相关论文: Discovery of Nonlinear Multiscale Systems: Samplin…
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,…
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) is a method for discovering nonlinear dynamical system models from data. Quantifying uncertainty in SINDy models is essential for assessing their reliability, particularly in…
The Sparse Identification of Nonlinear Dynamics (SINDy) framework has been frequently used to discover parsimonious differential equations governing natural and physical systems. This includes recent extensions to SINDy that enable the…
Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinear Dynamical Systems (SINDy) framework, which uses sparse…
The moment quantities associated with the nonlinear Schrodinger equation offer important insights towards the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment…
Data-driven learning is rapidly evolving and places a new perspective on realizing state-space dynamical systems. However, dynamical systems derived from nonlinear ordinary differential equations (ODEs) suffer from limitations in…
Data-driven transformations that reformulate nonlinear systems in a linear framework have the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. The Koopman operator has…
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 dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
The increasing penetration of renewable energy sources, characterised by low inertia and intermittent disturbances, presents substantial challenges to power system stability. As critical indicators of system stability, frequency dynamics…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and…
Networks are landmarks of many complex phenomena where interweaving interactions between different agents transform simple local rule-sets into nonlinear emergent behaviors. While some recent studies unveil associations between the network…
The present paper treats the identification of nonlinear dynamical systems using Koopman-based deep state-space encoders. Through this method, the usual drawback of needing to choose a dictionary of lifting functions a priori is…
Periodic orbits are among the simplest non-equilibrium solutions to dynamical systems, and they play a significant role in our modern understanding of the rich structures observed in many systems. For example, it is known that embedded…
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…
Sparse Identification of Nonlinear Dynamics (SINDy) is a powerful method for discovering parsimonious governing equations from data, but it often requires expert tuning of candidate libraries. We propose an LLM-aided SINDy pipeline that…
Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…
System identification plays a crucial role in physics and machine learning for discovering governing equations directly from data. A powerful approach is the Sparse Identification of Nonlinear Dynamics (SINDy) method, which assumes that…