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Use of explainable symbolic regression approaches for predicting nanomaterial-enhanced concrete performance

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REVIEWS ON ADVANCED MATERIALS SCIENCE
From the journal REVIEWS ON ADVANCED MATERIALS SCIENCE Volume 65 Issue 1

Abstract

The incorporation of nanomaterials in concrete improves mechanical strength, durability, and resistance to environmental effects, presenting a sustainable approach for modern construction. This research employs symbolic regression approaches, namely Gene Expression Programming (GEP) and Multi Expression Programming (MEP), to forecast the compressive strength of nano enhanced (nano TiO2 and nano SiO2) concretes. The developed models were trained and validated using a comprehensive experimental database and evaluated through multiple statistical metrics. Based on the comparative performance metrics, the MEP model clearly outperformed the GEP model, achieving higher predictive accuracy (R2 = 0.954), lower error values (RMSE = 5.427 MPa, MAE = 4.596 MPa, MAPE = 10.40 %), and stronger reliability (NSE = 0.953) compared to the GEP model (R2 = 0.914). Model performance was illustrated through Taylor’s diagram. Partial Dependence Plots (PDPs) and Individual Conditional Expectation (ICE) plots were used to examine feature importance and interaction effects, showing that concrete age, cement, slag, and nano silica enhance strength, whereas higher water content and fine aggregate proportions reduce it. These results highlight the potential of MEP-based modeling to optimize mix design and promote the sustainable use of nanomaterials and supplementary cementitious materials (SCMs) in concrete, offering valuable guidance for sustainable construction.

Keywords: nanomaterials-modified concrete; nano-TiO2 and nano-SiO2 ; compressive strength modeling

1 Introduction

Across the globe, concrete is used for a broad variety of construction purposes, including foundations, external surfaces, superstructures, floor construction, and public works projects like wastewater treatment facilities and parking lots [1]. Environmental concerns arise, however, due to the extensive usage of construction materials [2], 3]. The binder element in concrete is ordinary Portland cement (OPC), which is the most important component of the material [4], 5]. The manufacture of OPC, however, results in a substantial amount of CO2 emissions and uses a lot of natural resources [3]. A great deal of time and energy has been devoted to studying the possibility of using concrete instead of OPC as a means to lessen the environmental impact of OPC production [4], 6], 7].

A variety of additives, including cement, water, sand, and coarse aggregate, are often mixed to produce concrete. Different kinds of supplemental resources are finding new uses as technology progresses [8], [9], [10]. A group of chemicals with wide-ranging uses in concrete, supplemental cementitious materials (SCMs) are either mixed into cement or given to the mixer separately. In the concrete construction business, using SCMs is a great way to reduce waste and CO2 emissions, which means cleaner manufacturing overall. Research on SCMs has shown that they significantly improve concrete’s characteristics [11], [12], [13]. Numerous concrete problems, both immediate and distant, can be effectively mitigated by adding nanomaterials to the mix [14], 15]. Improvements in mechanical strength and durability were brought about by the incorporation of nanoparticles into concrete, which sped up the hydration process by refining the pore structure [5], [16], [17], [18]. Still, concrete’s performance might take a hit if nanomaterials are added in excess [19], [20], [21]. It is usual practice to combine SCMs with nanomaterials when improving concrete’s overall performance [22]. Several studies have documented the synergistic effect of SCMs and nanomaterials. As an example, carbon nanotubes can help improve fly ash’s early-age strength, which is one of its drawbacks [23]. In a similar vein, research has shown that adding nano-TiO2 to concrete with fly ash and slag improves its mechanical qualities, increases its unit weight, decreases its setting time, and speeds up its early age rate of hydration [16], 20], 24]. Also, adding nano-SiO2 to concrete and cement paste improves their rheological properties and compressive strength [25]. Though it may be time- and resource-consuming to conduct experiments with various mixes of SCMs and nanomaterials to find out how they affect mechanical performance, the results show that SCMs and nanomaterials increase concrete’s performance, which in turn lowers the carbon footprint of the construction industry. A possible answer to the aforementioned problem in concrete research could be machine learning models trained in experimental data.

The strongest and most widely used way to assess concrete’s strength is by its compressive strength (CS) [26], 27]. Correlation with other important concrete qualities allows for a crucial evaluation of the material’s load-bearing and failure-resistant capabilities. There have been studies on predicting the CS of concrete with different compositions using different machine learning algorithms [28], 29]. Radiation shielding, flow behavior, chloride diffusion, and water permeability are among the additional concrete properties that have been investigated and predicted using machine learning techniques [30], [31], [32], [33], [34]. However, most studies have concentrated on compressive strength as it is one of the few concrete qualities for which data is readily available. Research has extensively examined materials such as lightweight concrete [35], high-performance concrete [36], concrete incorporating recycled aggregates [37], and mixtures containing diverse nanomaterials and nanoparticles [28], 29], 35], 38], 39]. The most frequently employed models in the literature include artificial neural networks (ANN), random forests (RF), Multi Expression Programming (MEP), support vector machines (SVM), K-nearest neighbors (KNNs), decision trees (DT), Gene Expression Programming (GEP), extreme gradient boosting (XGB), and several others.

Recent advancements have demonstrated the growing integration machine learning approaches for predicting the mechanical and durability behavior of cementitious and composite materials under various conditions [40], [41], [42], [43], [44], [45], [46]. These studies collectively highlight the potential of data-driven modeling in enhancing prediction accuracy and interpretability, aligning closely with the scope of the present research. Machine learning approaches with a variety of input features and numerical analysis are lacking in studies that aim to forecast how SCMs and nanomaterials would affect the CS of concrete. Employing ANN and XGB, Mughees et al. [28] predicted the compressive strength of nanoparticle-and SCM-containing concrete using two different kinds of SCMs: fly ash and silica fume. The model does not take into account other important factors affecting concrete strength, such as the concrete’s age or the amount of coarse material. On top of that, nobody seems to be talking about whether or not there is a universally accepted geometry for concrete samples based on their compressive strength. Nazar et al. employed machine learning techniques to estimate the compressive strength of nanomodified concrete devoid of SCMs [29]. When it comes to SCMs, which are frequently employed in concrete building, machine learning models that don’t include them in their input parameters could not be very useful.

The compressive strength of nanomaterial-infused concrete was forecasted using symbolic regression methods such as Multi-Expression Programming (MEP) and Gene Expression Programming (GEP). Multiple parameters are used to validate the model’s performance, including R2, RMSE, R, MAE, NSE, MAPE, and Taylor’s diagram. Partial Dependence Plots (PDPs) and Individual Conditional Expectation (ICE) plots were used to better understand how input features affected the expected outcome. The dataset was derived from previously published experimental research and contains 206 data points. Each point has 12 input variables and 1 output variable, compressive strength. Through these methods, the study aims to deliver accurate and interpretable predictions while identifying key factors affecting concrete performance. The outcomes are expected to support the optimization of concrete mixes, particularly those incorporating nanomaterials and supplementary cementitious materials, thereby contributing to sustainable construction. This research offers valuable insights for both academic researchers and practicing engineers, promoting data-driven decision-making in material design and structural applications.

2 Machine learning approach

2.1 Data characteristics and preparation

An extensive and trustworthy dataset is essential for building strong data-driven predictive models [47]. The 206 experimental records on nanoparticles and SCMs-based concrete (NSCs) that make up the curated dataset in this work were sourced from credible, peer-reviewed international journals [48], [49], [50], [51], [52], [53], [54], [55], [56], [57]. 12 of the most important input factors found to be strong predictors of compressive strength (CS) are included in the dataset: cement (OPO), water (Wt), fine aggregate (FAg), coarse aggregate (CAg), high range water reducer (HRW), fly ash (Fa), silica fume (SF), slag (Sl), nano-TiO2, Nano-SiO2, concrete age (Ca), and curing temperature (CT). The input parameters were measured in kilograms per cubic meter (kg/m3), with the exception of curing age, recorded in days, and curing temperature, expressed in degrees Celsius (°C). These variables were carefully chosen due to their proven significance and consistent application in prior studies reported in the literature. The compressive strength, expressed in megapascals (MPa), is the desired output factor. The output parameter and these input attributes are shown in Figure 1’s schematic. The predictive algorithms employed in this study are trained and evaluated using this dataset.

Figure 1: Illustration of model inputs and output variable.
Figure 1:

Illustration of model inputs and output variable.

2.1.1 Dataset splitting and outliers identification

The idea of separating the dataset used to train algorithms from the one used to verify their accuracy has been put forth on several occasions; this would allow for more efficient model building [58]. A training set with 144 data points (or 70 % of the total) and a testing set with 62 data points (or 30 % of the total) were created from the gathered dataset. To avoid overfitting and guarantee good performance when tested against unknown data, ML models were trained using training data before making predictions on unseen test data. When dealing with data-driven models, it is also important to think about how the data was distributed. The distribution of the training data has a direct correlation to the efficiency of a machine learning model [59]. Outlier detection was initially performed through visual inspection using frequency distribution plots, followed by statistical analysis to identify and remove extreme values. The elimination of outliers was necessary to prevent data distortion, enhance model training efficiency, and improve prediction reliability. This two-step approach ensured a cleaner and more representative dataset for machine learning–based modeling. Frequency distribution plots in Figure 2(a)–(m) provide insights into the spread and balance of variables in the dataset, allowing identification of skewness, concentration ranges, and outliers within the dataset. Such visualization is essential in machine learning studies as it highlights data irregularities that may bias model training [60]. For instance, the frequency plot of OPC content shows a unimodal distribution peaking around 400 kg/m3, where the count exceeds 60 samples, indicating this is the most common density. Moderate frequencies are seen near 300 kg/m3 and 500–600 kg/m3, while extreme values below 200 kg/m3 and above 600 kg/m3 are rare. This central tendency and tapering pattern suggest a near-normal distribution, useful for machine learning models. The fly ash (Fa) content distribution is heavily skewed, with a dominant peak at 0 kg/m3 (≈140 samples), indicating most samples contain no fly ash. Minor peaks appear around 50, 100, and 250 kg/m3, each with fewer than 20 samples. Compared to the OPC plot, which showed a near-normal distribution centered around 400 kg/m3, the Fa plot reflects a sparse and imbalanced feature. Such distribution plots are essential in machine learning studies as they reveal the underlying structure and balance of input features. They guide preprocessing decisions like normalization, outlier handling, and feature selection, ultimately improving model robustness and predictive accuracy.

Figure 2: Frequency distribution of input/ouput features: (a) OPC; (b) Wt; (c) FAg; (d) CAg; (e) HWR; (f) Fa; (g) Sl; (h) Sf; (i) nT; (j) nS; (k) Ca; (l) CT; (m) CS.
Figure 2:

Frequency distribution of input/ouput features: (a) OPC; (b) Wt; (c) FAg; (d) CAg; (e) HWR; (f) Fa; (g) Sl; (h) Sf; (i) nT; (j) nS; (k) Ca; (l) CT; (m) CS.

2.1.2 Multicollinearity detection

The Kendall rank correlation heatmap is an effective tool for assessing multicollinearity among input variables, as it measures monotonic associations rather than assuming linearity like Pearson correlation. It produces values between −1 and +1, where coefficients closer to +1 or −1 indicate strong positive or negative monotonic relationships, respectively, while values near 0 suggest weak or no association. In practice, variables showing >±0.8 are generally considered highly correlated and may introduce redundancy in machine learning models [61]. In heatmap provided in Figure 3, all correlation coefficients fall between −0.42 and +0.65, meaning none of the variables exhibit strong correlations beyond the ±0.8 threshold. This implies low multicollinearity among the input features, which is ideal for machine learning models as it minimizes redundancy and enhances model stability and interpretability.

Figure 3: Correlation metrices for the variables.
Figure 3:

Correlation metrices for the variables.

2.2 Machine learning modeling

The compressive strength of nanoparticle and SCMs-based concrete (NSCs) was the primary topic of this work. To do this, researchers employed a dataset with 12 input variables sourced from various sources. Gen Expression Programming (GEP) and Multi-Expression Programming (MEP) are two examples of cutting-edge machine learning techniques that were used to accurately predict the CS of NSCs. It is common practice to examine the input data when evaluating machine learning algorithms. In this study, 70 % of the dataset was utilized for model training and the remaining 30 % for testing, following the commonly adopted practice reported in the literature [58]. A low R2 value indicates a significant divergence, highlighting the models’ applicability, while a high R2 number indicates excellent agreement between expected and actual results [62]. Additional methods utilized to validate the model’s accuracy included statistical tests and appraisals of errors. Table 1 provides a summary of the hyper-parameters utilized by the GEP and MEP models, and Figure 4 illustrates a simplified event model diagram. A random iterative approach was adopted for tuning the hyperparameters of the GEP and MEP models, following ranges reported in previous studies [63], 64]. Multiple combinations of population size, number of generations, and mutation/crossover rates were tested to identify the most accurate and computationally efficient model configuration.

Table 1:

Adopted parameters of GEP and MEP methods.

Models Descriptions Settings
GEP/MEP selection Justification/test data 62
Training data 144
MEP parameters Error measure Mean absolute error (MAE)
Number of sub-populations 50
Sub-populations size 250
Code length 50
Cross-over probability 0.9
Number of generations 250
Functions +, −, ÷, ×, √, ˆ
Mutation probability 0.01
GEP parameters Number of chromosomes 50
Head size 10
Number of genes 6
Linking function Addition
Functions +, −, ÷, ×, √, ˆ
Figure 4: Framework of the adopted approach.
Figure 4:

Framework of the adopted approach.

2.2.1 GEP modeling approach

An evolutionary technique first proposed by Ferreira, GEP allows for the generation of computer programs capable of solving complex problems. [65], 66]. Below are some key components of the GEP technique:

  1. First steps in population generation: The procedure starts by making a random assortment of chromosomes. Mathematical models or algorithms are represented by symbolic sequences encoded in each chromosome.

  2. Fitness evaluation: For every chromosome, we calculate a fitness score that shows how well it handles the current task. In this context, fitness is the capacity of a chromosome to predict the CS of NSCs.

  3. Evolutionary selection phase: The process prioritizes the chromosomes with the fewest prediction errors. These chromosomes are then selected for reproduction. All things considered, these people represent the cream of the crop when it comes to current applications.

  4. Genetic operations: Some chromosomes can be modified by genetic operators such as mutations, which alter gene sequences, or crossings, which swap segments between chromosomes. The next generation that emerges from these processes may be more capable than the one before it.

  5. Loop of fitness measurement: Collection and genetic processes allows the population to adapt and get better at handling problems over many generations. This allows for progression across generations.

  6. Generational progression: GEP produces mathematical expressions optimized from the training data after numerous iterations; this is the final model output. By using these formulas, it is feasible to make accurate predictions about the desired material properties. An illustration of the GEP process is shown in Figure 5.

Figure 5: Stepwise framework of GEP model development (modified from [67]).
Figure 5:

Stepwise framework of GEP model development (modified from [67]).

2.2.2 MEP modeling approach

Using genetic programming techniques, such as those described in GEP, MEP develops a sophisticated evolutionary algorithm [68]. The following steps comprise the MEP process:

  1. Initial population generation: Similar to GEP, MEP begins with creating a chromosomal population at random. One unique aspect of MEP, though, is that every chromosome potentially encodes many mathematical expressions all at once.

  2. Evaluation of fitness: The accuracy with which each chromosomal expression makes predictions is called its fitness, and it is evaluated on an individual basis.

  3. Best performer selection: Selecting the most fit or finest expressions to become parents guarantees that strong solutions will be passed down through the generations.

  4. Genetic modification: Mutation and crossover are two examples of genetic operations that are applied to selected expressions. These changes produce new generations that might have better prediction skills.

  5. Evolution through generations: This repeated cycle of fitness appraisal, selection, and genetic change fine-tunes the population’s performance over numerous generations.

  6. Advanced remedies: MEP culminates in optimal expression generation, which provides accurate predictions of target properties such as compressive strength (CS) of NSC. The MEP workflow is illustrated graphically in Figure 6.

Figure 6: Stepwise framework of GEP model development (modified from [67]).
Figure 6:

Stepwise framework of GEP model development (modified from [67]).

2.3 Models validation

To ensure that the created models can effectively resolve the issue, it is essential to test the efficiency of ML models [69]. As a result, the models built for this study’s performance evaluation made use of a number of error metrics proposed by researchers. Among these metrics are MAE, RMSE, MAPE, and others. Among the many metrics used to evaluate ML models, the three most important are MAE, RMSE, and MAPE [64]. That is, MAE provides the mean difference between the values predicted by ML and those obtained by experimentation, and MAPE, also known as mean absolute percentage deviation (MAPD), is a statistical measure for evaluating the accuracy of a forecasting method, it is commonly used in trend estimation in statistics and as a loss function in machine learning regression problems. All three of these metrics should be kept as close to zero as possible. In order to understand how well a model predicts, MAPE measures the size of the mistake in percentage terms. Whereas, root-mean-squared error (RMSE) is a measure of greater errors; this is due to the fact that RMSE squares the residuals before averaging them, which gives larger errors more weight. In addition, R-squared is a popular statistic for gauging the overall precision of models. Since R is unaffected by the division or multiplication of output with a constant, it should never be relied upon as the only indication of the model’s efficacy [58]. For a model to be deemed satisfactory in terms of performance, the correlation value should be larger than 0.8 [69]. Similarly, one commonly used metric in hydrological modeling to evaluate how well a model matches up with observable data is the Nash-Sutcliffe efficiency (NSE). Nash and Sutcliffe created it in 1970, Normalized to both the model’s residual variance and the measured data’s variance, NSE is a useful statistic for comparing the two. The possible values of NSE are between −1 and 1. When the observed data is perfectly fitted to the model, the NSE is 1, meaning that the simulated and observed values are completely in agreement. If the NSE is zero, then the model’s predictions are on par with those made by just taking the mean of the data, and if it’s negative, then the mean of the data gives better forecasts than the model [70]. In (Table 2), you can see a summary of the error evaluation metrics and the criteria that were proposed for this study.

Table 2:

Summary of error evaluation metrics.

Metric Abbreviation Formula Range Suggested values Equation no.
Pearson’s correlation coefficient R R = ∑ i = 1 n a i − a ‾ i p i − p i ‾ ∑ i = 1 n a i − a i ‾ 2 ∑ i = 1 n p i − p ‾ i 2 −1 to 1 Close to 1 (1)
Mean absolute error MAE MAE = 1 n ∑ i = 1 n p i − a i 0 to ∞ Close to zero (2)
Root mean square error RMSE RMSE = ∑ p i − a i 2 n 0 to ∞ Close to zero (3)
Mean absolute error MAPE MAPE = 100 % n ∑ i = 1 n p i − a i a i 0 to ∞ Close to zero (4)
Nash Sutcliffe model efficiency coefficient NSE NSE = 1 − ∑ i = 1 n a i − p i 2 ∑ i = 1 n a i − p i ‾ 2 −∞ to 1 Close to 1 (5)

  1. Here, a i , observed values; p i ‾ , estimated values; n, total data point.

In addition to its application in statistical validation, the Taylor diagram provides a visual way to assess the precision of model predictions. It shows the level of agreement between several models and the reference data by providing important performance metrics including root mean square error, correlation, and standard deviation all at once. With this integrated visualization, you can easily and thoroughly compare the models’ accuracy and reliability, helping you to select the best ones [71], 72]. A Taylor diagram illustrates model performance by integrating three statistical measures into a single plot. The spread of data is captured through radial distances representing standard deviation, while the alignment between predicted and observed values is reflected along the x- and y-axes via the correlation coefficient. Additionally, concentric arcs centered on the reference observation quantify the root mean square error (RMSE), providing a visual gauge of overall model accuracy. The most accurate model in a comparison will be the one that fits the data best and has the most ideal points on the graph for its predictions [71].

3 Results interpretation and comparison

3.1 CS prediction using GEP

The GEP model provides a systematic and interpretable description of how input factors influence the output through the generation of Expression Trees (ETs) shown in Figure 7(a)–(g). These ETs are used to forecast the compressive strength (CS) of concrete by representing the relationships between variables in a symbolic form. The trees were constructed using a set of mathematical operators, including multiplication (×), division (÷), addition (+), subtraction (−), power (ˆ), and square root (√), allowing the model to capture complex nonlinear interactions among the 12 input parameters. Through evolutionary optimization, the model identified the most influential parameters and their interactions, ultimately formulating a precise and generalizable mathematical equation Equation (6). Beyond predictive accuracy, this equation reveals the underlying physical trends of mix behavior: it highlights the positive contribution of cement, slag, and nano-silica contents to strength development, which aligns with their roles in improving hydration and microstructure densification. Conversely, higher water and fine aggregate contents were associated with reduced strength, reflecting increased porosity and weaker paste–aggregate bonding. Thus, the equation not only enables reliable strength estimation but also provides a physically meaningful understanding of material interactions, supporting informed decisions in sustainable mix design and optimization.

Figure 7: GEP model tree for CS prediction: (a) Sub-ET 1; (b) Sub-ET 2; (c) Sub-ET 3; (d) Sub-ET 4; (e) Sub-ET 5; (f) Sub-ET 6; (g) Sub-ET 7.
Figure 7:

GEP model tree for CS prediction: (a) Sub-ET 1; (b) Sub-ET 2; (c) Sub-ET 3; (d) Sub-ET 4; (e) Sub-ET 5; (f) Sub-ET 6; (g) Sub-ET 7.

Figure 8(a) shows a scatter plot demonstrating a perfect linear alignment around the ideal y = x line, which compares the experimental data with the projected CS-values. The high level of agreement between the two sets of data is illustrated by the R2-value of 0.914, which means that the GEP model accounts for 91.4 % of the variation in the experimental data. Figure 8(b) shows the absolute error, a third trace shows the experimental and projected compressive strengths, and a left sub-figure combines line and symbol plots. The fact that the experimental and projected trends are visually similar indicates that there is high agreement across the dataset. Furthermore, the absolute error among samples is shown in Figure 8(c). It varies, but it stays within a reasonable range, indicating that the GEP model is consistent and accurate across different mix compositions. With an average of 4.98 MPa, the absolute errors ranged from a maximum of 14.10 MPa to a minimum of a minuscule 0.13 MPa. In all, 44 samples had errors below 4 MPa, 15 samples had errors between 4 and 8 MPa, and 17 samples had errors greater than 8 MPa. The accuracy of the model is demonstrated by these data, which show that most forecasts have a small margin of error. All things considered, this thorough evaluation proves that the GEP model is very accurate at predicting future results and can be used to estimate compressive strength in complicated cementitious systems including nanoparticles and SCMs.

(6) C S = − 2.451 4.894 − C a + F a × S l + C a + S l + C A g + O P C + C T − W t − n S − C T × H W R + − 3.92 + 8.753 − 2.334 + n S − n S + 8.753 − C A g + 8.753 − 0.00062 × F A g + 0.043 × S f + 0.415 × n T

Where, OPC: cement, Wt: water, FAg: fine aggregate, CAg: coarse aggregate, HWR: High range water reducer, Fa: fly ash, Sl: slag, Sf: silica fume, nT: nano-TiO2, nS: nano-SiO2, Ca: concrete age, CT: curing temperature, and CS: compressive strength.

Figure 8: Compressive strength modeling with GEP: (a) Predicted-observed correlation; (b) comparison of predicted results and corresponding error distribution; (c) absolute errors.
Figure 8:

Compressive strength modeling with GEP: (a) Predicted-observed correlation; (b) comparison of predicted results and corresponding error distribution; (c) absolute errors.

3.2 CS prediction using GEP

Equation (7) generated using the MEP model, predicts the CS of nanoparticles and SCMs-based concrete grounded on 12 key inputs variables. Constructed using mathematical operators (+, −, ×, ÷, √, ˆ), the equation captures nonlinear relationships among the inputs. An accurate, concise, and interpretable depiction of the effect of nanoparticles and auxiliary materials on concrete strength is provided by this equation.

(7) C S = n T + n S + H W R − n S 2 C a 4 +   C a   O P C + F a − F a + C a + S l · H W R + W t + H W R − 2 C a 4 + 0.001   F A g + 0.001   C A g + 0.05   S f + 0.01   C T

Where, OPC: cement, Wt: water, FAg: fine aggregate, CAg: coarse aggregate, HWR: High range water reducer, Fa: fly ash, Sl: slag, Sf: silica fume, nT: nano-TiO2, nS: nano-SiO2, Ca: concrete age, CT: curing temperature, and CS: compressive strength.

There is a high degree of agreement between the experimental and MEP-predicted values for compressive strength (CS), as shown in Figure 9(a) scatter plot, which has an R2 value of 0.954. This outperforms the Genetic Expression Programming (GEP) model, which, under analogous circumstances, obtained a lower R2 value of 0.914. Figure 9(b) shows the errors, experimental and projected values plotted against each other, further demonstrating that the MEP model is accurate. Absolute errors from the model outcomes are shown in Figure 9(c). The small and stable absolute error and the high degree of congruence between predicted and observed values for all data points demonstrate the robustness of the model. Based on the data, we can see that the average error is a meager 4.60 MPa, with roughly 34 predictions having an error below 4 MPa, 23 falling within 4–8 MPa, and only 11 above 8 MPa. Taken together, our findings demonstrate that the MEP model outperforms the GEP model in terms of prediction accuracy and generalizability, giving credence to its use in determining the compressive strength of concrete including nanoparticles and SCMs.

Figure 9: Compressive strength modeling with MEP: (a) Predicted-observed correlation; (b) comparison of predicted results and corresponding error distribution; (c) absolute errors.
Figure 9:

Compressive strength modeling with MEP: (a) Predicted-observed correlation; (b) comparison of predicted results and corresponding error distribution; (c) absolute errors.

3.3 Accuracy assessment through statistical indicators

Table 3 presents the outcomes of the performance and error evaluations conducted using the earlier defined Equations (1)–(5). These evaluations encompass a range of statistical indicators, including RMSE, MAPE, MAE, NSE, and R, to comprehensively assess the prediction capabilities of the developed models. The statistical performance metrics provide a comparative evaluation of the GEP and MEP models for predicting the compressive strength of nanoparticles and SCMs-based concrete. Among the error-based metrics, both models demonstrate satisfactory accuracy; however, the MEP model consistently outperforms the GEP model, as reflected by lower RMSE (5.427 vs. 6.439 MPa), MAE (4.596 vs. 4.981 MPa), and MAPE (10.40 % vs. 12.20 %), indicating reduced prediction errors and improved reliability in capturing experimental variability. On the efficiency side, the MEP model also shows higher correlation with experimental results (R = 0.977 vs. 0.956) and superior predictive efficiency (NSE = 0.953 vs. 0.913), both of which are close to unity and confirm the robustness of the model. Collectively, these results confirm that the MEP model provides more accurate and efficient predictions compared to the GEP model, making it a more reliable approach for modeling compressive strength in advanced concrete systems. By comparing the built models’ correlation, standard deviation, and centered RMSE, the Taylor’s diagram (Figure 10) clearly depicts their statistical performance. In comparison to the GEP model, the MEP model shows better accuracy and predictive performance due to its tighter alignment with the reference point. Because of this, MEP is able to capture the data trend more efficiently than before. The results show that the MEP model is a better tool for sustainable material design and practical engineering applications because it provides a more precise framework for forecasting the CS of NSCs.

Table 3:

Performance metrics from statistical assessment.

Metric Unit GEP model MEP model
RMSE MPa 6.439 5.427
MAE MPa 4.981 4.596
R – 0.956 0.977
MAPE % 12.20 10.40
NSE – 0.913 0.953
Figure 10: Performance evaluation using taylor diagram.
Figure 10:

Performance evaluation using taylor diagram.

3.4 Partial dependence plots (PDPs)

Partial dependence plots (PDPs) are employed to interpret the marginal influence of key input features on the predicted compressive strength, providing insight into the model’s learned relationships beyond feature importance rankings [73]. PDPs of the most influential input parameters are shown in Figure 11. The PDP for Ca in Figure 11(a) (concrete age in days) reveals a clear positive relationship with CS. Initially, from 0 to around 100 days, CS increases rapidly, indicating active hydration and strength gain. Between 100 and 400 days, the growth continues but slows down, and beyond 400 days, CS plateaus, suggesting that the concrete has reached maturity and further aging yields minimal strength improvement. Similarly, the PDP for High Range Water Reducer (HWR) in Figure 11(b) shows that increasing HWR up to around 4 kg/m3 leads to a noticeable improvement in compressive strength. Beyond this point, the effect fluctuates slightly and then stabilizes after 8 kg/m3, indicating diminishing returns with higher dosages. Whereas, the partial dependence plot in Figure 11(c) for Coarse Aggregate content (CAg) in kg/m3 shows a complex, non-linear impact on compressive strength. CS is initially high around 750 kg/m3, drops sharply near 800 kg/m3, and remains low until about 1,100 kg/m3, after which it rises steeply again. This suggests that both low and high CAg levels may enhance strength, while mid-range values tend to reduce it. Moreover, Figure 11(d) shows that increasing water content (Wt) generally leads to a decrease in compressive strength, indicating that excess water negatively impacts concrete performance. Whereas, Figure 11(e) shows that OPC (cement content) has a strong positive effect on compressive strength, especially beyond 400 kg/m3, where CS rises sharply and then stabilizes near its peak as OPC approaches 600 kg/m3. Furthermore, the pattern observed in Figure 11(f) for slag content (Sl) reflects the material’s latent hydraulic properties. Initially, low slag levels (below 100 kg/m3) contribute little to compressive strength due to insufficient activation. However, once slag exceeds this threshold, it begins to react with calcium hydroxide from cement hydration, forming additional C–S–H gel, which significantly boosts strength. This explains the sharp rise in CS beyond 100 kg/m3, followed by stabilization as the reaction potential is maximized. Figure 11(g) shows that increasing fine aggregate content (FAg) up to around 700 kg/m3 improves compressive strength, but beyond this point, CS drops sharply and stabilizes at a lower level, suggesting that excess fine aggregate may weaken the concrete matrix. Prominently, Figure 11(h) shows that Nano-SiO2 (nS) content positively influences compressive strength up to around 10 kg/m3, after which the effect slightly dips near 20 kg/m3 and then stabilizes. This pattern suggests that optimal nS dosage enhances microstructure densification, but excessive amounts may lead to particle agglomeration, reducing efficiency. Only the top eight parameters are shown, as less influential variables produced negligible or flat PDPs, and the results confirm that binder composition and water balance are the primary factors governing strength development.

Figure 11: Partial dependence plots illustrating the individual effects of input features; (a) Ca; (b) HWR; (c) CAg; (d) Wt; (e) OPC; (f) Sl; (g) Fag; (h) nS.
Figure 11:

Partial dependence plots illustrating the individual effects of input features; (a) Ca; (b) HWR; (c) CAg; (d) Wt; (e) OPC; (f) Sl; (g) Fag; (h) nS.

3.5 Individual conditional expectation (ICE) plots

ICE plots in Figure 12(a–h) provide sample-level insights into how each input variable influences the predicted compressive strength, complementing PDPs by exposing heterogeneity across observations [74]. In Figure 12(a), increasing concrete age (Ca) consistently raises CS due to the continued hydration of cementitious compounds and the progressive formation of calcium silicate hydrate (C–S–H), which densifies the microstructure; beyond 400 days, strength stabilizes as hydration reaches completion [75]. Figure 12(b) shows that increasing High-Range Water Reducer (HWR) content up to around 4 kg/m3 enhances particle dispersion and workability, promoting better packing and reduced porosity; however, further addition shows minimal improvement, aligning with the saturation of fluidity effects [76]. The non-linear pattern of Coarse Aggregate (CAg) in Figure 12(c) indicates that excessive aggregate disrupts paste continuity and weakens the interfacial transition zone (ITZ), while optimal levels improve packing density and load transfer. Figure 12(d) reveals that increasing water content (Wt) leads to strength reduction, as higher water-to-binder ratios produce more capillary voids and a weaker paste–aggregate bond. In Figure 12(e), Ordinary Portland Cement (OPC) content exhibits a strong positive influence, especially beyond 400 kg/m3, owing to increased availability of reactive clinker phases (C3S and C2S) that accelerate hydration and microstructure refinement [77]. Figure 12(f) shows that slag (Sl) has little effect below 100 kg/m3 but significantly enhances strength thereafter through latent hydraulic reactions, consuming calcium hydroxide and forming secondary C–S–H that refines the pore network. In Figure 12(g), fine aggregate (FAg) initially improves strength up to around 700 kg/m3 by enhancing particle packing and reducing voids; beyond this point, excessive fines disrupt paste cohesion and increase surface area demand [78]. Finally, Figure 12(h) demonstrates that nano-silica (nS) enhances strength up to approximately 10 kg/m3 through its nucleation and filler effects, accelerating hydration and densifying the matrix, while higher contents may cause agglomeration and reduced dispersion efficiency. Overall, these ICE plots confirm that hydration kinetics, binder reactivity, and particle packing collectively govern the local and global strength behavior of nano- and SCM-modified concretes.

Figure 12: ICE plots illustrating the individual effects of input features: (a) Ca; (b) HWR; (c) CAg; (d) Wt; (e) OPC; (f) Sl; (g) Fag; (h) nS.
Figure 12:

ICE plots illustrating the individual effects of input features: (a) Ca; (b) HWR; (c) CAg; (d) Wt; (e) OPC; (f) Sl; (g) Fag; (h) nS.

4 Discussions

In order to predict and optimize the compressive strength (CS) of concrete including nanoparticles and SCMs, this study investigated the application of two cutting-edge machine learning algorithms: Gene Expression Programming (GEP) and Mutli Expression Programming (MEP). A robust dataset consisting of 206 data points was utilized for the purpose of building and training the models. Compressive strength was the only output variable in this dataset that consisted of 12 input factors culled from the available literature. R, RMSE, MAE, MAPE, and NSE metrics, in addition to Taylor’s diagram, were used to validate the model’s performance. Higher correlation coefficient (R = 0.977 vs. 0.956), decreased root-mean-squared error (RMSE) (5.427 MPa vs. 6.439 MPa), reduced mean absolute error (MAE) (4.596 MPa vs. 4.981 MPa), and enhanced mean absolute percentage of precision (MAPE) (10.40 % vs. 12.20 %) all indicate that the MEP model outperformed the GEP model in terms of prediction accuracy. The improved reliability of the MEP model was further confirmed by its higher NSE value (0.953 vs. 0.913). Concrete age, cement, slag, and nano-silica continuously increase compressive strength, while fine aggregate and excessive water decrease it. This information was uncovered through the use of Partial Dependence Plots (PDPs) and Individual Conditional Expectation (ICE) plots, which improved interpretability. ICE plots further expose sample-level variability and interaction effects, offering deeper interpretability than PDPs alone and highlighting the non-linear, instance-specific behavior of input features in the predictive model. These findings align with existing literature highlighting the superior robustness and adaptability of the MEP model over traditional approaches. Importantly, such predictive modeling supports the broader adoption of nanomaterials and supplementary cementitious materials (SCMs) in concrete, promoting sustainable construction through optimized mix designs and reliable performance forecasting.

Both MEP and GEP excel at handling complicated, nonlinear datasets without simplifying relationships. This makes them perfect for modeling complicated processes in heterogeneous materials, such as nanoparticles and SCMs-based concrete. Explicit mathematical formulations describing the link between input features and output are generated by evolutionary algorithms, which also provide great prediction accuracy. This makes them more transparent, interpretable, and practical in engineering design compared to many black-box ML models. Having said that, there are some significant drawbacks as well. Because little changes can have a large impact on the model’s accuracy, it is critical that the input units be consistent. The second issue is that models aren’t always robust to dataset changes; for example, adding new data or rebalancing old points might affect the resulting equations and predictions. Third, adjusting parameters, deciphering outcomes, and honing model architectures still necessitate domain knowledge and human supervision. The resultant equations may become unnecessarily big or nonlinear, diminishing their use, and overfitting can happen if the complexity of the model is not appropriately controlled. Improving performance and generalizability could be possible in future research by utilizing more contemporary AI or hybrid ML methods like deep learning or ensemble learning. The accuracy of the predictions might be much improved if the dataset had other variables such as curing conditions, temperature affects, and water absorption, as well as a wider range of mix designs. To have a better picture of how NSCs work and to make these prediction models more applicable, it would be wise to study additional important qualities such workability, thermal resistance, shrinkage, and durability. Moreover, Future research should extend beyond compressive strength prediction to include other key performance aspects of nanomaterial-enhanced concrete, such as durability, workability, thermal resistance, and shrinkage behavior. Investigating these properties will provide a more comprehensive understanding of nanomaterials’ multifunctional effects and further enhance the practical applicability of the developed predictive modeling framework.

5 Conclusions

Nanoparticle and SCM-based concrete compressive strength predictions were achieved in this study by utilizing Gene Expression Programming (GEP) and Model Expression Programming (MEP). An big dataset and a number of performance measures and interpretability tools were used to validate the modeling method. The following inferences are possible from the data:

  1. The MEP model proved its dependability in modeling complicated concrete systems by showing improved predicted accuracy for compressive strength with a R2 value of 0.954, which was much higher than the GEP model (R2 = 0.914).

  2. Based on the comparative performance metrics, the MEP model clearly outperforms the GEP model, achieving higher predictive accuracy (R = 0.977), lower error values (RMSE = 5.427 MPa, MAE = 4.596 MPa, MAPE = 10.40 %), and stronger reliability (NSE = 0.953). These results underscore MEP’s suitability for optimizing concrete mixes, especially those incorporating nanomaterials and SCMs for sustainable construction.

  3. Partial dependence plots revealed that features like concrete age, cement, slag, and nano-silica have a strong positive marginal effect on compressive strength, while excess water and fine aggregate content negatively impact it, guiding optimal mix design strategies.

  4. Individual conditional expectation plots revealed that while some features like concrete age and cement consistently enhance compressive strength, others such as slag and nano-silica exhibit varied effects across instances, emphasizing the need for customized mix designs when incorporating SCMs and nanomaterials in concrete.

Constraints on the study’s applicability include its narrow emphasis on compressive strength, its dependence on a single dataset, and its vulnerability to changes in the consistency of the input units. Future studies should investigate current or hybrid AI approaches, investigate additional mechanical and durability aspects, and increase the size of datasets in order to make models more applicable and generalizable.

Corresponding authors: Fahad Alsharari, Civil Engineering Department, Jouf University, Sakaka, Jouf, 72388, Saudi Arabia, E-mail: ; and Asad Naeem, Department of Structural Engineering, Military College of Engineering, National University of Sciences and Technology (NUST), Risalpur Campus, Risalpur, 24080, Pakistan, E-mail:

  1. Funding information: This work was funded by the Deanship of Graduate Studies and Scientific Research at Jouf University under grant No. (DGSSR-2025-02-01137).

  2. Author contributions: F.A.: conceptualization, funding acquisition, project administration, resources, supervision, writing, reviewing, and editing. R-U-D.N.: conceptualization, supervision, investigation, writing, reviewing, and editing. T.O.A.: data acquisition, formal analysis, methodology, visualization, writing, reviewing, and editing. A.N.: software, validation, investigation, formal analysis, writing-original draft. T.A.: resources, data acquisition, conceptualization, writing, reviewing, and editing. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflicts of interest: The authors state no conflict of interest.

  4. Data availability statement: The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.

References

1. Van Damme, H. Concrete material science: past, present, and future innovations. Cement Concr Res 2018;112:5–24. https://doi.org/10.1016/j.cemconres.2018.05.002.Search in Google Scholar

2. Ahmad, W, McCormack, SJ, Byrne, A. Biocomposites for sustainable construction: a review of material properties, applications, research gaps, and contribution to circular economy. J Build Eng 2025;105:112525. https://doi.org/10.1016/j.jobe.2025.112525.Search in Google Scholar

3. Bukhari, SJS, Khanzadeh Moradllo, M. Multicriteria performance assessment of ‘low w/c + low cement + high dosage admixture’ concrete: environmental, economic, durability, and mechanical performance considerations. J Clean Prod 2025;523:146419. https://doi.org/10.1016/j.jclepro.2025.146419.Search in Google Scholar

4. Bouchelil, L, Jafar, SBS, Khanzadeh Moradllo, M. Evaluating the performance of internally cured limestone calcined clay concrete mixtures. J Sustain Cement-Based Mater 2025;14:198–208. https://doi.org/10.1080/21650373.2024.2432002.Search in Google Scholar

5. Fahim, AA, Bukhari, SJS, Khanzadeh Moradllo, M. Additive manufacturing of carbonatable ternary cementitious systems with cellulose nanocrystals. Constr Build Mater 2025;495:143753. https://doi.org/10.1016/j.conbuildmat.2025.143753.Search in Google Scholar

6. Ahmed, W, Ye, C, Lu, G, Ng, ST, Liu, G, Wang, Y. Low-carbon concrete comprising high-volume pozzolan and recycled aggregate: evaluating mechanical performance, microstructure, environmental impact, and cost efficiency. J Clean Prod 2025;518:145796. https://doi.org/10.1016/j.jclepro.2025.145796.Search in Google Scholar

7. Hu, J, Ahmed, W, Jiao, D. A critical review of the technical characteristics of recycled brick powder and its influence on concrete properties. Buildings 2024;14:3691. https://doi.org/10.3390/buildings14113691.Search in Google Scholar

8. Song, Y, Xu, R, Hong, J, Zhou, Y, Shi, T, Wang, C, et al.. Preparation of a novel green lithium slag expansive agent: enhancing deformation control, crack resistance, and durability of mortar. Constr Build Mater 2025;495:143644. https://doi.org/10.1016/j.conbuildmat.2025.143644.Search in Google Scholar

9. Wei, X, Xie, S, Luo, A, Liu, Y, Li, Y, Wu, L. Performance improvement of ecologically friendly ultra-high performance concrete with waste tire recycled steel fiber. Constr Build Mater 2025;495:143607. https://doi.org/10.1016/j.conbuildmat.2025.143607.Search in Google Scholar

10. Zhou, X, Lu, D, Du, X, Wang, G, Meng, F. A 3D non-orthogonal plastic damage model for concrete. Comput Methods Appl Mech Eng 2020;360:112716. https://doi.org/10.1016/j.cma.2019.112716.Search in Google Scholar

11. Lothenbach, B, Scrivener, K, Hooton, RD. Supplementary cementitious materials. Cement Concr Res 2011;41:1244–56. https://doi.org/10.1016/j.cemconres.2010.12.001.Search in Google Scholar

12. Amran, M, Murali, G, Khalid, NHA, Fediuk, R, Ozbakkaloglu, T, Lee, YH, et al.. Slag uses in making an ecofriendly and sustainable concrete: a review. Constr Build Mater 2021;272:121942. https://doi.org/10.1016/j.conbuildmat.2020.121942.Search in Google Scholar

13. Awang, H, Aljoumaily, ZS. Influence of granulated blast furnace slag on mechanical properties of foam concrete. Cogent Eng 2017;4:1409853. https://doi.org/10.1080/23311916.2017.1409853.Search in Google Scholar

14. Goel, G, Sachdeva, P, Chaudhary, AK, Singh, Y. The use of nanomaterials in concrete: a review. Mater Today Proc 2022;69:365–71. https://doi.org/10.1016/j.matpr.2022.09.051.Search in Google Scholar

15. Mydin, MAO, Jagadesh, P, Bahrami, A, Dulaimi, A, Özkılıç, YO, Abdullah, MMAB, et al.. Use of calcium carbonate nanoparticles in production of nano-engineered foamed concrete. J Mater Res Technol 2023;26:4405–22. https://doi.org/10.1016/j.jmrt.2023.08.106.Search in Google Scholar

16. Huang, D. The impact of curing temperature on the hydration, microstructure, mechanical properties, and durability of nanomodified cementitious composites [Doctoral dissertation]. Indiana: Purdue University Graduate School; 2022.Search in Google Scholar

17. Meddah, MS, Praveenkumar, TR, Vijayalakshmi, MM, Manigandan, S, Arunachalam, R. Mechanical and microstructural characterization of rice husk ash and Al2O3 nanoparticles modified cement concrete. Constr Build Mater 2020;255:119358. https://doi.org/10.1016/j.conbuildmat.2020.119358.Search in Google Scholar

18. Ahmed, HU, Mohammed, AA, Mohammed, AS. Effectiveness of silicon dioxide nanoparticles (nano SiO2) on the internal structures, electrical conductivity, and elevated temperature behaviors of geopolymer concrete composites. J Inorg Organomet Polym Mater 2023;33:3894–914. https://doi.org/10.1007/s10904-023-02672-2.Search in Google Scholar

19. Moro, C, El Fil, H, Francioso, V, Velay-Lizancos, M. Influence of water-to-binder ratio on the optimum percentage of nano-TiO2 addition in terms of compressive strength of mortars: a laboratory and virtual experimental study based on ANN model. Constr Build Mater 2021;267:120960. https://doi.org/10.1016/j.conbuildmat.2020.120960.Search in Google Scholar

20. Huang, D, Velay-Lizancos, M, Olek, J. Scaling risk index of concretes containing Nano-TiO2 and supplementary cementitious materials. Transp Res Rec 2024;2678:148–61. https://doi.org/10.1177/03611981231178806.Search in Google Scholar

21. Mydin, MAO, Jagadesh, P, Bahrami, A, Dulaimi, A, Özkılıç, YO, Omar, R. Enhanced fresh and hardened properties of foamed concrete modified with nano-silica. Heliyon 2024;10.10.1016/j.heliyon.2024.e25858Search in Google Scholar PubMed PubMed Central

22. Abdel-Raheem, A, Dulaimi, A, Mohamed, AS, Moussa, GS, Özkılıç, YO, Mashaan, N, et al.. Investigating the potential of high-density polyethylene and nano clay asphalt-modified binders to enhance the rutting resistance of asphalt mixture. Sustainability 2023;15:13992. https://doi.org/10.3390/su151813992.Search in Google Scholar

23. Kaur, R, Kothiyal, NC. Synergic influence of fly ash and graphene oxide-carbon nanotubes hybrid on mechanical, microstructural and porosity properties of cement mortars. J Adhes Sci Technol 2021;35:1777–805. https://doi.org/10.1080/01694243.2020.1860548.Search in Google Scholar

24. Huang, D, Velay-Lizancos, M, Olek, J. The effects of curing temperature on the hydration kinetics of plain and fly ash pastes and compressive strength of corresponding mortars with and without nano-TiO2 addition. In: International Conference on Durability of Concrete Structures; 2022, vol 7. https://docs.lib.purdue.edu/icdcs/2022/partiv/7.Search in Google Scholar

25. Mohammed, A, Rafiq, S, Mahmood, W, Noaman, R, Ghafor, K, Qadir, W, et al.. Characterization and modeling the flow behavior and compression strength of the cement paste modified with silica nano-size at different temperature conditions. Constr Build Mater 2020;257:119590. https://doi.org/10.1016/j.conbuildmat.2020.119590.Search in Google Scholar

26. Ahmad, W, Veeraghantla, VSSCS, Byrne, A. Advancing sustainable concrete using biochar: experimental and modelling study for mechanical strength evaluation. Sustainability 2025;17:2516. https://doi.org/10.3390/su17062516.Search in Google Scholar

27. Alsharari, F, Iftikhar, B, Uddin, MA, Deifalla, AF. Data-driven strategy for evaluating the response of eco-friendly concrete at elevated temperatures for fire resistance construction. Results Eng 2023;20:101595. https://doi.org/10.1016/j.rineng.2023.101595.Search in Google Scholar

28. Mughees, A, Sharma, A, Ansari, SS, Ibrahim, SM. Prediction of the compressive strength of nano-titanium based concrete composites using machine learning. Mater Today Proc 2023. https://doi.org/10.1016/j.matpr.2023.03.540.Search in Google Scholar

29. Nazar, S, Yang, J, Ahmad, W, Javed, MF, Alabduljabbar, H, Deifalla, AF. Development of the new prediction models for the compressive strength of nanomodified concrete using novel machine learning techniques. Buildings 2022;12:2160. https://doi.org/10.3390/buildings12122160.Search in Google Scholar

30. Alsubai, S, Alqahtani, A, Hashim Muhodir, S, Alanazi, A, Ahmed, M, Jasim, DJ, et al.. The remarkable potential of machine learning algorithms in estimating water permeability of concrete incorporating nano natural pozzolana. Sci Rep 2024;14:12532. https://doi.org/10.1038/s41598-024-62020-3.Search in Google Scholar PubMed PubMed Central

31. Tran, VQ. Machine learning approach for investigating chloride diffusion coefficient of concrete containing supplementary cementitious materials. Constr Build Mater 2022;328:127103. https://doi.org/10.1016/j.conbuildmat.2022.127103.Search in Google Scholar

32. Alkharisi, MK, Dahish, HA, Youssf, O. Prediction models for the hybrid effect of nano materials on radiation shielding properties of concrete exposed to elevated temperatures. Case Stud Constr Mater 2024;21:e03750. https://doi.org/10.1016/j.cscm.2024.e03750.Search in Google Scholar

33. Salih, A, Rafiq, S, Mahmood, W, Al-Darkazali, H, Noaman, R, Ghafor, K, et al.. Systemic multi-scale approaches to predict the flowability at various temperature and mechanical properties of cement paste modified with nano-calcium carbonate. Constr Build Mater 2020;262:120777. https://doi.org/10.1016/j.conbuildmat.2020.120777.Search in Google Scholar

34. Yang, H, Li, S, Shu, J, Yu, H, Liu, H, Xu, Y, et al.. Data-driven high-resolution total focus imaging from array ultrasonic time-domain signals of reinforced concrete material. Constr Build Mater 2025;492:143048. https://doi.org/10.1016/j.conbuildmat.2025.143048.Search in Google Scholar

35. Alghrairi, NS, Aziz, FN, Rashid, SA, Mohamed, MZ, Ibrahim, AM. Machine learning-based compressive strength estimation in nanomaterial-modified lightweight concrete. Open Eng 2024;14:20220604. https://doi.org/10.1515/eng-2022-0604.Search in Google Scholar

36. Jin, L, Duan, J, Jin, Y, Xue, P, Zhou, P. Prediction of HPC compressive strength based on machine learning. Sci Rep 2024;14:16776. https://doi.org/10.1038/s41598-024-67850-9.Search in Google Scholar PubMed PubMed Central

37. Tran, VQ, Dang, VQ, Ho, LS. Evaluating compressive strength of concrete made with recycled concrete aggregates using machine learning approach. Constr Build Mater 2022;323:126578. https://doi.org/10.1016/j.conbuildmat.2022.126578.Search in Google Scholar

38. Alahmari, TS, Arif, K. Machine learning approaches to predict the strength of graphene nanoplatelets concrete: optimization and hyper tuning with graphical user interface. Mater Today Commun 2024;40:109946. https://doi.org/10.1016/j.mtcomm.2024.109946.Search in Google Scholar

39. Jiao, H, Wang, Y, Li, L, Arif, K, Farooq, F, Alaskar, A. A novel approach in forecasting compressive strength of concrete with carbon nanotubes as nanomaterials. Mater Today Commun 2023;35:106335. https://doi.org/10.1016/j.mtcomm.2023.106335.Search in Google Scholar

40. Yang, G, Zhao, H, Hu, Z, Zhang, W, Xiang, Y, Jin, M, et al.. Prediction of restrained stress for UHPC: considering relationship between long-term and in-situ creep. Constr Build Mater 2025;484:141722. https://doi.org/10.1016/j.conbuildmat.2025.141722.Search in Google Scholar

41. Yu, H, Zhao, Z, Taleghani, AD, Lian, Z, Zhang, Q. Modeling thermal-induced wellhead growth through the lifecycle of a well. Geoenergy Sci Eng 2024;241:213098. https://doi.org/10.1016/j.geoen.2024.213098.Search in Google Scholar

42. Ren, D, Wang, C, Wei, X, Zhang, Y, Han, S, Xu, W. Harmonizing physical and deep learning modeling: a computationally efficient and interpretable approach for property prediction. Scr Mater 2025;255:116350. https://doi.org/10.1016/j.scriptamat.2024.116350.Search in Google Scholar

43. Niu, Y, Wang, W, Su, Y, Jia, F, Long, X. Plastic damage prediction of concrete under compression based on deep learning. Acta Mech 2024;235:255–66. https://doi.org/10.1007/s00707-023-03743-8.Search in Google Scholar

44. Hao, WQ, Shi, DQ, Yang, XG, Li, NN, Su, S, Fan, YS. Multi-mode fatigue life prediction using machine learning inspired by damage physics. Int J Mech Sci 2025;304:110723. https://doi.org/10.1016/j.ijmecsci.2025.110723.Search in Google Scholar

45. Sun, L, Wang, X, Zhang, C. Three-dimensional high fidelity mesoscale rapid modelling algorithm for concrete. In: Structures. Amsterdam: Elsevier; 2024, vol 70:107561 p.10.1016/j.istruc.2024.107561Search in Google Scholar

46. Hu, D, Liu, J, Li, Y, Tan, Z. Prediction method of ground settlement for rectangular tunnel construction. Tunn Undergr Space Technol 2025;164:106814. https://doi.org/10.1016/j.tust.2025.106814.Search in Google Scholar

47. Inqiad, WB, Siddique, MS, Alarifi, SS, Butt, MJ, Najeh, T, Gamil, Y. Comparative analysis of various machine learning algorithms to predict 28-day compressive strength of self-compacting concrete. Heliyon 2023;9:e22036. https://doi.org/10.1016/j.heliyon.2023.e22036.Search in Google Scholar PubMed PubMed Central

48. Palla, R, Karade, SR, Mishra, G, Sharma, U, Singh, LP. High strength sustainable concrete using silica nanoparticles. Constr Build Mater 2017;138:285–95. https://doi.org/10.1016/j.conbuildmat.2017.01.129.Search in Google Scholar

49. Zhang, MH, Islam, J. Use of nano-silica to reduce setting time and increase early strength of concretes with high volumes of fly ash or slag. Constr Build Mater 2012;29:573–80. https://doi.org/10.1016/j.conbuildmat.2011.11.013.Search in Google Scholar

50. Ji, T. Preliminary study on the water permeability and microstructure of concrete incorporating nano-SiO2. Cement Concr Res 2005;35:1943–7. https://doi.org/10.1016/j.cemconres.2005.07.004.Search in Google Scholar

51. Li, G. Properties of high-volume fly ash concrete incorporating nano-SiO2. Cement Concr Res 2004;34:1043–9. https://doi.org/10.1016/j.cemconres.2003.11.013.Search in Google Scholar

52. Huang, D, Velay-Lizancos, M, Olek, J. Improving scaling resistance of pavement concrete using titanium dioxide (TiO2) and nanosilica. Washington: Purdue University. Joint Transportation Research Program; 2022.10.5703/1288284317583Search in Google Scholar

53. Sharaky, IA, Megahed, FA, Seleem, MH, Badawy, AM. The influence of silica fume, nano silica and mixing method on the strength and durability of concrete. SN Appl Sci 2019;1:575. https://doi.org/10.1007/s42452-019-0621-2.Search in Google Scholar

54. Zhang, M-h., Li, H. Pore structure and chloride permeability of concrete containing nano-particles for pavement. Constr Build Mater 2011;25:608–16. https://doi.org/10.1016/j.conbuildmat.2010.07.032.Search in Google Scholar

55. Du, H, Du, S, Liu, X. Durability performances of concrete with nano-silica. Constr Build Mater 2014;73:705–12. https://doi.org/10.1016/j.conbuildmat.2014.10.014.Search in Google Scholar

56. Said, AM, Zeidan, MS, Bassuoni, MT, Tian, Y. Properties of concrete incorporating nano-silica. Constr Build Mater 2012;36:838–44. https://doi.org/10.1016/j.conbuildmat.2012.06.044.Search in Google Scholar

57. Kumar, GV, Kumar, BN. Effect on mechanical, durability and micro structural properties of high strength self compacting concrete with inclusion of micro and nano silica. Mater Today Proc 60;2022:569–75. https://doi.org/10.1016/j.matpr.2022.02.064.Search in Google Scholar

58. Amin, MN, Al-Naghi, AAA, Nassar, R-U-D, Algassem, O, Khan, SA, Deifalla, AF. Investigating the rheological characteristics of alkali-activated concrete using contemporary artificial intelligence approaches. Rev Adv Mater Sci 2024;63:20240006. https://doi.org/10.1515/rams-2024-0006.Search in Google Scholar

59. Ilyas, I, Zafar, A, Afzal, M, Javed, M, Alrowais, R, Althoey, F, et al.. Advanced machine learning modeling approach for prediction of compressive strength of FRP confined concrete using multiphysics genetic expression programming. Polymers 2022;14:1789. https://doi.org/10.3390/polym14091789.Search in Google Scholar PubMed PubMed Central

60. Mishra, S, Mallick, PK, Jena, L, Chae, GS. Optimization of skewed data using sampling-based preprocessing approach. Front Public Health 2020;8:274. https://doi.org/10.3389/fpubh.2020.00274.Search in Google Scholar PubMed PubMed Central

61. Li, Z, Gao, X, Lu, D. Correlation analysis and statistical assessment of early hydration characteristics and compressive strength for multi-composite cement paste. Constr Build Mater 2021;310:125260. https://doi.org/10.1016/j.conbuildmat.2021.125260.Search in Google Scholar

62. Lee, BC, Brooks, DM. Accurate and efficient regression modeling for microarchitectural performance and power prediction. ACM SIGOPS – Oper Syst Rev 2006;40:185–94.10.1145/1168917.1168881Search in Google Scholar

63. Iftikhar, B, Alih, SC, Vafaei, M, Alkhattabi, L, Althoey, F, Ali, M, et al.. Sustainable use of plastic waste in plastic sand paver blocks: an experimental and modelling-based study. Structures 2024;62:106285. https://doi.org/10.1016/j.istruc.2024.106285.Search in Google Scholar

64. Liu, H, Khan, SA, Amin, MN, Althoey, F, Qadir, MT. Evaluating the strength loss and the effectiveness of glass and eggshell powder for cement mortar under acidic conditions. Rev Adv Mater Sci 2024;63:20240042. https://doi.org/10.1515/rams-2024-0042.Search in Google Scholar

65. Khawaja, L, Javed, MF, Asif, U, Alkhattabi, L, Ahmed, B, Alabduljabbar, H. Indirect estimation of resilient modulus (Mr) of subgrade soil: gene expression programming vs multi expression programming. In: Structures. Amsterdam: Elsevier; 2024, vol 66:106837 p.10.1016/j.istruc.2024.106837Search in Google Scholar

66. Nematzadeh, M, Shahmansouri, AA, Fakoor, M. Post-fire compressive strength of recycled PET aggregate concrete reinforced with steel fibers: optimization and prediction via RSM and GEP. Constr Build Mater 2020;252:119057. https://doi.org/10.1016/j.conbuildmat.2020.119057.Search in Google Scholar

67. Amin, MN, Ahmad, W, Khan, K, Deifalla, AF. Optimizing compressive strength prediction models for rice husk ash concrete with evolutionary machine intelligence techniques. Case Stud Constr Mater 2023;18:e02102. https://doi.org/10.1016/j.cscm.2023.e02102.Search in Google Scholar

68. Guan, QT, Tong, ZL, Amin, MN, Iftikhar, B, Qadir, MT, Khan, K. Analyzing the efficacy of waste marble and glass powder for the compressive strength of self-compacting concrete using machine learning strategies. Rev Adv Mater Sci 2024;63:20240043. https://doi.org/10.1515/rams-2024-0043.Search in Google Scholar

69. Rostami, A, Raef, A, Kamari, A, Totten, MW, Abdelwahhab, M, Panacharoensawad, E. Rigorous framework determining residual gas saturations during spontaneous and forced imbibition using gene expression programming. J Nat Gas Sci Eng 2020;84:103644. https://doi.org/10.1016/j.jngse.2020.103644.Search in Google Scholar

70. Gandomi, AH, Roke, DA. Assessment of artificial neural network and genetic programming as predictive tools. Adv Eng Software 2015;88:63–72. https://doi.org/10.1016/j.advengsoft.2015.05.007.Search in Google Scholar

71. Band, SS, Heggy, E, Bateni, SM, Karami, H, Rabiee, M, Samadianfard, S, et al.. Groundwater level prediction in arid areas using wavelet analysis and Gaussian process regression. Eng Appl Comput Fluid Mech 2021;15:1147–58. https://doi.org/10.1080/19942060.2021.1944913.Search in Google Scholar

72. Taylor, KE. Summarizing multiple aspects of model performance in a single diagram. J of Geophys Res atmospheres 2001;106:7183–92. https://doi.org/10.1029/2000jd900719.Search in Google Scholar

73. Molnar, C, Freiesleben, T, König, G, Herbinger, J, Reisinger, T, Casalicchio, G, et al.. Relating the partial dependence plot and permutation feature importance to the data generating process. In: World Conference on Explainable Artificial Intelligence. Switzerland: Springer Nature; 2023, vol 1901:456–79 pp.10.1007/978-3-031-44064-9_24Search in Google Scholar

74. Goldstein, A, Kapelner, A, Bleich, J, Pitkin, E. Peeking inside the Black box: visualizing statistical learning with plots of individual conditional expectation. J Comput Graph Stat 2015;24:44–65. https://doi.org/10.1080/10618600.2014.907095.Search in Google Scholar

75. Ranjan, M, Kumar, S, Sinha, S. Nanosilica’s influence on concrete hydration, microstructure, and durability: a review. J Appl Eng Sci 2024;14:322–35. https://doi.org/10.2478/jaes-2024-0040.Search in Google Scholar

76. Kılıç, İ, Gök, SG. Investigation of the efficiency of ultra high range water reducing admixture in roller compacted concrete production. Sak Univ J Sci 2022;26:203–12.10.16984/saufenbilder.974399Search in Google Scholar

77. Kim, WW, Moon, JH. Analysis of mechanical properties and microstructure of nano-and micro-SiO2 materials as cementitious composite binder. Int J Concr Struct Mater 2023;17:68. https://doi.org/10.1186/s40069-023-00629-w.Search in Google Scholar

78. Ye, Z, Qu, X, Li, J, Ye, T, Li, G, Wang, H. Experimental investigation of the effect of nano silica fume on durability of concrete with close-packing aggregate. Materials 2025;18:4061. https://doi.org/10.3390/ma18174061.Search in Google Scholar PubMed PubMed Central

Received: 2025-09-30
Accepted: 2025-11-05
Published Online: 2026-02-04

© 2026 the author(s), published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/rams-2025-0182
Keywords for this article
nanomaterials-modified concrete; nano-TiO2 and nano-SiO2; compressive strength modeling
Creative Commons
BY 4.0

Articles in the same Issue

  1. Research Articles
  2. A green and sustainable biocomposite materials: environmentally robust, high performance, low-cost materials for helicopter lighter structures
  3. Microstructural and UCS behavior of clay soils stabilized with hybrid nano-enhanced additives
  4. Optimization of microstructure and mechanical properties of microwave-sintered V/Ta/Re-doped tungsten heavy alloys
  5. Experimental and numerical study on the axial compression behavior of circular concrete columns confined by BFRP spirals and ties
  6. Effect of A-site calcium substitution on the energy storage and dielectric properties of ferroelectric barium titanate system
  7. Comparative analysis of aggregate gradation variation in porous asphalt mixtures under different compaction methods1
  8. Thermal and mechanical properties of bricks with integrated phase change and thermal insulation materials
  9. Nonlinear molecular weight dependency in polystyrene and its nanocomposites: deciphering anomalous gas permeation selectivity in water vapor-oxygen-hydrogen barrier systems
  10. ZnO nanophotocatalytic solution with antimicrobial potential toward drug-resistant microorganisms and effective decomposition of natural organic matter under UV light
  11. Predicting fracture energy and durability parameters of concrete through hybrid machine learning models
  12. α-hemihydrate gypsum crystal concerning the anionic surfactants with vary chain structure: syntheses, morphology controlling, formation mechanisms
  13. Advanced machine learning-driven prediction in construction materials: comparative analysis and software implementation for fiber-reinforced graphene nano-engineered concrete
  14. Innovative development of self-healing high-strength concrete using a polymeric air-entraining agent and Bacillus sphaericus: durability performance in aggressive saline environments
  15. Influence of welding speed on the microstructure and mechanical properties of CMT+P WAAM-based 205C aluminum alloy
  16. EcoMarble: macro-performance and carbon footprint optimization of concrete using cement-substituted Al-Kharj marble dust
  17. Predicting properties of lightweight strain-hardening ultra-high-performance concrete using smart hybrid AI-based framework
  18. Microstructural evolution and dry sliding wear behavior of composite shear flow casting M50 steel under different tempering conditions
  19. Long-term durability and microstructure of advanced high-performance concrete with cement kiln dust, boiler slag and PP fibers: flexural response and sustainability assessment
  20. Development of lightweight roof tiles using spent mushroom material: enhancing thermal insulation and sustainability
  21. Tailoring rheology and mechanical properties of 3D printed mortars with nanoclays and superplasticizer
  22. Review Articles
  23. Granite powder in concrete: a review on durability and microstructural properties
  24. Properties and applications of warm mix asphalt in the road construction industry: a comprehensive review and insights toward facilitating large-scale adoption
  25. Artificial Intelligence in the synthesis and application of advanced dental biomaterials: a narrative review of probabilities and challenges
  26. Recycled tire rubber as a fine aggregate replacement in sustainable concrete: a comprehensive review
  27. Performance evaluation of blended cement mortar with supplementary cementitious materials: from pozzolans to industrial wastes
  28. A review on rutting in asphalt concrete in Saudi Arabia: mitigation strategies, innovations, and future directions
  29. Rapid Communication
  30. Recent advances in resistive strain sensors: from materials and fabrication to applications in plant wearables
  31. Special Issue on AI-Driven Advances for Nano-Enhanced Sustainable Construction Materials - Part II
  32. Sustainable approach to control autogenous shrinkage in low water–cement ratio concretes
  33. Use of explainable symbolic regression approaches for predicting nanomaterial-enhanced concrete performance
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