Related papers: Towards an Adaptive Dynamic Mode Decomposition
We present a data-driven model predictive control (MPC) framework for systems with high state-space dimensionalities. This work is motivated by the need to exploit sensor data that appears in the form of images (e.g., 2D or 3D spatial…
This note proposes a simple and general framework of dynamic mode decomposition (DMD) and a mode selection for large datasets. The proposed framework explicitly introduces a preconditioning step using an incremental proper orthogonal…
The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…
Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…
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…
There is a broad need in the neuroscience community to understand and visualize large-scale recordings of neural activity, big data acquired by tens or hundreds of electrodes simultaneously recording dynamic brain activity over minutes to…
Simulating dynamics of open quantum systems is sometimes a significant challenge, despite the availability of various exact or approximate methods. Particularly when dealing with complex systems, the huge computational cost will largely…
Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…
Koopman operator theory shows how nonlinear dynamical systems can be represented as an infinite-dimensional, linear operator acting on a Hilbert space of observables of the system. However, determining the relevant modes and eigenvalues of…
Any autonomous nonlinear dynamical system can be viewed as a superposition of infinitely many linear processes, through the so-called Koopman mode decomposition. Its data-driven approximation- Dynamic Mode Decomposition (DMD)- has been…
A data-driven and equation-free approach is proposed and discussed to model ships maneuvers in waves, based on the dynamic mode decomposition (DMD). DMD is a dimensionality-reduction/reduced-order modeling method, which provides a linear…
Modern computational science and engineering applications are being improved by the advances in scientific machine learning. Data-driven methods such as Dynamic Mode Decomposition (DMD) can extract coherent structures from spatio-temporal…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
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…
Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear, computationally intensive, and can be difficult to interpret, while often only…
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…
This paper discusses the application of Dynamic Mode Decomposition (DMD) to the extraction of modal properties of linear mechanical systems, i.e., experimental modal analysis (EMA). First, theoretical background of the DMD is briefly…
Dynamic mode decomposition (DMD) and its variants have emerged as popular methods for the post-processing of fluid dynamics' simulations in order to visualize dominant coherent structures and to reduce the practical degrees of freedom to a…
In this work, we present a method which determines optimal multi-step dynamic mode decomposition (DMD) models via entropic regression, which is a nonlinear information flow detection algorithm. Motivated by the higher-order DMD (HODMD)…
Reconstruction-based anomaly detection models achieve their purpose by suppressing the generalization ability for anomaly. However, diverse normal patterns are consequently not well reconstructed as well. Although some efforts have been…