Research on Solving Damped Oscillation Systems using Physics-Informed Neural Networks

In recent years, physics-informed neural networks (PINNs) have gained significant attention for solving data-driven solvers for ordinary and partial differential equations (ODEs/PDEs). Traditional numerical methods often face limitations when dealing with complex boundary conditions and high-dimensional problems. PINNs address these challenges by embedding the constraints of physical equations directly into the loss function of the neural network, offering a more effective solution. The damped oscillation system, a physical system where internal resistance gradually diminishes the vibration, has widespread applications in engineering, physics, and many other fields. Traditional numerical methods for solving these equations typically require mesh discretization and complex boundary condition handling. In contrast, PINNs effectively solve these issues by incorporating physical equation constraints directly into the loss function. This paper uses the motion equation of a damped oscillation system as an example to first introduce the mathematical model of the system, including the motion equation, initial conditions, and boundary conditions. Then, it explains in detail how to apply PINNs using the DeepXDE library to accurately predict the system's dynamic behavior. Finally, a comparison between the predicted results and the analytical solution is conducted to validate the effectiveness and reliability of the model.