# Research Progress on Machine Learning Prediction of Compressive Strength of Nano-Modified Concrete
## 4 The Application of Machine Learning in Nano-Modified Concrete
### Artificial Neural Network (ANN) Algorithm  
Artificial Neural Networks have the advantage of high parallel distributed processing capability, distributed storage and learning capability, ability to adequately approximate complex nonlinear relationships, associative memory capabilities, and so on. The input layer receives characteristic parameters such as nanomaterial dosage and water-cement ratio, the hidden layer implements nonlinear mapping through activation functions, and the output layer generates a predicted value of compressive strength. This hierarchical information processing mode is similar to the hierarchical response mechanism of cerebral cortical neurons, but focuses more on mathematical modeling rather than biological mechanism reproduction. As demonstrated by [PERSON] et al., the ANN model with a network structure (three hidden layers, 12 neurons per layer) effectively captured the nonlinear relationship between nano-TiO\({}_{2}\) dosage (0-2%) and compressive strength, achieving an R\({}^{2}\) of 0.94. This validated the ANN's capability in characterizing the interfacial effects of nanomaterials. [PERSON] et al. [52] conducted a study to establish accurate correlations between input and output variables of concrete mixes by employing various AI methods. The three AI methods used in this study were ANN, SVM, and Linear Regression (LR). The effectiveness of the models was evaluated through a sample dataset of 1030 concrete compressive strength tests conducted at the University of California, Irvine. Simulation results show that these AI methods can build reliable predictive models and reduce expensive and time-consuming laboratory tests. [PERSON] et al. [22] used ANN and integration methods to combine individual learners to form a powerful learner. The overall accuracy was improved by incorporating the weak learner with the smallest prediction error and the strongest correlation. As shown in Figure 11, the integrated ANN model achieved a prediction error (MAE = 1.2 MPa) for nano-SiO\({}_{2}\) cement paste that was 58% lower than that of the single model, demonstrating the advantage of feature cross-interaction in capturing the interfacial transition zone (ITZ) effects between nanoparticles and cement. Figure 11 explains the significantly lower error of the ANN-based integration model showing its superiority in predicting the properties of nano-silica cement paste. The ANN models presented in Figure 11 reflect different structures and training strategies used in previous studies. Some adopt conventional feedforward neural networks, while others incorporate optimization techniques such as genetic algorithms (GA-ANN) or particle swarm optimization (PSO \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ML Method** & **Input** & **Dataset Size** & **Best R\({}^{2}\)/MAE** & **Key References** \\ \hline ANN & Nano-SiO\({}_{2}\) dosage, W/C, curing time & 0–1030 & R\({}^{2}\) = 0.94, MAE = 1.2 MPa & [21; 22; 52] \\ SVM & Cement, aggregate, nano-additives, age & 100–500 & R\({}^{2}\) = 0.88–0.92 & [24; 31; 38] \\ RF & Similarly to SVM + feature importance & 1000+ & R\({}^{2}\) = 0.93–0.97 & [22; 23] \\ GEP & CNT, NS, NC, MS, porosity & 200–500 & Good trend fitting, empirical expression & [24; 26] \\ KNN & Nano-SiO\({}_{2}\) \%, specific surface area & \textless{}500 & MAE = 2.8 MPa (k = 5) & [42] \\ DT & Nano-CaCO\({}_{3}\) dosage, temperature & \textless{} R\({}^{2}\) = 0.72–0.89 & [23; 53] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of machine learning models used for predicting compressive strength of nano-modified concrete. ANN) to improve performance. These variations lead to differences in predictive accuracy and model stability. [PERSON] et al.