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Balanced data is required for deep neural networks (DNNs) when learning to perform power system stability assessment. However, power system measurement data contains relatively few events from where power system dynamics can be learnt. To…
Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…
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…
Dynamic Mode Decomposition (DMD) is a useful tool to effectively extract the dominant dynamic flow structure from a unsteady flow field. However, DMD requires massive computational resources with respect to memory consumption and the usage…
Operational forecasting centers are investing in decadal (1-10 year) forecast systems to support long-term decision making for a more climate-resilient society. One method that has previously been employed is the Dynamic Mode Decomposition…
Dynamic magnetic resonance imaging (MRI) plays an indispensable role in cardiac diagnosis. To enable fast imaging, the k-space data can be undersampled but the image reconstruction poses a great challenge of high-dimensional processing.…
Elastic topological states have been receiving increased intention in numerous scientific and engineering fields due to their defect-immune nature, resulting in applications of vibration control and information processing. Here, we present…
Decoding behavior, perception, or cognitive state directly from neural signals has applications in brain-computer interface research as well as implications for systems neuroscience. In the last decade, deep learning has become the…
Dendritic spines are key structural components of excitatory synapses in the brain. Given the size of dendritic spines provides a proxy for synaptic efficacy, their detection and tracking across time is important for studies of the neural…
Modal decomposition techniques, such as Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Singular Spectrum Analysis (SSA), have advanced time-frequency signal analysis since the early 21st century. These methods…
Deep metric learning maps visually similar images onto nearby locations and visually dissimilar images apart from each other in an embedding manifold. The learning process is mainly based on the supplied image negative and positive training…
Sleep spindles are neurophysiological phenomena that appear to be linked to memory formation and other functions of the central nervous system, and that can be observed in electroencephalographic recordings (EEG) during sleep. Manually…
The state-space models (SSMs) are widely utilized in the analysis of time-series data. SSMs rely on an explicit definition of the state and observation processes. Characterizing these processes is not always easy and becomes a modeling…
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…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
We present an extension of optimal mode decomposition (OMD) for autonomous systems to systems with controls. The extension is developed along the same lines as the extension of dynamic mode decomposition (DMD) to DMD with control (DMDc).…
Modal decomposition methods are important for characterizing the low-dimensional dynamics of complex systems, including turbulent flows. Different methods have varying data requirements and produce modes with different properties. Spectral…
Graph Neural Networks (GNNs) have emerged as fundamental tools for a wide range of prediction tasks on graph-structured data. Recent studies have drawn analogies between GNN feature propagation and diffusion processes, which can be…
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…
Brain-wide recordings of large-scale networks of neurons now provide an unprecedented view into how the brain drives behavior. However, brain activity contains both information directly related to behavior as well as the potential for many…