Related papers: Brief Communication: Dimensionality Reduction in T…

Accurate and efficient wave-optics simulation of partially coherent light transport systems is critical for the design of advanced optical systems, ranging from computational lithography to diffraction-limited storage rings (DLSR). However,…

The Dynamic Mode Decomposition (DMD) and the more general Extended DMD (EDMD) are powerful tools for computational analysis of dynamical systems in data-driven scenarios. They are built on the theoretical foundation of the Koopman…

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).…

Recently, acoustic communication employing Orbital Angular Momentum (OAM) opens another avenue for efficient data transmission in aquatic environments. Current topological charge (TC) detection of OAM beams relies on the orthogonality among…

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…

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…

Harmonic instability occurs frequently in the power electronic converter system. This paper leverages multi-resolution dynamic mode decomposition (MR-DMD) as a data-driven diagnostic tool for the system stability of power electronic…

Dynamic mode decomposition (DMD) is a data-driven method that models high-dimensional time series as a sum of spatiotemporal modes, where the temporal modes are constrained by linear dynamics. For nonlinear dynamical systems exhibiting…

We propose two novel data-driven dynamic mode decomposition (DMD)-type methods, the Crank--Nicolson DMD and the semi-implicit DMD, to predict the highly oscillatory dynamics of the semiclassical Schr\"odinger equations efficiently and…

We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…

Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…

We develop a domain-decomposition model reduction method for linear steady-state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equations with random diffusivities, and the…

Radiation-induced photocurrent in semiconductor devices can be simulated using complex physics-based models, which are accurate, but computationally expensive. This presents a challenge for implementing device characteristics in high-level…

The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…

This work investigates variational compilation methods for simulating quantum systems with internal SU(2) symmetry. The central component of the research is the application of the Dynamic Mode Decomposition (DMD) method to extrapolate…

Presented is an algorithm based on dynamic mode decomposition (DMD) for acceleration of the power method (PM). The power method is a simple technique for determining the dominant eigenmode of an operator $\mathbf{A}$, and variants of the…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

This paper develops a robust dynamic mode decomposition (RDMD) method endowed with statistical and numerical robustness. Statistical robustness ensures estimation efficiency at the Gaussian and non-Gaussian probability distributions,…

Efficiently estimating system dynamics from data is essential for minimizing data collection costs and improving model performance. This work addresses the challenge of designing future control inputs to maximize information gain, thereby…

Simple aerodynamic configurations under even modest conditions can exhibit complex flows with a wide range of temporal and spatial features. It has become common practice in the analysis of these flows to look for and extract physically…