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We present a data-driven model predictive control (MPC) framework for systems with high state-space dimensionalities. This work is motivated by the need to exploit sensor data that appears in the form of images (e.g., 2D or 3D spatial…

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)…

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…

Ensuring the reliability of power electronic converters is a matter of great importance, and data-driven condition monitoring techniques are cementing themselves as an important tool for this purpose. However, translating methods that work…

The problem of identifying change points in high-dimensional Gaussian graphical models (GGMs) in an online fashion is of interest, due to new applications in biology, economics and social sciences. The offline version of the problem, where…

This work develops compressive sampling strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled or output-projected data. The resulting DMD eigenvalues are equal to DMD eigenvalues from the full-state data. It…

We propose an analytical construction of observable functions in the extended dynamic mode decomposition (EDMD) algorithm. EDMD is a numerical method for approximating the spectral properties of the Koopman operator. The choice of…

Agnostic domain shift is the main reason of model degradation on the unknown target domains, which brings an urgent need to develop Domain Generalization (DG). Recent advances at DG use dynamic networks to achieve training-free adaptation…

Accurate monitoring of lithium-ion battery (LIB) degradation is essential, yet it remains challenging due to the complex, nonlinear, and time-varying nature of electrochemical aging processes. Conventional equivalent circuit models (ECMs)…

Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing nonstationary data that provides a localized time-frequency representation by decomposing the data into adaptively defined modes. EMD can be used to estimate a…

We revisit the setting and the assumptions that underlie the methodology of Dynamic Mode Decomposition (DMD) in order to highlight caveats as well as potential measures of when the applicability is warranted.

Dynamic Mode Decomposition (DMD) is a widely used data-driven algorithm for estimating the Koopman Operator.This paper investigates how the estimation process is affected when the data is quantized. Specifically, we examine the fundamental…

Non-Hermitian physics enables novel control over open quantum and wave systems, but selectively isolating individual modes without delicate balancing of gain and loss remains challenging. Here we introduce a gauge-engineering method in…

This paper builds on the theoretical foundations for dynamic mode decomposition (DMD) of control-affine dynamical systems by leveraging the theory of vector-valued reproducing kernel Hilbert spaces (RKHSs). Specifically, control Liouville…

Link prediction in dynamic networks remains a fundamental challenge in network science, requiring the inference of potential interactions and their evolving strengths through spatiotemporal pattern analysis. Traditional static network…

Extended dynamic mode decomposition (EDMD) is a data-driven algorithm for approximating spectral data of the Koopman operator associated to a dynamical system, combining a Galerkin method of order N and collocation method of order M.…

Human motion prediction is challenging due to the complex spatiotemporal feature modeling. Among all methods, graph convolution networks (GCNs) are extensively utilized because of their superiority in explicit connection modeling. Within a…

Chaotic trajectories in multi-body dynamical systems play a crucial role in designing low-energy trajectories in astrodynamics. However, predicting these trajectories is inherently difficult, as small errors in initial conditions can grow…

A new concept, decomposition-unstable (DU) variety of a parametric polynomial system, is introduced in this paper and the stabilities of several triangular decomposition methods, such as characteristic set decomposition, relatively…

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,…