相关论文: Sparsity-Promoting Dynamic Mode Decomposition Appl…

Convective features, represented here as warm bubble-like patterns, reveal essential high-level information about how short-term weather dynamics evolve within a high-dimensional state space. In this paper, we introduce a data-driven…

We study nonlinear dynamics of the Earth's tropical climate system. For that, we apply a recently developed technique for feature extraction and mode decomposition of spatiotemporal data generated by ergodic dynamical systems. The method…

Sea ice cover in the Arctic and Antarctic is an important indicator of changes in the climate, with important environmental, economic and security consequences. The complexity of the spatio-temporal dynamics of sea ice makes it difficult to…

Koopman decomposition is a non-linear generalization of eigen-decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques such as the dynamic mode decomposition (DMD) and its linear…

The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically…

In recent years more and more long-term broadband data sets are collected in geosciences. Therefore there is an urgent need of algorithms which semi-automatically analyse and decompose these data into separate periods which are associated…

Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this…

This paper tackles the data-driven approximation of unknown dynamical systems using Koopman-operator methods. Given a dictionary of functions, these methods approximate the projection of the action of the operator on the finite-dimensional…

An important problem in modern applied science is characterizing the behavior of systems with complex internal dynamics subjected to external forcings from their environment. While a great variety of techniques has been developed to analyze…

Finding the governing equations from data by sparse optimization has become a popular approach to deterministic modeling of dynamical systems. Considering the physical situations where the data can be imperfect due to disturbances and…

Dynamic mode decomposition (DMD) is a data-driven method of extracting spatial-temporal coherent modes from complex systems and providing an equation-free architecture to model and predict systems. However, in practical applications, the…

Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…

Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated…

This paper develops a novel data-driven technique to compute the participation factors for nonlinear systems based on the Koopman mode decomposition. Provided that certain conditions are satisfied, it is shown that the proposed technique…

Glasses are traditionally characterized by their rugged landscape of disordered low-energy states and their slow relaxation towards thermodynamic equilibrium. Far from equilibrium, dynamical forms of glassy behavior with anomalous algebraic…

We introduce the dynamics mode decomposition for monitoring wide-area power grid networks from sparse measurement data. The mathematical framework fuses data from multiple sensors based on multivariate statistics, providing accurate full…

System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the…

Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…

Spectral decomposition of dynamical systems is a popular methodology to investigate the fundamental qualitative and quantitative properties of these systems and their solutions. In this chapter, we consider a class of nonlinear cooperative…

The analysis of nonlinear dynamical systems based on the Koopman operator is attracting attention in various applications. Dynamic mode decomposition (DMD) is a data-driven algorithm for Koopman spectral analysis, and several variants with…