks.
Figure 9a,b show the different plots of performance of the model, the scatter plot, and plot for probability density function comparing actual values and predicted values. Both plots reveal that model designed to predict the size of the particle performs well. For predicting the size of the nanoparticle in a model, each feature has its own importance and from
Figure 10, we observe that plant extract contributes the most, giving a feature score of 0.750. As shown in
Figure 11, we can observe more scattering of points in the plot, showing that there is a decrease in accuracy as we remove the most important feature from the model as compared to
Figure 9a. The predictive ability of the model has decreased. When the most significant feature is not taken into account, the model’s
R2 score is 0.93, which is less than the score obtained when the feature is taken into account.
The fourth set of data was obtained from Shabanzadeh et al. [
21]. Here, the research group has used an ANN with four neurons in one hidden layer to model the optimum size of AgNP nanoparticles to investigate the effects of different input parameters—AgNO
3 concentration, temperature, wavelength, and MMT interlayer d-spacing. The dataset was split into a test, train, and validation set to determine the best model.
RMSE and
R2 score values are 0.7917 and 0.955 for test set.
Table 6 shows the performance measures of the tree-based models in which the DT model shows the best performance giving the coefficient of determination as nearly 1.
Figure 12a shows the plot for the actual versus predicted values. Both visualizations in
Figure 12a,b offer valuable insights into the regression model’s performance: the scatter plot directly compares the model’s predictions to the actual values, while the probability density function plot provides a deeper understanding of error distribution. Here in the scatter plot, the points lie almost on the line and the kernel density plots overlap each other, showing the decision tree models predict extremely well. The data are split in the ratio of 80:20. The model gives the best train score of 100 and test score of 99.95. The
RMSE value is 0. 045. The concentration of silver nitrate is the most important feature that contributes to the prediction of size of AgNPs, giving a score of 0.964.
Figure 13 shows the feature importance of the model.
Figure 14 illustrates the scatter plot avoiding the most significant feature of the model. The model’s accuracy has declined, resulting in a lower
R2 score of 0.65.