Approximate solution of Hamiltonian systems

In this study, ordinary differential equations explaining the time dependent variation of simple mechanical systems are solved using deep learning methods. In the first part of the thesis, which consists of five parts, the historical development of the subject is expressed and the purpose of the study is explained. In the second part, the basic concepts in the study are explained. Then, the solution of differential equations with artificial neural networks is examined. In part 4, Hamilton systems and Symplectic transformations are explained. In the study, an approach to the solution with data driven artificial neural networks is provided by increasing the data points obtained by solving with an iterative method such as Symplectic Euler, Verlet for simple Hamiltonian systems and using the energy-conserving loss function. In the 5. chapter, the proposed method is applied to simple harmonic oscillator, nonlinear oscillator and Lotka-Volterra equation and compared with iterative methods.