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Wasserstein gradient and Hamiltonian flows have emerged as essential tools for modeling complex dynamics in the natural sciences, with applications ranging from partial differential equations (PDEs) and optimal transport to quantum…

This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…

This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…

We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…

We developed fast direct solver for 3D Helmholtz and Maxwell equations in layered medium. The algorithm is based on the ideas of cyclic reduction for separable matrices. For the grids with major uniform part (within the survey domain in the…

In this article, we propose a strategy for the active manipulation of scalar Helmholtz fields in bounded near field regions of an active source while maintaining desired radiation patterns in prescribed far field directions. This control…

In this paper, new boundary differential equations for the two-dimensional exterior scattering problem have been derived. It has been shown that the Helmholtz equation can be reduced to an inhomogeneous Bessel's equation in a body-fitted…

We propose a fast method for high order approximation of potentials of the Helmholtz type operator Delta+kappa^2 over hyper-rectangles in R^n. By using the basis functions introduced in the theory of approximate approximations, the cubature…

This contribution presents substantial computational advancements to compare measures even with varying masses. Specifically, we utilize the nonequispaced fast Fourier transform to accelerate the radial kernel convolution in unbalanced…

We develop efficient and high-order accurate solvers for the Helmholtz equation on complex geometry. The schemes are based on the WaveHoltz algorithm which computes solutions of the Helmholtz equation by time-filtering solutions of the wave…

Variational quantum algorithms are one of the most promising methods that can be implemented on noisy intermediate-scale quantum (NISQ) machines to achieve a quantum advantage over classical computers. This article describes the use of a…

The aim of this paper is to extend the method of improving cloaking structures in the conductivity to scattering problems. We construct very effective near-cloaking structures for the scattering problem at a fixed frequency. These new…

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…

We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…

This paper proposes a fast multi-band image fusion algorithm, which combines a high-spatial low-spectral resolution image and a low-spatial high-spectral resolution image. The well admitted forward model is explored to form the likelihoods…

Subspace clustering methods have been widely studied recently. When the inputs are 2-dimensional (2D) data, existing subspace clustering methods usually convert them into vectors, which severely damages inherent structures and relationships…

In this paper we describe a methodology for tailoring the design of metamaterial dielectric resonators, which represent a promising path toward low-loss metamaterials at optical frequencies. We first describe a procedure to decompose the…

Fast and high-order accurate algorithms for three dimensional elastic scattering are of great importance when modeling physical phenomena in mechanics, seismic imaging, and many other fields of applied science. In this paper, we develop a…

This paper deals with solving the 2D Helmholtz equation on non-parametric domains, leveraging a physics-informed neural operator network based on the DeepONet framework. We consider a 2D square domain with an inclusion of arbitrary boundary…

The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…