Zobrazeno 1 - 10
of 56
pro vyhledávání: '"Zaslavsky, Mikhail"'
Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to the measurement arrays with reciprocally collocated transmitters a
Externí odkaz:
http://arxiv.org/abs/2112.09634
Data-driven reduced order models (ROMs) are combined with the Lippmann-Schwinger integral equation to produce a direct nonlinear inversion method. The ROM is viewed as a Galerkin projection and is sparse due to Lanczos orthogonalization. Embedding in
Externí odkaz:
http://arxiv.org/abs/2101.12317
Autor:
Borcea, Liliana, Druskin, Vladimir, Mamonov, Alexander V., Zaslavsky, Mikhail, Zimmerling, Jörn
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 models unknown
Externí odkaz:
http://arxiv.org/abs/1910.13014
We generate data-driven reduced order models (ROMs) for inversion of the one and two dimensional Schr\"odinger equation in the spectral domain given boundary data at a few frequencies. The ROM is the Galerkin projection of the Schr\"odinger operator
Externí odkaz:
http://arxiv.org/abs/1909.06460
Autor:
Druskin, Vladimir, Zaslavsky, Mikhail
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 problems
Externí odkaz:
http://arxiv.org/abs/1909.01299
Graph-Laplacians and their spectral embeddings play an important role in multiple areas of machine learning. This paper is focused on graph-Laplacian dimension reduction for the spectral clustering of data as a primary application. Spectral embedding
Externí odkaz:
http://arxiv.org/abs/1809.03048
We introduce a novel algorithm for nonlinear processing of data gathered by an active array of sensors which probes a medium with pulses and measures the resulting waves. The algorithm is motivated by the application of array imaging. We describe it
Externí odkaz:
http://arxiv.org/abs/1805.03747
Rational Krylov subspace (RKS) techniques are well-established and powerful tools for projection-based model reduction of time-invariant dynamic systems. For hyperbolic wavefield problems, such techniques perform well in configurations where only a f
Externí odkaz:
http://arxiv.org/abs/1711.00942
Publikováno v:
Inverse Problems 34(6):065008, 2018
The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the inversion is to determine from these measurements the s
Externí odkaz:
http://arxiv.org/abs/1704.08375
Publikováno v:
SIAM Journal on Imaging Sciences, 11(1):164-196, 2018
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 the discre
Externí odkaz:
http://arxiv.org/abs/1704.06974