Related papers: Learning Nonlinear Dynamics Using Kalman Smoothing

This paper deals with the error processing problem of sparse identification of nonlinear dynamical systems(SINDy) through introducing the $L_\infty$ approximation to take place of the former $L_2$ approximation. The motivation is that the…

Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability…

We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…

System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods. Addressing the intricate challenges of…

In many fields of application, dynamic processes that evolve through time are well described by systems of ordinary differential equations (ODEs). The analytical solution of the ODEs is often not available and different methods have been…

Identification of nonlinear dynamical systems has been popularized by sparse identification of the nonlinear dynamics (SINDy) via the sequentially thresholded least squares (STLS) algorithm. Many extensions SINDy have emerged in the…

We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to…

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…

Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations…

Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…

Koopman spectral analysis plays a crucial role in understanding and modeling nonlinear dynamical systems as it reveals key system behaviors and long-term dynamics. However, the presence of measurement noise poses a significant challenge to…

In this study, we investigate the performance of the sparse identification of nonlinear dynamics (SINDy) algorithm and the neural ordinary differential equations (ODEs) in identification of the underlying mechanisms of open ocean Lagrangian…

Distilling physical laws autonomously from data has been of great interest in many scientific areas. The sparse identification of nonlinear dynamics (SINDy) and its variations have been developed to extract the underlying governing…

This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy). The algorithm is online in a sense that if performs…

We present a weak formulation and discretization of the system discovery problem from noisy measurement data. This method of learning differential equations from data fits into a new class of algorithms that replace pointwise derivative…

Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions they describe. Therefore researchers often seek simpler…

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…

In recent years there has been a push to discover the governing equations dynamical systems directly from measurements of the state, often motivated by systems that are too complex to directly model. Although there has been substantial work…

Model parsimony is an important \emph{cognitive bias} in data-driven modelling that aids interpretability and helps to prevent over-fitting. Sparse identification of nonlinear dynamics (SINDy) methods are able to learn sparse…

Sparse dynamics identification is an essential tool for discovering interpretable physical models and enabling efficient control in engineering systems. However, existing methods rely on batch learning with full historical data, limiting…