Related papers: A wavelet-based dynamic mode decomposition for mod…
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…
Any deterministic autonomous dynamical system may be globally linearized by its' Koopman operator. This object is typically infinite-dimensional and can be approximated by the so-called Dynamic Mode Decomposition (DMD). In DMD, the central…
Simulating the dynamics of a nonequilibrium quantum many-body system by computing the two-time Green's function associated with such a system is computationally challenging. However, we are often interested in the time diagonal of such a…
While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a…
We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of…
Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been…
There is a broad need in the neuroscience community to understand and visualize large-scale recordings of neural activity, big data acquired by tens or hundreds of electrodes simultaneously recording dynamic brain activity over minutes to…
Noise fundamentally limits the performance and predictive capabilities of classical and quantum dynamical systems by degrading stability and obscuring intrinsic dynamical characteristics. Characterizing such noise accurately is essential…
Harmonic instability occurs frequently in the power electronic converter system. This paper leverages multi-resolution dynamic mode decomposition (MR-DMD) as a data-driven diagnostic tool for the system stability of power electronic…
Reliable numerical computation of quantum dynamics is a fundamental challenge when the long-ranged quantum entanglement plays essential roles as in the cases governed by quantum criticality in strongly correlated systems. Here we apply a…
A novel approach to reduced-order modeling of high-dimensional time varying systems is proposed. It leverages the formalism of the Dynamic Mode Decomposition technique together with the concept of balanced realization. It is assumed that…
The modal decomposition techniques of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) have become a common method for analysing the spatio-temporal coherence of dynamical systems. In particular, these techniques…
Periodic control systems used in spacecrafts and automotives are usually period-driven and can be decomposed into different modes with each mode representing a system state observed from outside. Such systems may also involve intensive…
Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors.…
Dynamic Mode Decomposition (DMD) and its extensions (EDMD) have been at the forefront of data-based approaches to Koopman operators. Most (E)DMD algorithms assume that the entire state is sampled at a uniform sampling rate. In this paper,…
Temporal or spatial structures are readily extracted from complex data by modal decompositions like Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD). Subspaces of such decompositions serve as reduced order models…
Dynamic Mode Decomposition (DMD) is a powerful, data-driven method for diagnosing complex dynamics. Various DMD algorithms allow one to fit data with a low-rank model that decomposes it into a sum of coherent spatiotemporal patterns.…
Delay embeddings of time series data have emerged as a promising coordinate basis for data-driven estimation of the Koopman operator, which seeks a linear representation for observed nonlinear dynamics. Recent work has demonstrated the…
Periodic control systems used in spacecrafts and automotives are usually period-driven and can be decomposed into different modes with each mode representing a system state observed from outside. Such systems may also involve intensive…
This paper proposes Koopman operator theory and the related algorithm dynamical mode decomposition (DMD) for analysis and control of signalized traffic flow networks. DMD provides a model-free approach for representing complex oscillatory…