Related papers: Complex Orthogonal Decomposition (C.O.D.) using Py…
Most model reduction methods reduce the state dimension and then temporally evolve a set of coefficients that encode the state in the reduced representation. In this paper, we instead employ an efficient representation of the entire…
The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…
In the present work, we introduce a data-driven approach to enhance the accuracy of non-intrusive Reduced Order Models (ROMs). In particular, we focus on ROMs built using Proper Orthogonal Decomposition (POD) in an under-resolved and…
Out-of-Distribution (OOD) detection requires sensitivity to subtle shifts without overreacting to natural In-Distribution (ID) diversity. However, from the viewpoint of detection granularity, global representation inevitably suppress local…
Purpose. Localizing structures and estimating the motion of a specific target region are common problems for navigation during surgical interventions. Optical coherence tomography (OCT) is an imaging modality with a high spatial and…
This study employs scientific machine learning to identify transient time series of dynamical systems near a fold bifurcation of periodic solutions. The unique aspect of this work is that a convolutional neural network (CNN) is trained with…
Ordinary Differential Equations (ODE) are used throughout science where the capture of rates of change in states is sought. While both pieces of commercial and open software exist to study such systems, their efficient and accurate usage…
In this paper we propose a multiscale method for the acoustic wave equation in highly oscillatory media. We use a higher-order extension of the localized orthogonal decomposition method combined with a higher-order time stepping scheme and…
Many real-world time series exhibit multiple seasonality with different lengths. The removal of seasonal components is crucial in numerous applications of time series, including forecasting and anomaly detection. However, many…
Dynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. Conceptually, DMD performs a…
We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We…
This thesis examines the empirical mode decomposition (EMD), a method for decomposing multicomponent signals, from a modern, both theoretical and practical, perspective. The motivation is to further formalize the concept and develop new…
Space-time multivectors in Clifford algebra (space-time algebra) and their application to nonlinear electrodynamics are considered. Functional product and infinitesimal operators for translation and rotation groups are introduced, where…
Numerical homogenization methods aim at providing appropriate coarse-scale approximations of solutions to (elliptic) partial differential equations that involve highly oscillatory coefficients. The localized orthogonal decomposition (LOD)…
In time series forecasting, effectively disentangling intricate temporal patterns is crucial. While recent works endeavor to combine decomposition techniques with deep learning, multiple frequencies may still be mixed in the decomposed…
The recent explosion in the availability of echosounder data from diverse ocean platforms has created unprecedented opportunities to observe the marine ecosystems at broad scales. However, the critical lack of methods capable of…
This work is concerned with the classical wave equation with a high-contrast coefficient in the spatial derivative operator. We first treat the periodic case, where we derive a new limit in the one-dimensional case. The behavior is…
Recent studies have shown convolutional neural networks (CNNs) can be trained to perform modal decomposition using intensity images of optical fields. A fundamental limitation of these techniques is that the modal phases can not be uniquely…
Orthogonal Matching Pursuit (OMP) has been a powerful method in sparse signal recovery and approximation. However, OMP suffers computational issues when the signal has a large number of non-zeros. This paper advances OMP and its extension…
Concurrent Speaker Detection (CSD), the task of identifying active speakers and their overlaps in an audio signal, is essential for various audio applications, including meeting transcription, speaker diarization, and speech separation.…