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A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…
Inertial particles advected by a background flow can show complex structures. We consider inertial particles in a 2D Taylor-Green (TG) flow and characterize particle dynamics as a function of the particle's Stokes number using dynamic mode…
Data-driven methods for establishing quantum optimal control (QOC) using time-dependent control pulses tailored to specific quantum dynamical systems and desired control objectives are critical for many emerging quantum technologies. We…
The Dynamic Mode Decomposition (DMD) is a Koopman-based algorithm that straightforwardly isolates individual mechanisms from the compound morphology of direct measurement. However, many may be perplexed by the messages the DMD structures…
We review a dynamical approach to non-equilibrium MD (D-NEMD). We show how, using a proper simulation setup, is possible to treat interesting cases in which the initial condition is a stationary non-equilibrium state produced by a suitable…
Dynamic mode decomposition (DMD) is a data-driven technique widely used to analyze and model fluid problems including transonic buffet flows. Despite its strengths, DMD is known to suffer from sensitivities to the selected settings and the…
This paper presents unifying results for subspace identification (SID) and dynamic mode decomposition (DMD) for autonomous dynamical systems. We observe that SID seeks to solve an optimization problem to estimate an extended observability…
Extracting coherent patterns is one of the standard approaches towards understanding spatio-temporal data. Dynamic mode decomposition (DMD) is a powerful tool for extracting coherent patterns, but the original DMD and most of its variants…
Forecasting the short-term ridership among origin-destination pairs (OD matrix) of a metro system is crucial in real-time metro operation. However, this problem is notoriously difficult due to the high-dimensional, sparse, noisy, and skewed…
The decomposition of oceanic flow into its balanced and unbalanced motions carries theoretical and practical significance for the oceanographic community. These two motions have distinct dynamical characteristics and affect the transport of…
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…
Parker's mean-field model includes two processes generating large-scale oscillatory dynamo waves: stretching of magnetic field lines by small-scale helical flows, and by differential rotation. In this work, we investigate the capacity of…
In part I of the article, we demonstrated that a variant of the Dynamic Mode Decomposition (DMD) algorithm based on variable projection optimization, called Optimized DMD (OPT-DMD), enables a robust identification of the dominant…
Various neural network based methods are capable of anticipating human body motions from data for a short period of time. What these methods lack are the interpretability and explainability of the network and its results. We propose to use…
We describe a method to extract from experimental data the important dynamical modes in spatio-temporal patterns in a system driven out of thermodynamic equilibrium. Using a novel optical technique for controlling fluid flow, we create an…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
The most direct approach for characterizing the quantum dynamics of a strongly-interacting system is to measure the time-evolution of its full many-body state. Despite the conceptual simplicity of this approach, it quickly becomes…
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…
In this work we perform full-state LQR feedback control of fluid flows using non-intrusive data-driven reduced-order models. We propose a model reduction method called low-rank Dynamic Mode Decomposition (lrDMD) that solves for a…
The identification of reduced-order models from high-dimensional data is a challenging task, and even more so if the identified system should not only be suitable for a certain data set, but generally approximate the input-output behavior…