Related papers: Wavefield solutions from machine learned functions
In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate…
The accurate estimation of the state of complex uncertain physical systems requires reconciling theoretical models, with inherent imperfections, with noisy experimental data. In this work, we propose an effective hybrid approach that…
We introduce an efficient neural network (NN) architecture for classifying wave functions in terms of their localization. Our approach integrates a versatile quantum phase space parametrization leading to a custom 'quantum' NN, with the…
A recurring task in image processing, approximation theory, and the numerical solution of partial differential equations is to reconstruct a piecewise-smooth real-valued function f(x) in multiple dimensions from its truncated Fourier…
A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…
Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…
Passive imaging involves recording waves generated by uncontrolled, random sources and utilizing correlations of such waves to image the medium through which they propagate. In this paper, we focus on passive inverse obstacle scattering…
We examine the use of the Dirichlet-to-Neumann coarse space within an additive Schwarz method to solve the Helmholtz equation in 2D. In particular, we focus on the selection of how many eigenfunctions should go into the coarse space. We…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…
We present a variational neural network approach for solving quantum field theories in the field basis, focusing on the free Klein-Gordon model formulated in momentum space. While recent studies have explored neural-network-based…
To address the ill-posedness of the inverse source problem for the one-dimensional stochastic Helmholtz equations without attenuation, this study develops a novel computational framework designed to mitigate this inherent challenge at the…
We study a stationary scattering problem related to the nonlinear Helmholtz equation $-\Delta u - k^2 u = f(x,u) \ \ \text{in $\mathbb{R}^N$,}$ where $N \ge 3$ and $k>0$. For a given incident free wave $\varphi \in L^\infty(\mathbb{R}^N)$,…
Current neural operators often struggle to generalize to complex, out-of-distribution conditions, limiting their ability in seismic wavefield representation. To address this, we propose a generative neural operator (GNO) that leverages…
Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can be used for a variety of…
This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…
The random vector functional link (RVFL) network is well-regarded for its strong generalization capabilities in the field of machine learning. However, its inherent dependencies on the square loss function make it susceptible to noise and…
The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…
There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine…
We consider the solution of a scalar Helmholtz equation where the potential (or index) takes two positive values, one inside a disk of radius $\epsilon$ and another one outside. We derive sharp estimates of the size of the scattered field…
This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…