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With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics…

Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations…

Accurately modeling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data.…

The Sparse Identification of Nonlinear Dynamics (SINDy) is a method for discovering nonlinear dynamical system models from data. Quantifying uncertainty in SINDy models is essential for assessing their reliability, particularly in…

Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations…

Big data has become a critically enabling component of emerging mathematical methods aimed at the automated discovery of dynamical systems, where first principles modeling may be intractable. However, in many engineering systems, abrupt…

Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…

A general framework for recovering drift and diffusion dynamics from sampled trajectories is presented for the first time for stochastic delay differential equations. The core relies on the well-established SINDy algorithm for the sparse…

In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real…

This paper proposes a data-driven model predictive control for multirotor collision avoidance considering uncertainty and an unknown model from a payload. To address this challenge, sparse identification of nonlinear dynamics (SINDy) is…

Sparse identification of nonlinear dynamics (SINDy) has been widely used to discover the governing equations of a dynamical system from data. It uses sparse regression techniques to identify parsimonious models of unknown systems from a…

Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using…

The sparse identification of nonlinear dynamics (SINDy) has been established as an effective method to learn interpretable models of dynamical systems from data. However, for high-dimensional slow-fast dynamical systems, the regression…

The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. However, SINDy assumes the user has prior knowledge of the variables in the system and of a function library that…

Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic…

The sparse identification of nonlinear dynamics (SINDy) has been established as an effective technique to produce interpretable models of dynamical systems from time-resolved state data via sparse regression. However, to model parameterized…

Sparse regression has emerged as a popular technique for learning dynamical systems from temporal data, beginning with the SINDy (Sparse Identification of Nonlinear Dynamics) framework proposed by arXiv:1509.03580. Quantifying the…

Sparse Identification of Nonlinear Dynamics (SINDy) has been shown to successfully recover governing equations from data; however, this approach assumes the initial condition to be exactly known in advance and is sensitive to noise. In this…

The data-driven discovery of dynamics via machine learning is currently pushing the frontiers of modeling and control efforts, and it provides a tremendous opportunity to extend the reach of model predictive control. However, many leading…

SINDy is a method for learning system of differential equations from data by solving a sparse linear regression optimization problem [Brunton et al., 2016]. In this article, we propose an extension of the SINDy method that learns systems of…