Related papers: Attenuation Compensation in Lossy Media via the Wa…
We introduce a reduced order model (ROM) methodology for inverse electromagnetic wave scattering in layered lossy media, using data gathered by an antenna which generates a probing wave and measures the time resolved reflected wave. We…
In this work, we consider wave propagation in materials characterized by nonlinear properties or damage. To accelerate the simulations of the resulting high-dimensional problems, we apply model order reduction methods. Depending on the…
The problem of reconstructing the spatial support of an extended radiating electric current source density in a lossy dielectric medium from transient boundary measurements of the electric fields is studied. A time reversal algorithm is…
Pseudo-Hermitian operators can be used in modeling electromagnetic wave propagation in stationary lossless media. We extend this method to a class of non-dispersive anisotropic media that may display loss or gain. We explore three concrete…
Vision modeling has advanced rapidly with Transformers, whose attention mechanisms capture visual dependencies but lack a principled account of how semantic information propagates spatially. We revisit this problem from a wave-based…
Using the transfer-matrix approach and solving time-domain differential equations, we analyze the loss compensation mechanism in multilayer systems composed of an absorbing transparent conductive oxide and dielectric doped with an active…
Attenuation in acoustic waveguides with lossy impedance boundary conditions are associated with non-Hermitian and non-normal operators. This subject has been extensively studied in fundamental and engineering research, and it has been…
The performance of Schwarz Waveform Relaxation is critically dependent on the choice of transmission conditions. While classical absorbing conditions work well for wave propagation, they prove insufficient for damped wave equations,…
A seismic wavefield reconstruction framework based on compressed sensing using the data-driven reduced-order model (ROM) is proposed and its characteristics are investigated through numerical experiments. The data-driven ROM is generated…
We introduce a novel approach to waveform inversion, based on a data driven reduced order model (ROM) of the wave operator. The presentation is for the acoustic wave equation, but the approach can be extended to elastic or electromagnetic…
Exponential decay estimates of a general linear weakly damped wave equation are studied with decay rate lying in a range. Based on the $C^0$-conforming finite element method to discretize spatial variables keeping temporal variable…
We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…
We give an exact application of a recently developed, operator-based theory of wave propagation in dispersive, time-varying media. Using this theory we find that the usual symmetry of complex conjugation plus changing the sign of the…
Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…
This paper outlines an end-to-end optimized lossy image compression framework using diffusion generative models. The approach relies on the transform coding paradigm, where an image is mapped into a latent space for entropy coding and, from…
We introduce a novel nonlinear imaging method for the acoustic wave equation based on data-driven model order reduction. The objective is to image the discontinuities of the acoustic velocity, a coefficient of the scalar wave equation from…
Dissipation is a ubiquitous phenomenon in dynamical systems encountered in nature because no finite system is fully isolated from its environment. In optical systems, a key challenge facing any technological application has traditionally…
In this paper we present a reduced basis method which yields structure-preservation and a tight a posteriori error bound for the simulation of the damped wave equations on networks. The error bound is based on the exponential decay of the…
In modern communication systems such as the Internet, random losses of information can be mitigated by oversampling the source. This is equivalent to expanding the source using overcomplete systems of vectors (frames), as opposed to the…
Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…