Modeling Dynamical Systems Using Neural ODEs: A Study On Scientific Machine Learning Models

This paper explores the application of Neural Ordinary Differential Equations (Neural ODEs) for modeling and simulating complex dynamic systems. We begin with the classical 1D harmonic oscillator to show how Neural ODEs can learn unknown system parameters and initial conditions directly from data, achieving accurate and robust performance under various external forces. Extending our investigation to the chaotic Lorenz system, we demonstrate the model’s capacity to capture highly nonlinear and sensitive dynamics. The results highlight the ability of Neural ODEs to approximate continuous trajectories adapt to long-term dependencies inherent in chaotic systems. Our experiments show that Neural ODEs can accurately model various dynamic systems, handle chaotic behavior, and adapt to external forces. These findings highlight the potential of Neural ODEs for improving the robustness and efficiency of hybrid machine learning models in scientific applications.