相关论文: Fast multi-dimensional scattered data approximatio…
A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of…
The method of the fundamental solutions (MFS) is used to construct an approximate solution for a partial differential equation in a bounded domain. It is demonstrated by combining the fundamental solutions shifted to the points outside the…
An efficient numerical method is proposed for computing the Dirichlet-to-Neumann (DtN) map associated with the exterior Dirichlet problem for the two-dimensional Helmholtz equation with an inhomogeneous term. The exterior solution is…
Fractional PDEs involving the fractional Laplacian on bounded domains are challenging because of hypersingular nonlocal kernels, exterior Dirichlet constraints, reduced boundary regularity, and the high computational cost in high…
We present a novel approach to hard-constrain Neumann boundary conditions in physics-informed neural networks (PINNs) using Fourier feature embeddings. Neumann boundary conditions are used to described critical processes in various…
A fast and reliable algorithm for the optimal interpolation of scattered data on the torus by multivariate trigonometric polynomials is presented. The algorithm is based on a variant of the conjugate gradient method in combination with the…
In the high-dimensional data setting, the sample covariance matrix is singular. In order to get a numerically stable and positive definite modification of the sample covariance matrix in the high-dimensional data setting, in this paper we…
Our objective is to calculate the derivatives of data corrupted by noise. This is a challenging task as even small amounts of noise can result in significant errors in the computation. This is mainly due to the randomness of the noise,…
In this paper, a high-order exponential scheme is developed to solve the 1D unsteady convection-diffusion equation with Neumann boundary conditions. The present method applies fourth-order compact exponential difference scheme in spatial…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem…
In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…
We consider the numerical solution of time-harmonic acoustic scattering by obstacles with uncertain geometries for Dirichlet, Neumann, impedance and transmission boundary conditions. In particular, we aim to quantify diffracted fields…
This paper aims to investigate the distributed stochastic optimization problems on compact embedded submanifolds (in the Euclidean space) for multi-agent network systems. To address the manifold structure, we propose a distributed…
We construct least squares formulations of PDEs with inhomogeneous essential boundary conditions, where boundary residuals are not measured in unpractical fractional Sobolev norms, but which formulations nevertheless are shown to yield a…
We introduce a Fourier-based fast algorithm for Gaussian process regression in low dimensions. It approximates a translationally-invariant covariance kernel by complex exponentials on an equispaced Cartesian frequency grid of $M$ nodes.…
The complex Helmholtz equation $(\Delta + k^2)u=f$ (where $k\in{\mathbb R},u(\cdot),f(\cdot)\in{\mathbb C}$) is a mainstay of computational wave simulation. Despite its apparent simplicity, efficient numerical methods are challenging to…
We develop a unified nonparametric framework for sharp partial identification and inference on inequality indices when the data contain coarsened observations of the variable of interest. We characterize the extremal allocations for all…
This paper studies two structured approximation problems: (1) Recovering a corrupted low-rank Toeplitz matrix and (2) recovering the range of a Fourier matrix from a single observation. Both problems are computationally challenging because…