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Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…
We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…
Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in…
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous…
We propose a divide-and-conquer (DAC) algorithm for constrained convex optimization over networks, where the global objective is the sum of local objectives attached to individual agents. The algorithm is fully distributed: each iteration…
We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations with multiplicative noise. Our abstract framework can be applied to formulate a non-iterative domain decomposition approach. Such…
A novel, non-learning-based, saliency-aware, shape-cognizant correspondence determination technique is proposed for matching image pairs that are significantly disparate in nature. Images in the real world often exhibit high degrees of…
In this paper, the authors devise a new discretization scheme for div-curl systems defined in connected domains with heterogeneous media by using the weak Galerkin finite element method. Two types of boundary value problems are considered…
Image segmentation, one of the most critical vision tasks, has been studied for many years. Most of the early algorithms are unsupervised methods, which use hand-crafted features to divide the image into many regions. Recently, owing to the…
Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and…
This work introduces a novel Trefftz Continuous Galerkin (TCG) method for 2D Helmholtz problems based on evanescent plane waves (EPWs). We construct a new globally-conforming discrete space, departing from standard discontinuous Trefftz…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations,…
No existing spherical convolutional neural network (CNN) framework is both computationally scalable and rotationally equivariant. Continuous approaches capture rotational equivariance but are often prohibitively computationally demanding.…
The radiative transfer equation is a fundamental equation in transport theory and applications, which is a 5-dimensional PDE in the stationary one-velocity case, leading to great difficulties in numerical simulation. To tackle this…
Convergence analysis is a fundamental research topic in evolutionary computation (EC). The commonly used analysis method models the EC algorithm as a homogeneous Markov chain for analysis, which is not always suitable for different EC…
The randomized coordinate descent (RCD) method is a classical algorithm with simple, lightweight iterations that is widely used for various optimization problems, including the solution of positive semidefinite linear systems. As a linear…
In recent years, there has been an increasing interest in using deep learning and neural networks to tackle scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods, such…
In this paper, two high order complex contour discretization methods are proposed to simulate wave propagation in locally perturbed periodic closed waveguides. As is well known the problem is not always uniquely solvable due to the…
In this paper, the paradigm of sphere decoding (SD) based on lattice Gaussian distribution is studied, where the sphere radius $D>0$ in the sense of Euclidean distance is characterized by the initial pruning size $K>1$, the standard…