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In this paper we investigate the stationary profiles of a nonlinear Fokker-Planck equation with small diffusion and nonlinear in- and outflow boundary conditions. We consider corridors with a bottleneck whose width has a global…

The Fokker--Planck Equation can be used in a partially-coherent imaging context to model the evolution of the intensity of a paraxial x-ray wave field with propagation. This forms a natural generalisation of the transport-of-intensity…

This paper investigates deep neural network (DNN) compression from the perspective of compactly representing and storing trained parameters. We explore the previously overlooked opportunity of cross-layer architecture-agnostic…

This paper has proposed a new baseline deep learning model of more benefits for image classification. Different from the convolutional neural network(CNN) practice where filters are trained by back propagation to represent different…

DeepONet has recently been proposed as a representative framework for learning nonlinear mappings between function spaces. However, when it comes to approximating solution operators of partial differential equations (PDEs) with…

Highly localized kernels constructed by orthogonal polynomials have been fundamental in recent development of approximation and computational analysis on the unit sphere, unit ball and several other regular domains. In this work we first…

Based on a microcanonical picture that maps the steady-state quantum transport process to a drain-to-source excitation, we develop a constrained-search density functional formalism for finite-bias quantum transport calculations. By…

Deep neural networks (DNNs) have demonstrated their effectiveness in a wide range of computer vision tasks, with the state-of-the-art results obtained through complex and deep structures that require intensive computation and memory.…

Regression with non-Euclidean responses -- e.g., probability distributions, networks, symmetric positive-definite matrices, and compositions -- has become increasingly important in modern applications. In this paper, we propose deep…

The large computing and memory cost of deep neural networks (DNNs) often precludes their use in resource-constrained devices. Quantizing the parameters and operations to lower bit-precision offers substantial memory and energy savings for…

Precise boundary segmentation of volumetric images is a critical task for image-guided diagnosis and computer-assisted intervention, especially for boundary confusion in clinical practice. However, U-shape networks cannot effectively…

Precise boundary annotations of image regions can be crucial for downstream applications which rely on region-class semantics. Some document collections contain densely laid out, highly irregular and overlapping multi-class region instances…

Traditional numerical methods, such as the finite element method and finite volume method, adress partial differential equations (PDEs) by discretizing them into algebraic equations and solving these iteratively. However, this process is…

In this paper, we introduce a technique to estimate measured BRDFs from a sparse set of samples. Our approach offers accurate BRDF reconstructions that are generalizable to new materials. This opens the door to BDRF reconstructions from a…

To correct for respiratory motion in PET imaging, an interpretable and unsupervised deep learning technique, FlowNet-PET, was constructed. The network was trained to predict the optical flow between two PET frames from different breathing…

We propose methods to train convolutional neural networks (CNNs) with both binarized weights and activations, leading to quantized models that are specifically friendly to mobile devices with limited power capacity and computation…

The effect of uncertainties and noise on a quantity of interest (model output) is often better described by its probability density function (PDF) than by its moments. Although density estimation is a common task, the adequacy of…

The next-generation CMB experiments are expected to constrain the tensor-to-scalar ratio $r$ with high precision. Delensing is an important process as the observed CMB $B$-mode polarization that contains the primordial tensor perturbation…

For the task of subdecimeter aerial imagery segmentation, fine-grained semantic segmentation results are usually difficult to obtain because of complex remote sensing content and optical conditions. Recently, convolutional neural networks…

We deal with the solution of the forward problem for high-dimensional parabolic PDEs with random feature (projection) neural networks (RFNNs). We first prove that there exists a single-hidden layer neural network with randomized…