# Machine Learning for the Prediction of Thermodynamic Properties in Amorphous Silicon
## 1 Introduction  
Amorphous silicon (a-Si) is a non-crystalline form of silicon that plays a critical role in various technological applications, including thin-film solar cells, flat-panel displays, and photodetectors [1, 2, 3]. Its disordered atomic structure endows it with unique electronic and optical properties, making it particularly suitable for devices requiring tunable bandgaps and high absorption coefficients [4, 5]. Furthermore, understanding the properties of a-Si is essential for optimizing its performance and stability under different processing and operational conditions. However, accurately predicting these properties remains challenging due to the complex atomic dynamics inherent to amorphous materials. Molecular dynamics (MD) simulations serve as a valuable tool for exploring a-Si without incurring costly experiments. Various studies have focused on this approach, including thermal conductivity [6], Li-ion diffusion [7], oxidation rates [8], structure and stress during lithiation [9], deformation mechanisms in nanoporous a-Si [10], structural dynamics [11], and the exploration of tension-compression [12], among many others [12, 13, 14]. While MD simulations provide accurate, atomistic-level insights, they are time-consuming, especially for large systems or long simulation timescales. In this context, machine learning (ML) has emerged as a promising tool for predicting material properties. ML algorithms canefficiently identify complex patterns and relationships within vast datasets, enabling the rapid prediction of material behavior under diverse conditions. Although ML models require training on a previously constructed dataset, once trained, they can make rapid predictions across a wide range of conditions without the need for extensive computational resources. This capability significantly reduces the computational cost and time associated with traditional MD simulations, allowing researchers to explore larger parameter spaces and accelerate materials design. Researchers have developed supervised learning models for predicting the yield stress of high-entropy alloys [15], the Young's moduli and ultimate tensile strengths of nanocomposites [16], the mechanical properties of metallic glasses [17], and nanoparticle magnetization [18], among others. Physics-informed machine learning has also emerged as a promising approach to overcome the limitations of traditional numerical methods, such as finite element methods, by integrating physical laws with neural networks, enabling the efficient modeling of complex, high-dimensional, and noisy scientific problems [19,20]. In the case of a-Si, the literature is more limited. While there are some studies that have used ML-based interatomic potentials to model a-Si and for phase recognition [21, 22, 23], no studies have been conducted to date on predicting the properties of a-Si. The integration of ML models with MD simulations offers a powerful hybrid approach, leveraging the accuracy of atomistic simulations with the speed and scalability of data-driven methods, opening new avenues for materials discovery and optimization. To bridge this gap, 150 MD simulations were performed to calculate the thermodynamic properties of a-Si under different conditions. The resulting data were used to construct a dataset for property prediction using classical regression models. Specifically, the cooling rate, temperature, and pressure served as predictors, while the density, internal energy, and enthalpy were the target variables in the regression models. The models' effectiveness was demonstrated by analyzing the relationships between these variables across various thermodynamic conditions. This approach not only provided a comprehensive understanding of the impact of these parameters on the thermodynamic behavior of a-Si, but also enabled the identification of trends and anomalies that would be challenging to capture through MD simulations alone.