Related papers: Neural Mode Decomposition based on Fourier neural …

A novel unsupervised deep learning method is developed to identify individual-specific large scale brain functional networks (FNs) from resting-state fMRI (rsfMRI) in an end-to-end learning fashion. Our method leverages deep Encoder-Decoder…

This paper concerns the study of direct numerical simulation (DNS) data of a wavepacket in laminar turbulent transition in a Blasius boundary layer. The decomposition of this wavepacket into a set of "modes" (a basis that spans an…

This work introduces a hybrid approach that combines the Proper Generalised Decomposition (PGD) with deep learning techniques to provide real-time solutions for parametrised mechanics problems. By relying on a tensor decomposition, the…

Rough surface lubrication simulation is crucial for designing and optimizing tribological performance. Despite the growing application of Physical Information Neural Networks (PINNs) in hydrodynamic lubrication analysis, their use has been…

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…

There is an increasing interest in applying deep learning to 3D mesh segmentation. We observe that 1) existing feature-based techniques are often slow or sensitive to feature resizing, 2) there are minimal comparative studies and 3)…

Modular addition tasks serve as a useful test bed for observing empirical phenomena in deep learning, including the phenomenon of \emph{grokking}. Prior work has shown that one-layer transformer architectures learn Fourier Multiplication…

Spectral clustering, as a popular tool for data clustering, requires an eigen-decomposition step on a given affinity to obtain the spectral embedding. Nevertheless, such a step suffers from the lack of generalizability and scalability.…

The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency…

Multi-sensor clues have shown promise for object segmentation, but inherent noise in each sensor, as well as the calibration error in practice, may bias the segmentation accuracy. In this paper, we propose a novel approach by mining the…

The intrinsic mode function (IMF) provides adaptive function bases for nonlinear and non-stationary time series data. A fast convergent iterative method is introduced in this paper to find the IMF components of the data, the method is…

Functional brain dynamics is supported by parallel and overlapping functional network modes that are associated with specific neural circuits. Decomposing these network modes from fMRI data and finding their temporal characteristics is…

Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and the growth rates of physically significant modes. In this paper, we…

In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression…

Modal decomposition techniques are important tools for the analysis of unsteady flows and, in order to provide meaningful insights with respect to coherent structures and their characteristic frequencies, the modes must possess a robust…

The Empirical Mode Decomposition (EMD) provides a tool to characterize time series in terms of its implicit components oscillating at different time-scales. We apply this decomposition to intraday time series of the following three…

We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…

Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…

Large scale nonlinear classification is a challenging task in the field of support vector machine. Online random Fourier feature map algorithms are very important methods for dealing with large scale nonlinear classification problems. The…

Recent years have witnessed the unprecedented rising of time series from almost all kindes of academic and industrial fields. Various types of deep neural network models have been introduced to time series analysis, but the important…