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Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is further challenged if each component has an oscillatory pattern,…
The Dynamic Mode Decomposition (DMD) is a Koopman-based algorithm that straightforwardly isolates individual mechanisms from the compound morphology of direct measurement. However, many may be perplexed by the messages the DMD structures…
Functional magnetic resonance imaging (fMRI) is a notoriously noisy measurement of brain activity because of the large variations between individuals, signals marred by environmental differences during collection, and spatiotemporal…
Empirically observed time series in physics, biology, or medicine, are commonly generated by some underlying dynamical system (DS) which is the target of scientific interest. There is an increasing interest to harvest machine learning…
The DMD (Dynamic Mode Decomposition) method has attracted widespread attention as a representative modal-decomposition method and can build a predictive model. However, the DMD may give predicted results that deviate from physical reality…
We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…
In this paper we present a Fourier feature based deep domain decomposition method (F-D3M) for partial differential equations (PDEs). Currently, deep neural network based methods are actively developed for solving PDEs, but their efficiency…
Currently, it is challenging to investigate aneurismal hemodynamics based on current in-vivo data such as Magnetic Resonance Imaging or Computed Tomography due to the limitations in both spatial and temporal resolutions. In this work, we…
Models of misfolded proteins (MP) aim at discovering the bio-mechanical propagation properties of neurological diseases (ND) by identifying plausible associated dynamical systems. Solving these systems along the full disease trajectory is…
The decomposition of non-stationary signals is an important and challenging task in the field of signal time-frequency analysis. In the recent two decades, many signal decomposition methods led by the empirical mode decomposition, which was…
Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…
Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which…
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…
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…
Dynamic functional connectivity (dFC) using resting-state functional magnetic resonance imaging (rs-fMRI) is an advanced technique for capturing the dynamic changes of neural activities, and can be very useful in the studies of brain…
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…
Due to the diversity of brain anatomy and the scarcity of annotated data, supervised anomaly detection for brain MRI remains challenging, driving the development of unsupervised anomaly detection (UAD) approaches. Current UAD methods…
We propose a new framework for manifold denoising based on processing in the graph Fourier frequency domain, derived from the spectral decomposition of the discrete graph Laplacian. Our approach uses the Spectral Graph Wavelet transform in…
Objective While Alzheimer's disease (AD) and frontotemporal dementia (FTD) show some common memory deficits, these two disorders show partially overlapping complex spatiotemporal patterns of neural dynamics. The objective of this study is…
Magnetoencephalography (MEG) is an important noninvasive, nonhazardous technology for functional brain mapping, measuring the magnetic fields due to the intracellular neuronal current flow in the brain. However, most often, the inherent…