Comprehensive framework of machine learning and deep learning architectures with metaheuristic optimization for high-fidelity prediction of nanofluid specific heat capacity.

Accurately predicting the specific heat capacity of nanofluids is critical for optimizing their performance in engineering and industrial applications. This study explores twelve machine learning and deep learning models using conventional and stacking ensemble techniques. In the stacking framework, a linear regression model is employed as a meta-learner to improve base model performance. Additionally, two nature-inspired metaheuristic optimization algorithms-Particle Swarm Optimization and Grey Wolf Optimization-were used to fine-tune the hyperparameters of machine learning models. This research is based on a comprehensive dataset of 1,269 experimental nanofluid samples, with key inputs including nanofluid type (hybrid and direct), temperature, and volume concentration. To improve model generalization, data augmentation strategies inspired by polynomial/Fourier expansions and autoencoder-based methods were implemented. The results demonstrate that the stacked multi-layer perceptron model, integrated with linear regression, achieved the highest predictive accuracy, recording an R² score of 0.99927, a mean squared error of 466.06, and a root mean squared error of 21.58. Among standalone machine learning models, CatBoost was the best performer (R² score: 0.99923, MSE: 487.71, RMSE: 22.08), ranking second overall. The impact of metaheuristic optimization was significant; Grey Wolf Optimization, for instance, reduced the LightGBM model's mean squared error from 29386.43 to 6549.006. These findings underscore the efficacy of hybrid ML/DL frameworks, advanced data augmentation, and metaheuristic optimization in predictive modeling of nanofluid thermophysical properties, providing a robust foundation for future research in heat transfer applications.