Related papers: Featurizing Koopman Mode Decomposition For Robust …

This paper develops data-driven methods to identify eigenfunctions of the Koopman operator associated to a dynamical system and subspaces that are invariant under the operator. We build on Extended Dynamic Mode Decomposition (EDMD), a…

Factorization Machines (FMs) are effective in incorporating side information to overcome the cold-start and data sparsity problems in recommender systems. Traditional FMs adopt the inner product to model the second-order interactions…

We introduce a class of relative error decomposition measures that are well-suited for the analysis of shocks in nonlinear dynamic models. They include the Forecast Relative Error Decomposition (FRED), Forecast Error Kullback 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…

In this manuscript, we propose a multiclass data description model based on kernel Mahalanobis distance (MDD-KM) with self-adapting hyperparameter setting. MDD-KM provides uncertainty quantification and can be deployed to build…

In this paper, we introduce a novel approach to centroidal state estimation, which plays a crucial role in predictive model-based control strategies for dynamic legged locomotion. Our approach uses the Koopman operator theory to transform…

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves…

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…

The framework of Koopman operator theory is discussed along with its connections to Dynamic Mode Decomposition (DMD) and (Kernel) Extended Dynamic Mode Decomposition (EDMD). This paper provides a succinct overview with consistent notation.…

For many machine learning algorithms such as $k$-Nearest Neighbor ($k$-NN) classifiers and $ k $-means clustering, often their success heavily depends on the metric used to calculate distances between different data points. An effective…

In this work, the application of the multi-dimensional higher order dynamic mode decomposition (HODMD) is proposed for the first time to analyse combustion databases. In particular, HODMD has been adapted and combined with other…

Accurate spatiotemporal forecasting is critical for numerous complex systems but remains challenging due to complex volatility patterns and spectral entanglement in conventional graph neural networks (GNNs). While decomposition-integrated…

This paper presents DeepKalPose, a novel approach for enhancing temporal consistency in monocular vehicle pose estimation applied on video through a deep-learning-based Kalman Filter. By integrating a Bi-directional Kalman filter strategy…

We report a new approach to estimating power system inertia directly from time-series data on power system dynamics. The approach is based on the so-called Koopman Mode Decomposition (KMD) of such dynamic data, which is a nonlinear…

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)…

In recent years, there has been a growing interest in data-driven approaches in physics, such as extended dynamic mode decomposition (EDMD). The EDMD algorithm focuses on nonlinear time-evolution systems, and the constructed Koopman matrix…

This paper presents a Koopman lifting linearization method that is applicable to nonlinear dynamical systems having both stable and unstable regions. It is known that DMD and other standard data-driven methods face a fundamental difficulty…

Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…

Koopman mode decomposition and tensor component analysis (also known as CANDECOMP/PARAFAC or canonical polyadic decomposition) are two popular approaches of decomposing high dimensional data sets into low dimensional modes that capture 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…