Neural Ordinary Differential Equations for robust parameter estimation in dynamic systems with physical priors

Abstract

This study introduces a novel parameter estimation method based on Neural Ordinary Differential Equations (Neural ODE). The method addresses the challenges of limited data and noise interference in dynamic system modeling.By integrating neural networks with physical prior knowledge, the framework encodes the system's physical parameters as neural network parameters. This approach enables end-to-end learning from limited observational data. In numerical experiments on a damped oscillator system with Gaussian noise of standard deviation 0.2, the method estimates system parameters with relative errors below 2 %. For the complex nonlinear Lorenz system, it estimates key parameters σ, ρ, and β with relative errors of 0.1 %, 0.4 %, and 1.17 %, respectively. These results significantly outperform traditional methods.The numerical experiments demonstrate that the method provides accurate parameter estimation and effective system dynamics reconstruction. It performs well under small sample sizes and significant noise conditions.