Accurate estimation of parameters in complex nonlinear systems is of utmost importance in various scientific and engineering domains. In this study, we propose a novel approach for parameter estimation that utilizes a neural network with the Huber loss function. By leveraging the capabilities of deep learning, our method uncovers the parameters that govern intricate behaviors in nonlinear equations.
To validate our approach, we conduct experiments using synthetic data and predefined functions that accurately model the dynamics of the system. Through training the neural network with noisy time series data, we fine-tune the Huber loss function to converge towards accurate parameter estimates. We apply our method to various systems, such as damped oscillators, Van der Pol oscillators, Lotka-Volterra systems, and Lorenz systems under multiplicative noise.
The results demonstrate that our trained neural network accurately estimates the parameters, as evidenced by the close match between the estimated and true latent dynamics. Visual comparison of the true and estimated trajectories further reinforces the precision and robustness of our method.
Overall, our study highlights the versatility of the Huber loss-guided neural network as an effective tool for parameter estimation, enabling the discovery of complex relationships in nonlinear systems. Furthermore, our method adeptly handles noise and uncertainty, showcasing its adaptability to real-world challenges.