Related papers: A Dual-space Multilevel Kernel-splitting Framework…
This article presents a new high-order accurate algorithm for finding a particular solution to a linear, constant-coefficient partial differential equation (PDE) by means of a convolution of the volumetric source function with the Green's…
A variety of problems in computational physics and engineering require the convolution of the heat kernel (a Gaussian) with either discrete sources, densities supported on boundaries, or continuous volume distributions. We present a unified…
Hyperspectral imagery is rich in spatial and spectral information. Using 3D-CNN can simultaneously acquire features of spatial and spectral dimensions to facilitate classification of features, but hyperspectral image information spectral…
A multilevel kernel-based interpolation method, suitable for moderately high-dimensional function interpolation problems, is proposed. The method, termed multilevel sparse kernel-based interpolation (MLSKI, for short), uses both level-wise…
Extreme learning machines (ELMs), which preset hidden layer parameters and solve for last layer coefficients via a least squares method, can typically solve partial differential equations faster and more accurately than Physics Informed…
As vast databases of chemical identities become increasingly available, the challenge shifts to how we effectively explore and leverage these resources to study molecular properties. This paper presents an active learning approach for…
It is well accepted that acquiring downlink channel state information in frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems is challenging because of the large overhead in training and feedback. In this…
We discuss efficient algorithms for the accurate forward and reverse evaluation of the discrete Fourier-Bessel transform (dFBT) as numerical tools to assist in the 2D polar convolution of two radially symmetric functions, relevant, e.g., to…
We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…
Point cloud processing is a challenging task due to its sparsity and irregularity. Prior works introduce delicate designs on either local feature aggregator or global geometric architecture, but few combine both advantages. We propose…
A space-time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value…
When the data is distributed across multiple servers, lowering the communication cost between the servers (or workers) while solving the distributed learning problem is an important problem and is the focus of this paper. In particular, we…
Kernel fusion is a popular and effective approach for combining multiple features that characterize different aspects of data. Traditional approaches for Multiple Kernel Learning (MKL) attempt to learn the parameters for combining the…
The Helmholtz equation is fundamental to wave modeling in acoustics, electromagnetics, and seismic imaging, yet high-frequency regimes remain challenging due to the ``pollution effect''. We propose FD-MGDL, an adaptive framework integrating…
Recently, a versatile limited feedback scheme based on a Gaussian mixture model (GMM) was proposed for frequency division duplex (FDD) systems. This scheme provides high flexibility regarding various system parameters and is applicable to…
While deep learning algorithms demonstrate a great potential in scientific computing, its application to multi-scale problems remains to be a big challenge. This is manifested by the "frequency principle" that neural networks tend to learn…
Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…
Cell segmentation in single-shot quantitative phase microscopy (ssQPM) faces challenges from traditional thresholding methods that are sensitive to noise and cell density, while deep learning approaches using simple channel concatenation…
We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real-time using higher-order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this…
Work presented in this paper describes a general algorithm and its finite element implementation for performing concurrent multiple sub-domain simulations in linear structural dynamics. Using this approach one can solve problems in which…