# Machine Learning for the Prediction of Thermodynamic Properties in Amorphous Silicon
## 5 Conclusions  
This study successfully integrated molecular dynamics (MD) simulations with machine learning techniques, specifically Linear, Ridge, and Support Vector Regression, to model and predict the thermodynamic properties of amorphous silicon (a-Si). The MD simulations provided a comprehensive dataset that captured the atomic-level behavior of a-Si under varying thermodynamic conditions. By leveraging this data, this study explored how the cooling rate (\(R_{c}\)), temperature (\(T\)), and pressure (\(P\)) influenced the material's density (\(\rho\)), internal energy (\(U\)), and enthalpy (\(H\)). Key findings indicate that while the cooling rate had a minor influence, the temperature and pressure significantly affected the thermodynamic state of the a-Si, which is critical for understanding its behavior in applications such as materials processing and device fabrication.  
The combination of MD simulations and machine learning models demonstrated exceptional predictive accuracy, with \(R^{2}\) values that exceeded 0.95 and minimal root-mean-square errors. The ability to generate isobaric and isothermal curves using the models provided valuable insights into the thermodynamic behavior of the a-Si, which complemented traditional MD simulations by offering a more efficient and systematic approach to exploring its properties. These models allowed for a deeper understanding of the relationships between thermodynamic variables by revealing how changes in the temperature and pressure impacted the material's internal dynamics and phase behavior.  
Looking forward, the integration of machine learning with MD simulations holds significant promise for expanding the study of thermodynamic properties to a wide range of materials. As the field advances, further refinement of the models, including the addition of new structural descriptors and the use of more advanced machine learning techniques, could enhance the predictive accuracy and drive innovation in materials science, particularly for high-performance applications in electronics, coatings, and structural components.  
The following supporting information can be downloaded from [[https://www.mdpi.com/article/10.3390/app15105574/s1--Table](https://www.mdpi.com/article/10.3390/app15105574/s1--Table)]([https://www.mdpi.com/article/10.3390/app15105574/s1--Table](https://www.mdpi.com/article/10.3390/app15105574/s1--Table)) S1: Hyperparameters for the Ridge regression; Table S2: Hyperparameters for the Support Vector Regression; Figure S1: Coefficient of determination for the prediction of density; Figure S2: Coefficient of determination for the prediction of internal energy; Figure S3: Coefficient of determination for the prediction of enthalpy; Figure S4: Relationship between predicted and actual values for Lasso and Elastic Net methods.  
This project was supported by the Competition for Research Regular Projects, year 2023, code LPR23-05, Universidad Tecnologica Metropolitana. Powered@NLHPC: This research was partially supported by the supercomputing infrastructure of the NLHPC (ECM-02).  
Not applicable.  
The data that support the findings of this study are available upon reasonable request from the authors.  
The authors declare no conflicts of interest.