Related papers: Dynamic mode decomposition using a Kalman filter f…
We present a method for forecasting the foF2 and hmF2 parameters using modal decompositions of ionospheric electron density profile time series. Our method is based on the Dynamic Mode Decomposition (DMD), which provides a means of…
Dynamic mode decomposition (DMD) has proven to be a valuable tool for the analysis of complex flow-fields but the application of this technique to flows with moving boundaries is not straightforward. This is due to the difficulty in…
We introduce KFD-NeRF, a novel dynamic neural radiance field integrated with an efficient and high-quality motion reconstruction framework based on Kalman filtering. Our key idea is to model the dynamic radiance field as a dynamic system…
Nonlinear dynamical systems with input delays pose significant challenges for prediction, estimation, and control due to their inherent complexity and the impact of delays on system behavior. Traditional linear control techniques often fail…
The Koopman Mode Decomposition (KMD) is a data-analysis technique which is often used to extract the spatio-temporal patterns of complex flows. In this paper, we use KMD to study the dynamics of the lid-driven flow in a two-dimensional…
We study the convergence of Hermitian Dynamic Mode Decomposition (DMD) to the spectral properties of self-adjoint Koopman operators. Hermitian DMD is a data-driven method that approximates the Koopman operator associated with an unknown…
Koopman operators globally linearize nonlinear dynamical systems and their spectral information is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. However, Koopman operators are infinite-dimensional, and…
Data-driven techniques for analysis, modeling, and control of complex dynamical systems are on the uptake. Koopman theory provides the theoretical foundation for the popular kernel extended dynamic mode decomposition (kEDMD). In this work,…
This paper proposes a mode multigrid (MMG) method, and applies it to accelerate the convergence of the steady state flow on unstructured grids. The dynamic mode decomposition (DMD) technique is used to analyze the convergence process of…
Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the Koopman operator for deterministic and stochastic (control) systems. This operator is linear and encompasses full information on the (expected…
We present a data-efficient algorithm for learning models for model-predictive control (MPC). Our approach, Jacobian-Regularized Dynamic-Mode Decomposition (JDMD), offers improved sample efficiency over traditional Koopman approaches based…
Functional brain dynamics is supported by parallel and overlapping functional network modes that are associated with specific neural circuits. Decomposing these network modes from fMRI data and finding their temporal characteristics is…
In this two-part article, we evaluate the utility and the generalizability of the Dynamic Mode Decomposition (DMD) algorithm for data-driven analysis and reduced-order modelling of plasma dynamics in cross-field ExB configurations. The DMD…
Ill-posed inverse problems are ubiquitous in applications. Under- standing of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering…
We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…
Extended Dynamic Mode Decomposition (EDMD) is a widely-used data-driven approach to learn an approximation of the Koopman operator. Consequently, it provides a powerful tool for data-driven analysis, prediction, and control of nonlinear…
Studying nonlinear dynamical systems through their state space behavior can be challenging, and one possible alternative is to analyze them via their associated Koopman operator. This turns the nonlinear problem into a linear,…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…
We present a sparse sensing framework based on Dynamic Mode Decomposition (DMD) to identify flow regimes and bifurcations in large-scale thermo-fluid systems. Motivated by real-time sensing and control of thermal-fluid flows in buildings…
Kalman filters are widely used for object tracking, where process and measurement noise are usually considered accurately known and constant. However, the exact known and constant assumptions do not always hold in practice. For example,…