Related papers: Nonlinear mode decomposition with convolutional ne…

We introduce the Circular Directional Flow Decomposition (CDFD), a new framework for analyzing circularity in weighted directed networks. CDFD separates flow into two components: a circular (divergence-free) component and an acyclic…

Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in…

We present a single-layer feedforward artificial neural network architecture trained through a supervised learning approach for the deconvolution of flow variables from their coarse grained computations such as those encountered in large…

Time-frequency analysis is an important and challenging task in many applications. Fourier and wavelet analysis are two classic methods that have achieved remarkable success in many fields. However, they also exhibit limitations when…

We develop a unified model, known as MgNet, that simultaneously recovers some convolutional neural networks (CNN) for image classification and multigrid (MG) methods for solving discretized partial differential equations (PDEs). This model…

This paper proposes a mode multigrid (MMG) method, and applies it to accelerate the convergence of the steady state flow on unstructured grids. The dynamic mode decomposition (DMD) technique is used to analyze the convergence process of…

Deep learning can accurately represent sub-grid-scale convective processes in climate models, learning from high resolution simulations. However, deep learning methods usually lack interpretability due to large internal dimensionality,…

The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…

Identifying the heterogeneous conductivity field and reconstructing the contaminant release history are key aspects of subsurface remediation. Achieving these two goals with limited and noisy hydraulic head and concentration measurements is…

A novel convolution neural network model, abbreviated NL-CNN is proposed, where nonlinear convolution is emulated in a cascade of convolution + nonlinearity layers. The code for its implementation and some trained models are made publicly…

Modal decomposition techniques are showing a fast growth in popularity for their good properties as data-driven tools. There are several modal decomposition techniques, yet Proper Orthogonal Decomposition (POD) and Dynamic Mode…

Intrinsic image decomposition is the process of recovering the image formation components (reflectance and shading) from an image. Previous methods employ either explicit priors to constrain the problem or implicit constraints as formulated…

Electroencephalogram (EEG) has become increasingly popular in driver fatigue monitoring systems. Several decomposition methods have been attempted to analyze the EEG signals that are complex, nonlinear and non-stationary and improve the EEG…

Domain shift is a problem commonly encountered when developing automated histopathology pipelines. The performance of machine learning models such as convolutional neural networks within automated histopathology pipelines is often…

In end-to-end optimized learned image compression, it is standard practice to use a convolutional variational autoencoder with generalized divisive normalization (GDN) to transform images into a latent space. Recently, Operational Neural…

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…

Deep Learning research is advancing at a fantastic rate, and there is much to gain from transferring this knowledge to older fields like Computational Fluid Dynamics in practical engineering contexts. This work compares state-of-the-art…

Liquid-droplet coalescence and the mergers of liquid lenses are problems of great practical and theoretical interest in fluid dynamics and the statistical mechanics of multi-phase flows. During such mergers, there is an interesting and…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…