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We introduce a new adaptive decomposition tool, which we refer to as Nonlinear Mode Decomposition (NMD). It decomposes a given signal into a set of physically meaningful oscillations for any waveform, simultaneously removing the noise. NMD…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
In this work, a data-driven, modal decomposition method, the higher order dynamic mode decomposition (HODMD), is combined with a convolutional neural network (CNN) in order to improve the classification accuracy of several cardiac diseases…
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…
Nonlinear modal decoupling (NMD) was recently proposed to nonlinearly transform a multi-oscillator system into a number of decoupled oscillators which together behave the same as the original system in an extended neighborhood of the…
This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…
Construction of reduced-order models (ROMs) for hyperbolic conservation laws is notoriously challenging mainly due to the translational property and nonlinearity of the governing equations. While the Lagrangian framework for ROM…
Accurate readout of low-power optical higher-order spatial modes is of increasing importance to the precision metrology community. Mode sensors are used to prevent mode mismatches from degrading quantum and thermal noise mitigation…
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…
Nonlinear oscillations are commonly observed in complex systems far from equilibrium, such as living organisms. These oscillations are essential for sustaining vital processes, like neuronal firing, circadian rhythms, and heartbeats. In…
The interaction of multiple fluids through a heterogeneous pore space leads to complex pore-scale flow dynamics, such as intermittent pathway flow. The non-local nature of these dynamics, and the size of the 4D datasets acquired to capture…
Accurate modeling of the complex dynamics of fluid flows is a fundamental challenge in computational physics and engineering. This study presents an innovative integration of High-Order Singular Value Decomposition (HOSVD) with Long…
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…
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…
Understanding flow structures in urban areas is widely recognized as a challenging concern due to its effect on urban development, air quality, and pollutant dispersion. In this study, state-of-the-art data-driven methods for modal analysis…
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…
A dynamic mode decomposition (DMD) based reduced-order model (ROM) is developed for tracking, detection, and prediction of kinetic plasma behavior. DMD is applied to the high-fidelity kinetic plasma model based on the electromagnetic…
The simulation of atmospheric flows by means of traditional discretization methods remains computationally intensive, hindering the achievement of high forecasting accuracy in short time frames. In this paper, we apply three reduced order…
We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods…