Compressive Strength of Geopolymer Concrete Prediction Using Machine Learning Methods

Abstract

The implementation of machine learning methods as one of the artificial intelligence technologies has allowed bringing the construction process to a new qualitative level. Significant interest in these methods is observed in predictive modeling of the building materials’ properties. In the scientific field of innovative concretes, limitations exist regarding the disclosure of intelligent algorithms’ capabilities to predict material properties when altering specific chemical elements and process parameters. This article focuses on seven machine learning techniques that are used to solve the issue in forecasting geopolymer concrete’s compressive strength: from the simplest, such as Linear Regression, to more complex and modern methods, including the TabPFNv2 generative transformer model. The dataset was formed based on 204 datasets available in the public domain, including the author’s experimental data. The leading machine learning features were selected: blast-furnace granulated slag (kg/m³); NaOH molarity; NaOH content in the alkaline activator (%); Na₂SiO₃ content in the alkaline activator (%); fiber type; fiber dosage (%); and curing temperature (°C). The MAE, RMSE, MAPE metrics and the R² determination coefficient were used to evaluate the prediction quality. The kNN method (MAE = 0.37, RMSE = 0.63, MAPE = 1.62%, R² = 0.9996) and TabPFNv2 (MAE = 0.46, RMSE = 0.64, MAPE = 1.39%, R² = 0.9996) presented the highest accuracy in predicting compressive strength, as assessed by the chosen parameters. If computing resources are limited and interpretability is required, it is recommended to use the CatBoost or Random Forest algorithms; if a graphics processing unit and a small dataset are available, it is advisable to use TabPFN; if there is no need for manual parameter adjustment, H2O AutoML is suitable.

1. Introduction

Intelligent methods have become widespread across all sectors of the economy. Smart solutions, which provide accessible automation tools, improve operational processes in all areas of human activity. For example, in agriculture in many countries, such solutions help combat crop diseases [1] and harmful insects [2]. In medicine and healthcare, intelligent solutions are used to ensure the integrity of inventory and timely access to vital resources [3], as well as accurate and early diagnosis of various diseases [4,5,6]. In security and disaster monitoring, computer vision systems enable the rapid and accurate detection of fires and burned-out areas [7,8,9], and also assess the consequences of emergencies [10].

On construction sites, such technologies help ensure the safety of construction work [11]. Computer vision (CV) systems ensure seamless monitoring of working conditions and work progress at all stages [12,13,14]. CV systems are also adapted for monitoring construction materials, products, and structures. Accuracy in identifying defects and problem areas reaches 99% for detection, segmentation, and classification, as confirmed by studies [15,16,17,18].

With the advent of AI in the field of predictive modeling of building materials properties, tools have emerged that complement traditional methods [19,20,21]. For example, machine learning algorithms have proven themselves in determining the mechanical properties of concrete, which are among the most important parameters in the design and assessment of its performance properties [22,23,24]. Studies [25,26] examined how aggressive environments (freeze–thaw, chlorides, sulfates, wetting-drying cycles) affected the predicted strength of vibrocentrifuged variotropic concrete. Therefore, the MAPE for the top three models was 1–2%, and the coefficient of determination ranged from 0.99 to 0.999. This supports the idea that intelligent algorithms can enhance the life cycle management of this building material. Machine learning-based prediction of geopolymer composite properties is reported in [27,28,29,30,31,32]. The accuracy of the presented methods reaches 99%. Advanced ensemble models such as LightGBM, GBRT, XGBoost, and AdaBoost are increasingly emerging as robust and efficient alternatives to traditional testing methods, providing significant time and cost savings. They demonstrate high performance metrics, such as a coefficient of determination starting from 0.97 [33,34]. But they make little use of modern methods such as automated machine learning (AutoML) or the generative transform of the tabular prior network (TabPFN), which is a gap in the current scientific literature [35,36,37,38]. This study aims to implement seven different machine learning methods: from the most trivial, such as linear regression, to more complex and modern methods, including the TabPFNv2 generative transformer model. Their implementation and evaluation of the results will allow us to draw conclusions about the feasibility of using machine learning methods as tools for analyzing the mechanical properties of geopolymer concrete. This study is a first step toward understanding the internal relationships and dependencies when analyzing the influence of specific properties on the strength of geopolymer concretes. The results of the study revealed properties that should be prioritized when implementing materials science concepts that contribute to understanding the behavior of geopolymer concretes. Research objectives:

-

Data collection from [39,40,41,42,43,44,45,46,47] and dataset formation;

-

Exploratory Data Analysis;

-

Implementation, training, and quality assessment of AI models;

-

Developing recommendations regarding the practical implementation of the algorithms obtained.

-

Assessment of future prospects for enhanced forecasting performance.

The subsequent organization of this study is as described. Section 1, Introduction, summarizes the subject area and describes the main areas of application of intelligent algorithms, particularly in the construction industry. It identifies scientific gaps and formulates the purpose and objectives of the study. Section 2, Materials and Methods, presents the general framework of the study, describes the dataset acquisition process, describes its statistical characteristics, and substantiates the choice of intelligent algorithms and metrics for assessing the quality of forecasting results. Section 3, Results and Discussion, presents the results of the algorithm implementation and provides a comparative analysis with existing achievements in this subject area. Section 4, Conclusions, contains the main findings of the study and prospects for the development and improvement of forecasting results.

2. Materials and Methods

Figure 1 shows the overall research framework, which consists of six interconnected stages:

• Dataset collection.
• Exploratory Data Analysis (EDA).
• Selecting AI models.
• Implementation and training of AI models.
• Evaluation of quality metrics.
• Formulation of recommendations for practical use.

Figure 1. Research Steps.

Figure 1. Research Steps.

2.1. Dataset Collection

The first stage involved collecting data for further analysis. The initial dataset was drawn from open sources, specifically scientific studies [39,40,41,42,43,44,45,46,47]. During the search and data collection process, the most significant formulation and technological factors from a materials science perspective were identified. The key formulation factors primarily include the type of aluminosilicate component and the type of alkaline activator, which handle the formation of the geopolymer matrix. The presence of additives, such as fiber, is also an important formulation factor. Curing temperature is also a key technological factor. Selecting the optimal curing temperature allows for the activation of the dissolution of the aluminosilicate precursor and, consequently, the acceleration of geopolymerization reactions.

The collected dataset represents information on geopolymer concretes for further processing and ease of analysis, converted into a file with the extension (.xlsx). The file contains 204 rows and the following columns, which serve as features for machine learning models:

x1—blast-furnace granulated slag (kg/m³);

x2—NaOH molarity;

x3—NaOH content in the alkaline activator (%);

x4—Na₂SiO₃ content in the alkaline activator (%);

x5—fiber type;

x6—fiber dosage (%);

x7—curing temperature (°C).

The output (predicted) characteristic is the variable y—compressive strength (MPa).

Each of the characteristics from a compositional standpoint influences strength as follows.

Factor x1—blast-furnace granulated slag is the main binder aluminosilicate component and ensures the synthesis of the geopolymer structure.

Factors x2, x3, and x4 determine the composition of the alkaline activator. The alkaline activator serves as a medium for the dissolution of silicon and aluminum oxides and the synthesis of the geopolymer structure.

Factors x5 and x6—fibers—are a dispersed reinforcing additive and are introduced into the geopolymer composite to improve its strength properties. The effect of dispersed reinforcement can vary significantly depending on the fiber type and dosage.

Factor x7—curing temperature—affects the rate of geopolymer reactions. Increasing the temperature accelerates the curing process, which improves the physical and mechanical properties of geopolymer composites.

Thus, the factors described are key, and their optimal combination determines the future strength of geopolymer concrete.

2.2. Exploratory Data Analysis (EDA)

To understand the relationships within the data and subsequently correctly build artificial intelligence techniques, it is necessary to conduct “Exploratory Data Analysis”. An initial review of the data revealed that the data types of all values correspond to the logic of the subject domain, the measured values are represented numerically, and there are no gaps.

A description of the main statistics is presented in

Table 1. Data Statistics Description.

Attribute	Number	Average	Std	Min	25%	50%	75%	Max
x1	204.0	453.13	192.27	74.0	390.0	408.0	563.0	924.0
x2	204.0	10.91	2.32	4.0	10.0	12.0	12.0	14.0
x3	204.0	33.22	11.64	15.0	25.0	29.0	50.0	50.0
x4	204.0	66.78	11.64	50.0	50.0	71.0	75.0	85.0
x5	204.0	-	-	-	-	-	-	-
x6	204.0	1.30	1.39	0.0	0.5	1.1	2.0	10.0
x7	204.0	25.26	5.34	20.0	25.0	25.0	25.0	60.0
y	204.0	38.92	32.37	3.4	17.8	23.4	49.1	136.3

. The number of rows in the dataset under study is 204. The variable x5 is categorical, so only the “number” characteristic is presented for it.

A data visualization using the pairplot function from the seaborn library is shown in Figure 2. This function, by default, produces a grid of axes, with each numerical variable in the data allocated to the y-axes within a single row and the x-axes within a single column. The diagonal of the graph displays the distribution of values associated with each individual variable.

The graph displays the relationship between two variables. No atypical values (anomalies or outliers) that could subsequently influence the results of machine learning models were detected.

Figure 3a shows a correlation matrix, demonstrating the degree of relationship between different variables. Figure 3b shows the distance correlation (dCor). This matrix reflects a relationship of any shape.

Variable x1—granulated blast furnace slag (kg/m³)—has the greatest impact on the output variable. Granulated blast furnace slag is the main component of geopolymer concrete and acts as a binder. Variable x6—fiber dosage (%)—has the least impact on the output variable. The inclusion of dispersed reinforcing fiber in geopolymer concrete is an additional formulation decision, and depending on its dosage, compressive strength may show a slight increase. However, fiber in composite building materials is most actively involved in bending and tensile loads and demonstrates more significant increases in bending and tensile strength than in compressive strength [48,49,50,51].

Analyzing the matrices in Figure 3a,b, we can conclude that a nonlinear relationship exists in pairs where the value in the dCor matrix (threshold of 0.5) is higher than in the Pearson matrix (threshold of 0.3). This is observed for the pairs x1/x7 and x7/y.

2.3. Selecting AI Models

Seven ML techniques were selected for predicting the compressive strength of geopolymer concrete in this study: from simple ones, such as linear regression, to more complex and modern methods, including the TabPFNv2 generative transformer model. The implementation was performed in Python (v. 3.12.12) using the following libraries: numpy 2.0.2, pandas 2.2.2, seaborn 0.13.2, matplotlib 3.10.0, catboost 1.2.8, optuna 4.5.0, sklearn 1.6.1, torch 2.7.1 + cu126, tabpfn_extensions 0.1.4, joblib 1.5.1, tabpfn = 2.2.1, h2o: 3.46.0.7, tabpfn: 2.1.3, tabpfnp-extension: 0.1.6, OS Linux-6.6.105.

Figure 4 shows the hyperparameter selection and model evaluation with Optuna and three-box cross-validation.

The main dataset was divided into an 80/20 split for training and testing purposes. To select the optimal model hyperparameters, a three-fold cross-validation procedure was used on the training set using the Optuna optimization algorithm, with the data from each fold split 2/3 for training and 1/3 for validation. The final model quality assessment was performed on an independent test set (20% of the original data), minimizing the risk of information leakage and ensuring the objectivity of the results.

2.4. Implementation and Training of AI Models

2.4.1. Linear Regression

The initial model selected was Linear Regression. This statistical methodology is designed to model the correlation between a dependent variable and one or more independent variables, predicated on the assumption of a linear relationship. This method is often used as a baseline for subsequent comparison with other, more complex models.

The linear regression model can be represented as

$$f\left(x\right)={\beta }_0+{\displaystyle \sum _{j=1}^p{X}_j{\beta }_j},$$

(1)

where ${\beta }_j$ are the model coefficients (weights);

${\beta }_0$ is the mixing coefficient.

This model is sensitive to data dimensionality and does not handle categorical features. Therefore, before feeding the intelligent model, the data was preprocessed using the following:

-

A class from the scikit-learn StandardScaler library, which converts the data to a standard normal distribution; this approach standardizes features by subtracting the mean and dividing by the standard deviation;

-

One-Hot Encoding, a method for transforming categorical data.

One-Hot Encoding was implemented without extracting a baseline. According to this principle, all 8 fiber types (feature categories x5) were converted into 8 separate binary features. This approach differs from skip coding, which creates only N-1 features (N is the number of categories) and treats one fiber type as the baseline.

The Optuna library was used to select optimal hyperparameters. This hyperparameter optimization method is based on Bayesian search using the TPE (Tree-structured Parzen Estimator) algorithm [52].

During training of this model, the following equation was obtained:

$$\begin{array}{ll}\hfill y=& -1.3969+0.1090x1+2.2709x2+0.4995x3-0.4995x4+0.8302x6-0.6258x7-\hfill \\ & -10.1559x5\_1+19.6404x5\_2+25.952x5\_3+4.539x5\_4-29.731x5\_5-\hfill \\ & -7.915x5\_6-28.373x5\_7+26.044x5\_8\hfill \end{array}$$

(2)

where x5_1—is basalt fiber content; x5_2—ultra-high-molecular-weight polyethylene fiber; $x5\_3$—polyvinyl alcohol fiber; $x5\_4$—ceramic fiber; $x5\_5$—polypropylene fiber; $x5\_6$—polyethylene fiber; $x5\_7$—sisal fiber; and $x5\_8$—steel fiber.

2.4.2. CatBoost

The next model chosen was the gradient boosting model CatBoost [53]. This method is designed for efficient processing of categorical features and robust performance on heterogeneous data. Since the dataset has a categorical feature (x5), this should presumably improve forecasting quality.

Since we initially had a small dataset, special attention should be paid to optimizing the model’s hyperparameters. To optimize the hyperparameters, the Optuna library was used, similar to the first model. Optimization was performed using the following parameters: number of iterations (500–2000), learning rate (0.01–0.3), tree depth (4–10), L2 leaf regularization (1–10), and feature share (rsm, 0.5–1.0). For methods based on a tree structure, the trees should not be too deep, and measures against overfitting must be taken. During the training process, a categorical feature was taken into account, and an early stopping principle (stopping if there is no significant improvement within 50 iterations) was applied to prevent overfitting. Figure 5 shows the model training graph, with iterations plotted on the x-axis and the error plotted on the y-axis. It is worth noting the stability of the training, with the error steadily declining.

2.4.3. Random Forest

Unlike gradient boosting, Random Forest builds trees in parallel using a bagging method, which helps reduce variance and improve the stability of predictions.

The search for optimal values was conducted using key parameters: number of trees (100–500), maximum tree depth (5–20), minimum number of features for splitting a node (2–20), minimum number of features per leaf (1–10), and feature selection strategy at each split (max_features: sqrt, log2, None).

2.4.4. KNN

The next model chosen was the efficient nonparametric k-nearest neighbors (KNN) model, based on the principle of feature similarity in the feature space.

Before training, categorical features were encoded using One-Hot Encoding, and continuous features were standardized using Standard Scaler, as this method is sensitive to feature scale. Euclidean, Manhattan, and Minkowski distance metrics were considered, the latter with optimization of the p parameter. The Optuna library was used to tune the hyperparameters—the number of neighbors (k in the range 1–50), the weighting strategy (uniform, distance), the neighbor search algorithm, and the distance metric.

2.4.5. AutoML

Automated approaches such as AutoML are currently undergoing rapid development. These technologies allow for the automation of the creation, optimization, and deployment of machine learning models. The current investigation utilized an automated ML framework developed to build, optimize, and evaluate diverse models, such as gradient boosting, linear models, ensembles, and random forests [54]. It implements a full machine learning pipeline, including data preprocessing, hyperparameter selection, cross-validation, and ensemble building [55].

For this study, AutoML was run with a 60-s time limit to ensure comparability with other models and efficient use of computational resources. Cross-validation was performed using the 3-Fold CV scheme using scikit-learn, with the data converted to H2OFrame format at each fold for compatibility with the framework. Categorical features were explicitly transformed into factor variables using the asfactor() method, allowing H2O to correctly process them across various algorithms. Ultimately, the H2O GBM (Gradient Boosting Machine) model was selected to achieve the best results.

2.4.6. MLP

A standard deep learning architecture, the fully connected multilayer perceptron, was used as the foundational neural network method, and it is capable of modeling intricate nonlinear relationships between variables. This method is particularly effective when assuming the presence of hidden patterns and interrelations between variables.

Before training, all features were standardized using StandardScaler, and categorical variables were standardized using One-Hot Encoding. The hyperparameter space included the number of hidden layers (1–5), the number of neurons in each layer (10–200), activation functions (ReLU, tanh, logistic), optimizer type (Adam, LBFGS), L2 regularization coefficient (${10}^{-5}\dots {10}^{-1}$), learning rate type (constant, adaptive), and the initial learning rate (${10}^{-5}\dots {10}^{-1}$) for Adam. Early stopping was also used to prevent overfitting.

2.4.7. TabPFN v2

The TabPFN v2 method, a generative transformer specifically designed for solving regression problems on tabular data, was implemented in the study as the most modern and promising model. Unlike traditional machine learning algorithms, this approach does not require manual hyperparameter selection or retraining on a specific dataset. Instead, it uses a pre-trained model trained on millions of synthetic tasks and employs an attention mechanism to generate predictions in a few-shot learning mode.

For integration into the experimental pipeline, the AutoTabPFNRegressor wrapper, which implements post hoc ensembling, was used. This wrapper generates an ensemble of predictions by averaging the results of multiple model runs, improving stability and accuracy without requiring user intervention in parameter tuning.

Unlike traditional algorithms, TabPFN has no external hyperparameters to optimize. All key parameters, including the model architecture, weights, and attention strategy, are fixed in the pre-trained model. Automatic ensemble management and selection of the best predictions are implemented within AutoTabPFNRegressor, making the use of external hyperparameter optimization methods such as Optuna redundant.

Model limitations:

-

Supports up to 50,000 data rows (a technical limitation of the Transformer architecture);

-

Uses a GPU (Graphics Processing Unit) if CUDA (Compute Unified Device Architecture) support is available; otherwise, a CPU (Central Processing Unit) is used.

The model was trained on synthetic data, which may not cover all the specifics of a particular subject area. If the real data differs significantly from the synthetic training data, further training may be required. When applied to construction materials data, which has a unique internal structure, distribution estimation and in-depth analysis are required.

2.5. Evaluation of Quality Metrics

When implementing machine learning models, it is important to evaluate them using various metrics to gain a comprehensive understanding of the algorithm’s predictive capabilities. In this study, the following metrics were evaluated:

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

(3)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{(y_i-{\widehat{y}}_i)}^2}}$$

(4)

$$MAPE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|\frac{y_i-{\widehat{y}}_i}{{\widehat{y}}_i}\right|}\times 100$$

(5)

$$R^2=1-{\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}}{{\displaystyle \sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}}}$$

(6)

2.6. Formation of Recommendations for Practical Use

After obtaining stable training results and quality metrics that satisfy the subject area, the corresponding models can be implemented in real systems in the field of predictive modeling of building materials properties.

3. Results and Discussion

The following values were obtained during hyperparameter selection using Optuna (

Table 2. Best Parameter Values for the Models.

№	Model	Best Parameters/Meta-Model
1	Linear Regression	{‘model_type’: ‘ridge’, ‘alpha’: 0.7982803713496193}
2	CatBoost	{‘iterations’: 920, ‘learning_rate’: 0.18190538763505498, ‘depth’: 4, ‘l2_leaf_reg’: 7.478453558099906, ‘rsm’: 0.7537872840036406}
3	Random Forest	{‘n_estimators’: 352, ‘max_depth’: 14, ‘min_samples_split’: 2, ‘min_samples_leaf’: 1, ‘max_features’: None}
4	KNN	{‘n_neighbors’: 1 (or 3), ‘weights’: ‘uniform’, ‘metric’: ‘minkowski’, ‘algorithm’: ‘kd_tree’, ‘p’: 3}
5	AutoML	{‘ntrees’: 89, ‘max_depth’: 6, ‘min_rows’: 1, ‘learn_rate’: 0.1, ‘learn_rate_annealing’: 1.0, ‘sample_rate’: 0.5, ‘col_sample_rate’: 0.7, ‘distribution’: ‘gaussian’, ‘stopping_rounds’: 3, ‘stopping_tolerance’: 0.05, ‘histogram_type’: ‘UniformAdaptive’, ‘categorical_encoding’: ‘Enum’}
6	MLP	{‘n_layers’: ‘2’, ‘n_units_l0’: ‘96’,’ n_units_l1’: ‘55’, ‘activation’: ‘logistic’, ‘solver’: ‘lbfgs’, ‘alpha’: ‘0.008686426576670337’, ‘learning_rate’: ‘adaptive’}

).

Figure 6 shows scatter plots obtained during model testing, with the x-axis representing actual values and the y-axis representing values predicted by the linear regression model. Points lying on a straight line (y = x) indicate accurate forecasting. Deviations from this line indicate poor forecasting. On the residual graph, the points are distributed randomly, without clusters or trends, and no “fan” is observed.

The metrics obtained from the model validation on the test set are provided in

Table 3. Test set model validation.

№	Model Type	MAE	RMSE	MAPE, %	R2
1	Linear Regression	7.75	10.16	31.51	0.8977
2	CatBoost	0.93	1.39	5.35	0.9981
3	Random Forest	2.97	4.70	10.97	0.9782
4	KNN	0.37	0.63	1.62	0.9996
5	AutoML	0.51	0.68	2.12	0.9995
6	MLP	0.56	0.82	2.70	0.9993
7	TabPFN v2	0.46	0.64	1.39	0.9996

.

Figure 7 visualizes the data in Table 3. Within the MAE, RMSE and MAPE metrics, the models are distributed in ascending order of error, and R² in descending order.

In this study, cross-validation was used to evaluate the robustness of the models to different subsets. Figure 8 shows the results of the coefficient of determination of the models for each fold (this graph is not available for the AutoML model, as the architecture requires the output of the average value of this parameter without displaying it across folds). The largest deviations are observed for the LR (±0.0192) and MLP (±0.0195) models. Overall, stable training is observed on each fold, indicating that the models generalize well to the data and are not susceptible to overfitting, the parameters are optimally selected, and the analyzed data is representative.

Significant differences in the accuracy and robustness of the resulting solutions were revealed by a comparative analysis of seven machine learning models applied to the problem of predicting the properties of geopolymer concrete. The observed quality hierarchy in Figure 6 allows us to formulate the following generalizations:

• The basic linear regression model demonstrated satisfactory quality (R² = 0.8977); however, this value is significantly inferior to more complex methods across all key metrics. High errors indicate the presence of nonlinear relationships between features not captured by the linear model.
• The nonparametric KNN method demonstrated high prediction accuracy (MAPE = 1.62%) due to well-chosen parameters and the small dimensionality of the original dataset. In this study, the optimal number of neighbors and a correct distance metric made it possible to solve the problem using the closest data.
• Ensemble and boosted methods (CatBoost, Random Forest, AutoML) showed comparable and high results (R² = 0.9995…0.9981). H2O AutoML delivered stability and high quality without manual parameter selection, confirming the effectiveness of automated machine learning.
• The neural network model (MLP) demonstrated R² = 0.9993, but the average absolute percentage error reached 2.70%.
• The generatively trained transformer (TabPFN) demonstrated good results across all metrics—(MAE = 0.46, RMSE = 0.64, MAPE = 1.39%, R² = 0.9996). TabPFN does not require hyperparameter selection and ensures maximum accuracy with minimal computational costs during the retraining stage, making it a promising tool for practical application. This method is quite new in the line of intelligent models, which allows it to use modern approaches and the advantages of previously studied models.

Since the original dataset was relatively small, it was decided to expand it by 50 points to test the generalization capabilities of the models. The new data was also collected from open sources and differs in some statistical characteristics from the training set. This difference will allow for a more objective assessment of the generalization ability of the models.

The CatBoost algorithm was chosen for predicting robustness. This method is sensitive to changes in distributions and allows one to evaluate the impact of each characteristic on the final forecast.

Table 4. Testing the model at new points.

№	Model Type	MAE	RMSE	MAPE, %	R2
1	CatBoost	3.13	5.23	7.45	0.8480

shows the resulting metrics, and Figure 9 shows the Actual vs. Predicted plot. Analysis of the metrics and a visual assessment of Figure 9 suggest good generalization ability of the model.

The reliability of the metrics was assessed using the bootstrap method with 1000 iterations. At each iteration, a sample was generated with replacement from the test set, and the metrics were recalculated. Confidence intervals for R² [0.7995, 0.8863], RMSE [4.5892, 6.0124], and MAE [2.6347, 3.7185] demonstrate acceptable model stability.

For a more comprehensive interpretation of the model, the study is supplemented with a plot from the SHAP method. For the CB method, the contribution of each feature to the model prediction is shown (Figure 9). Feature x1 is the most significant for the model, based on the largest value along the x-axis. Feature x7 was also found to be significant. Understanding the influence of these variables on the final results allows us to conclude that when modeling compositions, it is worth focusing on the main aluminosilicate binder component and curing temperature.

Comparing the obtained results with similar studies in the field of predicting the mechanical properties of geopolymer concretes using machine learning methods, it can be noted that the obtained results are not inferior in terms of quality metrics to existing ones (

Table 5. Comparison of results with similar studies.

No.	Research	Number of Samples	Method	R2
1	This study	204	LR, CB, RF, KNN, AutoML, MLP, TabPFN	0.9996
2	[27]	162	ANN	0.9993
3	[29]	397	“gene expression program” (GEP) and “multi-expression programming” (MEP) methods	0.73–0.89

).

Thus, in work [27], a dataset of 162 mixture composition variants was used to train and validate the artificial neural network model, the determination coefficient reached a value of 0.92868 at the testing stage. In our study, R² = 0.9993, which confirms the ability of neural network models to capture complex dependencies in data describing the formation of strength characteristics of geopolymer concretes. In work [29], “gene expression program” (GEP) and “multi-expression programming” (MEP) methods were adapted to optimize the composition of geopolymer mixtures. The methods were implemented on a relatively small database, comprising results of 301 compressive strength tests and 96 tensile strength tests. The MAE metrics for the MEP and GEP-based techniques for compressive strength prediction were 5.09 MPa and 6.78 MPa. And for post-split tensile strength were 0.42 MPa and 0.51 MPa, respectively. The MAE metric values in this study for the best models ranged from 0.37 to 0.51 MPa.

Despite the small size of the dataset, it reflects the true relationships between factors, which are consistent with previous studies [27,28,29,30,39,40,41,42,43,44,45,46,47,55,56]. The obtained statistical characteristics and correlations affect the developed strength properties of geopolymer concrete.

For industrial applications of intelligent solutions, it is assumed that the trained model will adequately handle new data, i.e., be capable of generalization. However, in practice, changes in characteristics (e.g., changes in distribution or correlations) are often observed, which can lead to incorrect results. For correct application in real-world conditions, it is necessary to train the model on a representative and voluminous dataset that includes all influencing factors.

The strength properties of geopolymer concretes are largely determined by the properties of the main raw materials and their ratios. When designing geopolymer composites, ground granulated blast-furnace slag is a common choice as the aluminosilicate binder. The most popular alkaline activators are sodium hydroxide (NaOH) and sodium silicate (Na₂SiO₃). Proper selection of an aluminosilicate component with a high Si/Al ratio and the composition of the alkaline activator, including the molarity of NaOH and the ratio of the alkaline activators, enables the activation of geopolymer reactions and the production of a composite with superior strength properties. Curing temperature is the most important process parameter and influences the process and activity of geopolymerization reactions, which also impacts the strength properties. Dispersed reinforcement with various fiber types in rational dosages further improves the strength properties of geopolymer composites and ensures a more ductile, ductile failure mode compared to the brittle failure of unreinforced composites [39,40,41,42,43,44,45,46,47,48].

This study examines the x1–x7 characteristic set for geopolymer concrete. These characteristics are most significant for modeling the composition of this building material. If the developed models are to be applied to other building materials, it is worth evaluating the data distributions; if significant discrepancies are detected, further training of the models will be necessary. However, it is worth noting that training does not need to be performed from scratch, as the existing weights can provide a good starting point.

In addition to data limitations, technical challenges may arise. Integrating intelligent models requires computing power, the quantity and quality of which depend on the volume of data being processed. If real-time forecasting is required, the time delays that may occur during the operation of AI systems must be taken into account.

During the study, bottlenecks were identified that open up avenues for future work. The following actions offer opportunities to improve the developed intelligent models:

• Dataset development:

  -

  Expanding the training data by integrating information from open sources and laboratory test data to improve the prediction accuracy and generalizability of the algorithms;

  -

  Expanding the list of features in the dataset to account for a greater number of factors influencing the strength properties of geopolymers;

  -

  Creating an open, expandable data source for use by interested parties.

• Conducting additional analyses:

  -

  Examining additional plots from the SHAP method to accurately assess the impact of an expanded list of features on the strength properties of geopolymers;

  -

  Analyzing multicollinearity to fine-tune models sensitive to multicollinearity;

  -

  Adding complex residual analysis plots.

• Tuning model parameters:

  -

  Using additional methods to optimize models and evaluate performance. 4. Adaptation of developed models:

  -

  Adaptation of intelligent models to predict other physical and mechanical properties of geopolymer concrete in addition to strength;

  -

  Expanding the capabilities of developed models for use in predictive modeling systems for the properties of building materials.

4. Conclusions

This paper presents the implementation of seven machine learning methods (Linear Regression, CatBoost, Random Forest, KNN, AutoML, MLP, TabPFN v2) for predicting the properties of geopolymer concrete, in particular compressive strength. To ensure stable training, the parameters for the models were selected using Optuna. A database containing 204 rows and the following input parameters was compiled from published literature: x1—granulated blast furnace slag, kg/m³; x2—NaOH molarity; x3—NaOH content in the alkali activator, %; x4—Na₂SiO₃ content in the alkali activator, %; x5—fiber type; x6—fiber dosage, %; x7—curing temperature, °C. The assessment of the developed models’ performance was conducted using diverse quality metrics, namely, MAE, RMSE, MAPE, and R².

Key findings from the above study:

-

The best models in terms of all quality metrics used are the k-nearest neighbor model (MAE = 0.37, RMSE = 0.63, MAPE = 1.62%, R² = 0.9996) and TabPFNv2 (MAE = 0.46, RMSE = 0.64, MAPE = 1.39%, R² = 0.9996);

-

When computing resources are limited and interpretability is required, the CatBoost or Random Forest algorithms are recommended;

-

When a GPU and a small dataset are available, TabPFN is advisable;

-

When manual parameter tuning is not required, H2O AutoML is recommended.

Overall, this study makes a valuable contribution to the study and development of alternative methods for analyzing the strength properties of building materials.

Machine learning methods are essential and reliable tools for predictive modeling of building materials. The developed methods can be used as part of predictive systems in laboratory settings to reduce the time required to analyze the physical and mechanical properties of materials when changing specific chemical elements and process parameters.