# Methodology for the Prediction of the Thermal Conductivity of Concrete by Using Neural Networks
## 5 Conclusions  
This study proposed a comprehensive methodology using deep neural networks. In the initial phase, various architectures of a Multilayer Perceptron were explored, and the most effective one was selected for an in-depth case study. Subsequently, we introduced a Generative Adversarial Network to create synthetic datasets, facilitating the training of the Multilayer Perceptron with both real and synthetic data. The application of this methodology was specifically demonstrated in the context of concrete mixtures. The dataset was meticulously gathered from published papers. For a comprehensive evaluation of the case study, we compared and assessed three distinct scenarios: (a) training the MLP exclusively with the real database, (b) training the MLP with 200 synthetic data points followed by real data, and (c) training the MLP with 1000 synthetic data points followed by real data. The outcomes across all three scenarios demonstrated satisfactory and highly accurate predictions of concrete thermal conductivity. Notably, including synthetic data in the training process led to a remarkable enhancement in accuracy and a significant reduction in errors within the test dataset, which underscores the effectiveness of the CopulaGAN synthesizer in generating synthetic data and the efficiency of MLP training with a combined dataset. The evaluation of these scenarios utilized the performance metrics RMSE and R\({}^{2}\), yielding the following values for each scenario: scenario (a)--0.0581 and 0.9858; scenario (b)--0.0394 and 0.9935; and scenario (c)--0.0314 and 0.9959, respectively. This study aimed to develop a methodology for predicting the thermal properties of concrete using artificial neural networks. Our specific focus was to demonstrate the feasibility of forecasting concrete's thermal conductivity based on its constituents' mass composition. Additionally, we sought to show the benefits of integrating a Generative Adversarial Network for data augmentation. The implications of this study can offer insights that can be applied to the development and enhancement of prediction models using deep learning for other materials. One notable impact lies in advancing the field of energy efficiency in buildings, providing decision-makers and manufacturers with advanced knowledge of a building material's thermal properties. While this work has made valuable contributions, it is essential to acknowledge certain limitations. Notably, this study could be enhanced by including other influential input variables, such as temperature, aggregate types, and mineralogy, and by expanding the real dataset to improve predictions across a broader range of thermal conductivity values. Besides this, although the results are promising, we agree that additional validation using independent datasets would further strengthen the reliability of our findings. Future work will focus on validating the model using experimental setups to further ensure its generalizability and accuracy. Moreover, future research studies could explore the application of this methodology to other composite materials and consider the inclusion of additional information, such as mechanical properties. An additional option is to explore specific heat as an output variable, a fundamental property in transient conditions, complementing the importance of thermal conductivity in stationary scenarios. This way, we can understand how different materials behave and make the predictions even more accurate. This work underscores the importance of training models with sufficiently diverse datasets to ensure accuracy, and it highlights the potential of synthetic data to augment training when faced with a scarcity of real data. The authors confirm contributions to the paper as follows: study conceptualization and methodology: C.M., A.C. and D.B. ; data collection, software validation, analysis, and interpretation of results: A.C.R. and Y.E. ; original draft preparation: A.C.R. ; writing, reviewing, and editing: A.C.R., A.C. and D.B.