Related papers: Capturing the Diffusive Behavior of the Multiscale…

Transform and entropy models are the two core components in deep image compression neural networks. Most existing learning-based image compression methods utilize convolutional-based transform, which lacks the ability to model long-range…

We consider singularly perturbed convection-diffusion equations on one-dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling condition at inner vertices are…

Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…

Light-weight convolutional neural networks (CNNs) suffer performance degradation as their low computational budgets constrain both the depth (number of convolution layers) and the width (number of channels) of CNNs, resulting in limited…

Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…

A deep neural network is a parametrization of a multilayer mapping of signals in terms of many alternatively arranged linear and nonlinear transformations. The linear transformations, which are generally used in the fully connected as well…

In this work we first prove, by formal arguments, that the diffusion limit of nonlinear kinetic equations, where both the transport term and the turning operator are density-dependent, leads to volume-exclusion chemotactic equations. We…

In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and non-local diffusion is analyzed in the usual set-up for dynamical systems generated by differential equations with delay terms. This approach is…

Model compression methods are important to allow for easier deployment of deep learning models in compute, memory and energy-constrained environments such as mobile phones. Knowledge distillation is a class of model compression algorithm…

For multilayer structures, interfacial failure is one of the most important elements related to device reliability. For cohesive zone modelling, traction-separation relations represent the adhesive interactions across interfaces. However,…

In this paper, based on neural networks, we develop a data-driven model for extremely fast prediction of steady-state heat convection of a hot object with arbitrary complex geometry in a two-dimensional space. According to the governing…

We present a novel deep learning architecture in which the convolution operation leverages heterogeneous kernels. The proposed HetConv (Heterogeneous Kernel-Based Convolution) reduces the computation (FLOPs) and the number of parameters as…

In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain…

Energy-Dissipative Evolutionary Deep Operator Neural Network is an operator learning neural network. It is designed to seed numerical solutions for a class of partial differential equations instead of a single partial differential equation,…

Deep convolutional neural networks continue to advance the state-of-the-art in many domains as they grow bigger and more complex. It has been observed that many of the parameters of a large network are redundant, allowing for the…

In this paper, we investigate the joint device activity and data detection in massive machine-type communications (mMTC) with a one-phase non-coherent scheme, where data bits are embedded in the pilot sequences and the base station…

Convolutional Neural Networks (CNNs) have recently become a favored technique for image denoising due to its adaptive learning ability, especially with a deep configuration. However, their efficacy is inherently limited owing to their…

A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders with…

The Deep Operator Network (DeepONet) structure has shown great potential in approximating complex solution operators with low generalization errors. Recently, a sequential DeepONet (S-DeepONet) was proposed to use sequential learning models…

In this work, we propose an asymptotic preserving scheme for a non-linear kinetic reaction-transport equation, in the regime of sharp interface. With a non-linear reaction term of KPP-type, a phenomenon of front propagation has been proved…