![]() The revolution of deep learning begins when LeCunn et al. With the abundance of data and inexpensive yet powerful hardware, deep learning-based methods have attracted considerable attention. Many attempts have been made to autonomously extract physical laws from data. The process of refining the hypotheses, which should be falsifiable so that it can be meaningfully tested 1, from experimental data have been performed manually over the centuries automation of these processes have long been of great interest to the scientific community. Such models are desirable because they can be used to devise solutions to real-world problems. Researchers have attempted to develop models that can capture real-world phenomena since the early modern history of humanity. We believe this contribution is significant toward noise-tolerant computational method for explicit dynamics law extraction from data. The experimental results reveal that xL-SINDy is much more robust than the existing methods for extracting the governing equations of nonlinear mechanical systems from data with noise. In addition, we compared its performance with SINDy-PI (parallel, implicit) which is a latest robust variant of SINDy that can handle implicit dynamics and rational nonlinearities. ![]() Further, we demonstrated the effectiveness of xL-SINDy against different noise levels using four mechanical systems. We incorporated the concept of SINDy and used the proximal gradient method to obtain sparse Lagrangian expressions. In this study, we developed an extended version of Lagrangian-SINDy (xL-SINDy) to obtain the Lagrangian of dynamical systems from noisy measurement data. Few proposed methods proposed to date, such as Lagrangian-SINDy we have proposed recently, can extract the true form of the Lagrangian of dynamical systems from data however, these methods are easily affected by noise as a fact. ![]() The Lagrangian is substantially more concise than the actual equations of motion, especially for complex systems, and it does not usually contain rational functions for mechanical systems. However, SINDy faces certain difficulties when the dynamics contain rational functions. Data-driven modeling frameworks that adopt sparse regression techniques, such as sparse identification of nonlinear dynamics (SINDy) and its modifications, are developed to resolve difficulties in extracting underlying dynamics from experimental data. The autonomous distillation of physical laws only from data is of great interest in many scientific fields. ![]()
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