Related papers: Study of dynamics in post-transient flows using Ko…
This paper explores a novel data-driven approach based on recent developments in Koopman operator theory and dynamic mode decomposition (DMD) for modeling signalized intersections. Vehicular flow and queue formation on signalized…
This work continues the parametric investigation on the sampling nuances of the Dynamic Mode Decomposition (DMD) under the Koopman analysis. Through turbulent wakes, the investigation corroborated the generality of the universal convergence…
We apply dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) methods to flows in highly-heterogeneous porous media to extract the dominant coherent structures and derive reduced-order models via Galerkin projection.…
The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches…
The Strait of Gibraltar is a region characterized by intricate oceanic sub-mesoscale features, influenced by topography, tidal forces, instabilities, and nonlinear hydraulic processes, all governed by the nonlinear equations of fluid…
We present a parallel data-driven strategy to identify finite-dimensional functional spaces invariant under the Koopman operator associated to an unknown dynamical system. We build on the Symmetric Subspace Decomposition (SSD) algorithm, a…
We propose a data-driven algorithm for reconstructing the irregular, chaotic flow dynamics around two side-by-side square cylinders from sparse, time-resolved, velocity measurements in the wake. We use Proper Orthogonal Decomposition (POD)…
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…
Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic…
The accurate simulation of complex dynamics in fluid flows demands a substantial number of degrees of freedom, i.e. a high-dimensional state space. Nevertheless, the swift attenuation of small-scale perturbations due to viscous diffusion…
Extended dynamic mode decomposition (EDMD) is a popular data-driven method to predict the action of the Koopman operator, i.e., the evolution of an observable function along the flow of a dynamical system. In this paper, we leverage a…
Predicting traffic flow in data-scarce cities is challenging due to limited historical data. To address this, we leverage transfer learning by identifying periodic patterns common to data-rich cities using a customized variant of Dynamic…
Extended dynamic mode decomposition (EDMD) is a powerful tool to construct linear predictors of nonlinear dynamical systems by approximating the action of the Koopman operator on a subspace spanned by finitely many observable functions.…
The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a…
Representation of a dynamical system in terms of simplifying modes is a central premise of reduced order modelling and a primary concern of the increasingly popular DMD (dynamic mode decomposition) empirical interpretation of Koopman…
A stochastic data-driven reduced-order model applicable to a wide range of turbulent natural and engineering flows is presented. Combining ideas from Koopman theory and spectral model order reduction, the stochastic low-dimensional inflated…
This paper explores the integration of symmetries into the Koopman-operator framework for the analysis and efficient learning of equivariant dynamical systems using a group-convolutional approach. Approximating the Koopman operator by…
The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace. Observables of interest are typically linearly reconstructed from the Koopman eigenfunctions.…
In recent years, there has been a growing interest in data-driven approaches in physics, such as extended dynamic mode decomposition (EDMD). The EDMD algorithm focuses on nonlinear time-evolution systems, and the constructed Koopman matrix…