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As an extension of previous fourth-order compact gas kinetic scheme (GKS) on structured meshes (Ji et al. 2018), this work is about the development of a third-order compact GKS on unstructured meshes for the compressible Euler and…

Autoencoders have achieved great success in various computer vision applications. The autoencoder learns appropriate low dimensional image representations through the self-supervised paradigm, i.e., reconstruction. Existing studies mainly…

We present a method to reconstruct the initial linear-regime matter density field from the late-time non-linearly evolved density field in which we channel the output of standard first-order reconstruction to a convolutional neural network…

Different ways of implementing dimension-by-dimension CWENO reconstruction are discussed and the most efficient method is applied to develop a fourth order central scheme for multi-dimensional hyperbolic problems. Fourth order accuracy and…

The first partial boundary data complex geometrical optics based methods for electrical impedance tomography in three dimensions are developed, and tested, on simulated and experimental data. The methods provide good localization of targets…

In this paper, a simple and efficient third-order weighted essentially non-oscillatory (WENO) reconstruction is developed for three-dimensional flows, in which the idea of two-dimensional WENO-AO scheme on unstructured meshes…

Reconstructing photo-realistic large-scale scenes from images, for example at city scale, is a long-standing problem in computer graphics. Neural rendering is an emerging technique that enables photo-realistic image synthesis from…

We formulate a framework of polynomial diagrams, which are a generalisation of power diagrams (PDs) and anisotropic power diagrams (APDs) allowing for boundaries between cells to be algebraic curves of a prescribed degree. We show that they…

This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Non-oscillatory…

High-order gas-kinetic scheme (HGKS) has been well-developed in the past years. Abundant numerical tests including hypersonic flow, turbulence, and aeroacoustic problems, have been used to validate its accuracy, efficiency, and robustness.…

We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the…

We obtain upper bounds, independent of the ambient dimension, for the number of realizable zero-nonzero patterns and (over ordered fields) sign conditions of a finite family of polynomials $\mathcal P$ restricted to an algebraic subset $V$…

The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for…

In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…

Generation of 3D data by deep neural network has been attracting increasing attention in the research community. The majority of extant works resort to regular representations such as volumetric grids or collection of images; however, these…

Single-view 3D object reconstruction is a fundamental and challenging computer vision task that aims at recovering 3D shapes from single-view RGB images. Most existing deep learning based reconstruction methods are trained and evaluated on…

In this paper, we study the reconstruction of a bivariate function from weighted integrals along the edges of a triangular mesh, a problem of central importance in tomography, computer vision, and numerical approximation. Our approach…

This paper presents a novel method for the reconstruction of images from samples located at non-integer positions, called mesh. This is a common scenario for many image processing applications, such as super-resolution, warping or virtual…

In this paper we present a new algorithm based on a Cartesian mesh for the numerical approximation of kinetic models on complex geometry boundary. Due to the high dimensional property, numerical algorithms based on unstructured meshes for a…

We study end-to-end learning strategies for 3D shape inference from images, in particular from a single image. Several approaches in this direction have been investigated that explore different shape representations and suitable learning…