Sparse Identification of Lagrangian for Nonlinear Dynamical Systems Involving Dissipation Function

Accurately modeling nonlinear dynamic systems remains a significant challenge across numerous scientific fields, from physics to finance. Existing methods require prior knowledge of the system or are sensitive to noise, making them impractical to handle real-world tasks. Based on the sparse identification of nonlinear dynamics (SINDy) algorithm, our previous research proposed a variant of the SINDy algorithm. With the Lagrangian integrated, we named our method extended Lagrangian-SINDy (xL-SINDy). The xL-SINDy shows higher robustness than the competing method with a factor of 100, but it sacrifices the ability to deal with a nonconservative system. This paper introduces a new method that extends xL-SINDy's capabilities. We address its primary limitation by integrating the Rayleigh dissipation function into the xL-SINDy framework. Tests on four different pendulum systems show that our method maintains the same level of robustness as the xL-SINDy, but can identify nonconservative terms in the system. Making it better describe the real-world systems. While the proposed method is limited to specific types of dissipative forces that the Rayleigh dissipation can describe, the provided framework can be extended to include any form of the nonconservative terms.