Related papers: Characterization of elastic topological states usi…
This article presents the data-driven equation-free modeling of the dynamics of a hexafloat floating offshore wind turbine based on the application of dynamic mode decomposition (DMD). All the analyses are performed on experimental data…
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…
Elastic wave manipulation is important in a wide variety of scales in applications including information processing in tiny elastic devices and noise control in big solid structures. The recent emergence of topological materials opens a new…
We present an extension of optimal mode decomposition (OMD) for autonomous systems to systems with controls. The extension is developed along the same lines as the extension of dynamic mode decomposition (DMD) to DMD with control (DMDc).…
Two dynamical systems are topologically equivalent when their phase-portraits can be morphed into each other by a homeomorphic coordinate transformation on the state space. The induced equivalence classes capture qualitative properties such…
Data-driven methods for the identification of the governing equations of dynamical systems or the computation of reduced surrogate models play an increasingly important role in many application areas such as physics, chemistry, biology, and…
Over the last few years, crystalline topology has been used in photonic crystals to realize edge- and corner-localized states that enhance light-matter interactions for potential device applications. However, the band-theoretic approaches…
Topological feature has become an intensively studied subject in many fields of physics. As a witness of topological phase, the edge states are topologically protected and may be helpful in quantum information processing. In this paper, we…
We introduce a computationally efficient method for the automation of inverse design in science and engineering. Based on simple least-square regression, the underlying dynamic mode decomposition algorithm can be used to construct a…
Topological acoustic and elastic waves have recently emerged as an exciting interdisciplinary field which is still mainly focused on low-dimensional structures and model systems. Here we demonstrate numerically an elastic-wave analogue of…
Time series forecasting remains a central challenge problem in almost all scientific disciplines. We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system using Dynamic Mode Decomposition…
This paper considers the problem of detecting topology variations in dynamical networks. We consider a network whose behavior can be represented via a linear dynamical system. The problem of interest is then that of finding conditions under…
Recent advancements in topological metamaterials have unveiled fruitful physics and numerous applications. Whereas initial efforts focus on achieving topologically protected edge states through principles of structural symmetry, the…
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…
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…
There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…
Topological photonics holds the promise for enhanced robustness of light localization and propagation enabled by the global symmetries of the system. While traditional designs of topological structures rely on lattice symmetries, there is…
We investigate the robustness of {\it virtual} topological states -- topological phases away from the Fermi energy -- against the electron-electron interaction and band filling. As a case study, we employ a realistic model to investigate…
The pinning of an inhomogeneous elastic medium by a disordered substrate is studied analytically and numerically. The static and dynamic properties of a $D$-dimensional system are shown to be equivalent to those of the well known problem of…
Numerical approximation methods for the Koopman operator have advanced considerably in the last few years. In particular, data-driven approaches such as dynamic mode decomposition (DMD) and its generalization, the extended-DMD (EDMD), are…