Related papers: Simultaneous Identification and Denoising of Dynam…
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…
In recent years, identification of nonlinear dynamical systems from data has become increasingly popular. Sparse regression approaches, such as Sparse Identification of Nonlinear Dynamics (SINDy), fostered the development of novel governing…
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.…
Recent advances in the field of data-driven dynamics allow for the discovery of ODE systems using state measurements. One approach, known as Sparse Identification of Nonlinear Dynamics (SINDy), assumes the dynamics are sparse within a…
This work proposes an iterative sparse-regularized regression method to recover governing equations of nonlinear dynamical systems from noisy state measurements. The method is inspired by the Sparse Identification of Nonlinear Dynamics…
The sparse identification of nonlinear dynamics (SINDy) is a regression framework for the discovery of parsimonious dynamic models and governing equations from time-series data. As with all system identification methods, noisy measurements…
Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…
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…
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…
Sparse system identification of nonlinear dynamic systems is still challenging, especially for stiff and high-order differential equations for noisy measurement data. The use of highly correlated functions makes distinguishing between true…
Modern societies have an abundance of data yet good system models are rare. Unfortunately, many of the current system identification and machine learning techniques fail to generalize outside of the training set, producing models that…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system discovery that has been shown to successfully recover governing dynamical systems from data (Brunton et al., PNAS, '16; Rudy et al., Sci. Adv. '17). Recently, several…
A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary…
This work is concerned with uncertainty quantification in reduced-order dynamical system identification. Reduced-order models for system dynamics are ubiquitous in design and control applications and recent efforts focus on their…
Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the…
We consider the data-driven discovery of governing equations from time-series data in the limit of high noise. The algorithms developed describe an extensive toolkit of methods for circumventing the deleterious effects of noise in the…
The Sparse Identification of Nonlinear Dynamics (SINDy) framework is a robust method for identifying governing equations, successfully applied to ordinary, partial, and stochastic differential equations. In this work we extend SINDy to…
Identifying dynamical systems characterized by nonlinear parameters presents significant challenges in deriving mathematical models that enhance understanding of physics. Traditional methods, such as Sparse Identification of Nonlinear…
Identifying the governing equations of a dynamical system is one of the most important tasks for scientific modeling. However, this procedure often requires high-quality spatio-temporal data uniformly sampled on structured grids. In this…