Machine learning is a subset of computer science and studies algorithms whose performance improves with data (through experience). Machine learning can be defined as solving a scientific problem by gathering data sets and constructing a statistical model based on that data set. Machine learning is found abundant in everyday life such as data mining, robot control, handwriting recognition, pattern recognition (e.g. fingerprint identification), character and voice recognition software and etc. The potential energy surface is a valuable multidimensional function, which represents the potential energy of a system as a function of atomic positions. The concept of potential energy surface is based on the Born-Oppenheimer approximation. Recent advances in machine learning have now introduced an alternative method of estimating potential energy surface instead of electronic structure calculations, which is much faster and more accurate, so computational costs are reduced. In this thesis, we decide to present a general machine learning-based attitude in which we predict the formation energy of silicon clusters. For this purpose, first, atomic positions with appropriate descriptors should be presented to the machine learning algorithm. The descriptor converts the input information of the atomic structure into machine-understandable language. we used the QMML computational package For this project. This computation package includes the Column Matrix descriptor and the Many-Body Tensor descriptor. Gaussian approximation potential is an important method of potential based on machine learning that is based on the kernel that obtained by combining a suitable structural descriptor and a kernel to create a relationship between structure and energy. In this project, we used both the Laplacian and Gaussian kernels and made good predictions on silicon clusters.