  Nonlinear systems play a significant role in numerous scientific and
engineering disciplines, and comprehending their behavior is crucial for the
development of effective control and prediction strategies. This paper
introduces a novel data-driven approach for accurately modeling and estimating
parameters of nonlinear systems utilizing trust region optimization. The
proposed method is applied to three well-known systems: the Van der Pol
oscillator, the Damped oscillator, and the Lorenz system, which find broad
applications in engineering, physics, and biology. The results demonstrate the
efficacy of the approach in accurately identifying the parameters of these
nonlinear systems, enabling a reliable characterization of their behavior.
Particularly in chaotic systems like the Lorenz system, capturing the dynamics
on the attractor proves to be crucial. Overall, this article presents a robust
data-driven approach for parameter estimation in nonlinear dynamical systems,
holding promising potential for real-world applications.
